M.TECH — PROJECT ENGINEERING & MANAGEMENT

एम.टेक — प्रोजेक्ट इंजीनियरिंग एवं प्रबंधन

MID-SEMESTER EXAMINATION

MASTER INTEGRATED REFERENCE & REVISION NOTES

समेकित संदर्भ एवं पुनरीक्षण नोट्स (संशोधित एवं सत्यापित)

Part I	Materials Management (PEMP-4001)
Part II	Operations Research & Quantitative Techniques
Part III	Business Law
Part IV	Ergonomics & Human Factors Engineering

Editorial Note / संपादकीय टिप्पणी

This document consolidates all four subject note-sets into one corrected, cross-checked, and exam-ready reference. All arithmetic and legal statements have been re-verified; two errors found in the original Integer Programming solution and one imprecise legal statement have been corrected and are flagged clearly at the relevant place with a CORRECTION marker.

TABLE OF CONTENTS | विषय सूची

PART I — MATERIALS MANAGEMENT | सामग्री प्रबंधन

Course: PEMP-4001 | Examination: Mid-Semester

1.1 Definition & the 5 Rights | परिभाषा एवं पाँच अधिकार

Materials Management is the integrated management function responsible for planning, acquiring, storing, moving, and controlling materials so that production flows without interruption at minimum total cost.

#	Right	Meaning
1	Right Quality	Material must meet the specified technical/quality standard
2	Right Quantity	Neither excess (capital lock-up) nor shortage (stockout)
3	Right Time	Available exactly when production needs it
4	Right Price	Procured at the most economical total cost
5	Right Source	Purchased from a reliable, capable supplier

1.2 Objectives of Materials Management

● Reduce overall material and inventory cost

● Ensure uninterrupted production flow

● Maintain optimum inventory — avoid overstocking and stockouts

● Maintain required incoming material quality

● Improve inventory turnover ratio (capital efficiency)

● Minimize wastage, damage, pilferage and obsolescence

1.3 Core Functions — Mnemonic P-R-S-I-H

Function	Key Activities
P — Purchasing	Vendor selection, price negotiation, issuing Purchase Orders (PO), long-term contracts
R — Receiving & Inspection	Verify inbound goods against PO/challan; quality check before acceptance
S — Stores Management	Safe warehousing, bin-card updates, layout for easy retrieval, damage/pilferage prevention
I — Inventory Control	Setting Min/Max/ROL, periodic stock audit, balancing holding vs ordering cost
H — Material Handling	Internal movement via forklifts, cranes, conveyors to cut transit time and damage

1.4 Inventory Control Techniques — Overview

Technique	Basis	Main Purpose
EOQ	Order quantity	Minimize ordering + holding cost
ABC	Annual consumption value	Value-based, prioritised control
VED	Criticality of the item	Control of spare parts
FSN	Movement / turnover rate	Identify slow-moving and dead stock
JIT	Timing of supply	Eliminate/minimize inventory holding

ABC Analysis — Classification (Pareto 80/20 Rule)

Basis of classification: Annual Consumption Value = Annual Usage × Unit Price.

Category	% of Items	% of Annual Value	Control Level
A	10% – 20%	70% – 80%	Very strict, top-management monitoring
B	20% – 30%	15% – 25%	Moderate, periodic control
C	50% – 70%	5% – 10%	Simple, decentralised, bulk ordering

VED Analysis — Criticality

Class	Meaning	Stocking Policy
Vital (V)	Absence stops production immediately	Always keep in stock
Essential (E)	Absence causes operational inefficiency / minor downtime	Moderate stock
Desirable (D)	Non-availability does not affect immediate operations	Minimal / on-demand stock

Key distinction: ABC is a value (money) based classification; VED is a criticality (function) based classification.

1.5 Reorder Level (ROL) / Reorder Point (ROP)

ROL = Maximum Consumption Rate × Maximum Lead Time

ROP = (Average Daily Usage × Average Lead Time) + Safety Stock

Factors influencing ROL:

● Lead time — longer lead time requires a higher ROL

● Rate of consumption on the shop floor

● Safety stock (buffer against demand/supply variability)

● Supplier reliability and delivery consistency

1.6 EOQ — Core Formula and Solved Numerical

EOQ = √( 2·D·S / H )

N (orders/year) = D / EOQ

T (days between orders) = Working Days / N

Given data: Annual Demand D = 12,000 units | Ordering Cost S = ₹300/order | Holding Cost H = ₹26/unit/year | Working Days = 360.

Step	Calculation	Result
EOQ	√[(2 × 12,000 × 300) / 26] = √276,923.08	≈ 526 units/order
Orders/year (N)	12,000 / 526.24	≈ 22.8 ≈ 23 orders
Order interval (T)	360 / 22.8	≈ 15.79 working days

1.7 Worked Example — EOQ with Safety Stock & ROP

EOQ = √(2DS/H) SS = (d_max·L_max) − (d_avg·L_avg) ROP = (d_avg·L_avg) + SS Avg. Inventory = EOQ/2 + SS
Parameter	Formula / Working	Answer
EOQ	√[(2 × 6000 × 400)/12] = √400,000	2,000 units
Safety Stock	(30 × 10) − (20 × 6) = 300 − 120	180 units
Reorder Point	(20 × 6) + 180 = 120 + 180	300 units
Average Inventory	2000/2 + 180 = 1000 + 180	1,180 units
Annual Holding Cost	1,180 × ₹12	₹14,160 / year

Interpretation: When stock on hand falls to 300 units, a fresh order of 2,000 units must be placed immediately.

1.8 Worked Example — EOQ with Quantity Discount

Given: Annual demand D = 10,000 units | Ordering cost S = ₹500/order | Base price C = ₹100 | Carrying-cost rate I = 20% of price.

Tier	Order Qty	Unit Price	Holding Cost/unit
Tier 1	0 ≤ Q < 2,000	₹100	20% × 100 = ₹20
Tier 2	Q ≥ 2,000	₹95 (5% discount)	20% × 95 = ₹19
Total Cost (TC) = (D × C) + (D/Q × S) + (Q/2 × H)
Option	Unit Price	Purchase Cost	Ordering Cost	Holding Cost	Total Annual Cost
Q = 707 (EOQ of Tier 1)	₹100	₹10,00,000	₹7,071	₹7,071	₹10,14,142
Q = 2,000 (Tier 2 min.)	₹95	₹9,50,000	₹2,500	₹19,000	₹9,71,500

Decision: Accept the discount and order Q = 2,000 units per batch. Annual saving = ₹10,14,142 − ₹9,71,500 = ₹42,642, since the price saving outweighs the extra holding cost.

1.9 Reasons for Carrying Inventory

● Buffer against fluctuating/unexpected customer demand

● Protection against supplier delays and lead-time variability

● Economies of scale — bulk purchase discounts, lower per-unit shipping cost

● Decoupling of successive production stages so one breakdown doesn't halt the whole line

● Hedge against anticipated raw-material price inflation or scarcity

● Coverage for seasonal availability of certain materials

● Fewer, larger orders reduce administrative ordering costs

1.10 Materials Management — Formula Sheet

EOQ = √(2DS/H) N = D/EOQ T = Working Days/N

ROL = Max. Consumption × Max. Lead Time SS = (d_max·L_max) − (d_avg·L_avg)

ROP = (d_avg·L_avg) + SS Avg. Inventory = EOQ/2 + SS

Holding Cost = Avg. Inventory × H TC (with discount) = DC + (D/Q)S + (Q/2)H

1.11 Section A — Multiple Choice Questions (Materials Management)

No.	Question	Answer	Key Concept
1	Main objective of Materials Management	(b) Right material, right time, right cost	The 5-Rights principle
2	EOQ stands for	(a) Economic Order Quantity	Order size minimising total ordering + holding cost
3	ABC analysis is based mainly on	(b) Annual consumption value	Pareto's 80/20 rule
4	Point at which a new order is placed	(b) Reorder level	Triggers replenishment before shortage
5	Function of Materials Management	(d) All of the above	Procurement + inventory control + stores

PART II — OPERATIONS RESEARCH & QUANTITATIVE TECHNIQUES | संक्रिया अनुसंधान

Includes: Linear Programming, Transportation & Transshipment, Integer Programming (Branch & Bound), Queuing Theory, Goal Programming.

2.1 Section A — Multiple Choice Questions

No.	Question	Answer	Key Concept
A	Linear Programming is a	(d) All of the above	Optimization technique for resource allocation
B	Area bounded by constraints in graphical LP	(a) Feasible region	Set of all points satisfying every constraint
C	Branch and Bound divides solution space by	(a) Branching	Branch → Bound → Prune
D	Feasible solution needs positive allocations equal to	(c) m + n − 1	Non-degenerate transportation basic feasible solution

2.2 Transshipment Problem — Full Solution

A transshipment problem allows any node (factory or store) to act as a supply, demand, or intermediate node. A large buffer quantity B (= total supply = total demand) is added to every node to convert it into an equivalent balanced transportation problem: Source → Transshipment Node → Destination.

Data: Factory X = 200 units, Factory Y = 300 units (Total supply = 500). Store A = 100, Store B = 150, Store C = 250 (Total demand = 500). Buffer B = 500.

Cost Matrix (with buffer-adjusted supply/demand)

From \ To	X	Y	A	B	C	Supply
Factory X	0	8	7	8	9	700
Factory Y	6	0	5	4	3	800
Store A	7	2	0	5	1	500
Store B	1	5	1	0	4	500
Store C	8	9	7	8	0	500
Demand	500	500	600	650	750	3000

Optimal Shipping Schedule

Route	Units Shipped	Cost/Unit	Total Cost
Factory X → Store A	100	₹7	₹700
Factory X → Store B	100	₹8	₹800
Factory Y → Store B	50	₹4	₹200
Factory Y → Store C	250	₹3	₹750
TOTAL MINIMUM COST	500	—	₹2,450
Examination caution Vogel's Approximation Method / minimum-cost allocation gives only an initial basic feasible solution. Always verify true optimality with MODI or Stepping-Stone method before declaring a final answer in the exam.

2.3 Integer Programming — Branch & Bound Method

Maximize Z = 2x₁ + 3x₂

Subject to: 6x₁ + 5x₂ ≤ 25 and x₁ + 3x₂ ≤ 10 ; x₁, x₂ ≥ 0 and integer

Step 1 — Continuous LP Relaxation (P₀)

Solving the two boundary equations simultaneously: 6x₁+5x₂=25 and x₁+3x₂=10 gives x₁ = 25/13 = 1.923, x₂ = 35/13 = 2.692, so Z₀ = 155/13 = 11.923 — fractional, so we must branch on x₂.

Step 2 — Branch Tree (corrected)

Node	Added Restriction	LP Solution	Objective Value	Status
P₀	Original LP (no integer restriction)	x₁ = 1.923, x₂ = 2.692	11.923	Fractional — branch
P₁	x₂ ≤ 2	x₁ = 2.5, x₂ = 2	11.0	Fractional — branch further
P₂	x₂ ≥ 3	x₁ = 1, x₂ = 3	11.0	INTEGER — new incumbent
P₃	x₁ ≤ 2, x₂ ≤ 2	x₁ = 2, x₂ = 2	10.0	Integer, inferior to P₂
P₄	x₁ ≥ 3, x₂ ≤ 2	x₁ = 3, x₂ = 1.4	10.2	Pruned (10.2 < 11)
⚠ CORRECTION to the original worked solution The original notes stated that node P₂ (x₁=1, x₂=3) gives Z = 10. This is an arithmetic error: Z = 2(1) + 3(3) = 2 + 9 = 11, not 10. Consequently the earlier claim of two alternative optima, (1,3) and (2,2) both at Z=10, is also incorrect — (2,2) at P₃ gives Z=10, which is inferior. The verified optimum is x₁ = 1, x₂ = 3 with Z(max) = 11. The bound at P₄ (Z=10.2) was correctly computed and correctly pruned since 10.2 < 11.
FINAL ANSWER: x₁ = 1, x₂ = 3, Z(max) = 11

2.4 Queuing Model — M/M/1 (Single Server)

Given: 10 repair sets arrive per 8-hour day. Average service (repair) time = 30 minutes.

λ (arrival rate) = 10/8 = 1.25 jobs/hour μ (service rate) = 1/0.5 = 2 jobs/hour ρ = λ/μ P₀ = 1 − ρ Lq = λ² / [μ(μ−λ)] L = λ/(μ−λ) Wq = λ / [μ(μ−λ)] W = 1/(μ−λ) Stability condition: λ < μ
Quantity	Working	Result
Utilisation ρ	1.25 / 2	0.625 (server busy 62.5% of the time)
Idle probability P₀	1 − 0.625	0.375
Expected idle time / day	8 × 0.375	3 hours/day
Avg. jobs in queue Lq	1.25² / [2(2−1.25)] = 1.5625/1.5	≈ 1.04 jobs
Terminology caution "Average number of jobs ahead of a just-arrived job" is commonly answered using Lq in elementary problems, though strictly it can also depend on whether the server is currently busy.

2.5 Goal Programming — Model Formulation

Decision variables: x₁ = units of Product A, x₂ = units of Product B produced next week.

Goal	Target	Goal Equation
Profit	₹700	100x₁ + 50x₂ + d₁⁻ − d₁⁺ = 700
Product A sales	5 units	x₁ + d₂⁻ − d₂⁺ = 5
Product B sales	4 units	x₂ + d₃⁻ − d₃⁺ = 4
Minimize Z = d₁⁻ + d₁⁺ + d₂⁻ + d₂⁺ + d₃⁻ + d₃⁺ , subject to x₁,x₂,dᵢ⁻,dᵢ⁺ ≥ 0

Note: a real-world model should weight deviations by actual managerial preference — e.g. an excess of profit (d₁⁺) may be desirable rather than penalised.

2.6 Short Notes

(a) Goal Programming

An extension of Linear Programming that handles multiple, often conflicting goals by minimising unwanted deviations (d⁻, d⁺) from stated targets rather than optimising a single objective.

Type	Description
Non-preemptive (Weighted) GP	All goals carry numerical weights reflecting relative importance; minimised together in one objective
Preemptive (Lexicographic) GP	Goals ranked by priority P₁ > P₂ > P₃…; a higher priority goal must be satisfied before the next is considered

(b) LPP vs. IPP

Feature	LPP	IPP
Variables	Continuous (fractions allowed)	Restricted to integers
Feasible region	Continuous convex region	Discrete set of points
Solution method	Simplex, Graphical	Branch & Bound, Cutting Plane (Gomory)
Complexity	Polynomial time — comparatively fast	NP-hard — computationally expensive
Typical use	Blending, general resource allocation	Scheduling, capital budgeting, project selection

2.7 Operations Research — Formula Sheet

Feasible Region = set of all points satisfying every constraint + non-negativity

Transportation non-degenerate BFS: allocations = m + n − 1

Branch & Bound = Branch → Bound → Prune

M/M/1: ρ=λ/μ, P₀=1−ρ, L=λ/(μ−λ), Lq=λ²/[μ(μ−λ)], W=1/(μ−λ), Wq=λ/[μ(μ−λ)]

Goal Programming: Goal + d⁻ − d⁺ = Target

PART III — BUSINESS LAW | वाणिज्यिक विधि

Indian Business & Commercial Law | Indian Contract Act 1872, Sale of Goods Act 1930, Indian Partnership Act 1932, IT Act 2000, Negotiable Instruments Act 1881.

3.1 Section A — Multiple Choice Questions

No.	Question	Answer	Governing Section
1	The Sale of Goods Act is of	(c) 1930	Sale of Goods Act, 1930
2	Seller is a person who	(a) Sells or agrees to sell	Sec. 2(13), Sale of Goods Act
3	A contract of indemnity is primarily to	(b) Compensate for loss	Sec. 124, Indian Contract Act
4	Under the Sale of Goods Act, 'goods' means	(c) Movable property	Sec. 2(7), Sale of Goods Act
5	A cheque is always drawn on a	(b) Bank	Sec. 6, Negotiable Instruments Act
Memory sequence — Acts by year Contract Act → 1872 \| Negotiable Instruments Act → 1881 \| Sale of Goods Act → 1930 \| Partnership Act → 1932 \| Companies Act → 2013

3.2 Business Law, E-Contracts & Digital Signatures

Business Law is the body of legal rules governing commercial transactions, contracts, sale/purchase, partnerships, companies, negotiable instruments, and electronic transactions.

Statute	Year
Indian Contract Act	1872
Negotiable Instruments Act	1881
Sale of Goods Act	1930
Indian Partnership Act	1932
Information Technology Act	2000
Companies Act	2013
Consumer Protection Act	2019

E-Contracts

An e-contract is an agreement formed and executed through electronic means (email, web forms, click-wrap). Section 10A, IT Act 2000 gives legal recognition to contracts formed electronically — provided the essential elements of a valid contract are still satisfied.

Digital Signatures

Recognised under Section 3, IT Act 2000. A digital signature uses an asymmetric cryptosystem (private + public key) to provide:

● Authentication — identifies the signatory

● Integrity — helps detect if signed data was altered

● Non-repudiation — evidentiary link to the signatory, subject to the applicable statutory framework

Precision point

A digital signature is not equivalent to "encrypting the whole document." Its primary legal function is authentication, integrity and evidentiary assurance.

3.3 Essential Elements of a Valid Contract — Sec. 10, Indian Contract Act 1872

#	Element	Explanation / Illustrative Case
1	Offer & Acceptance	A definite proposal unconditionally accepted — Carlill v. Carbolic Smoke Ball Co.
2	Intention to create legal relations	Purely social/domestic promises are generally not contracts — Balfour v. Balfour
3	Lawful consideration	Quid pro quo — something of value given in return (Sec. 2(d), 23)
4	Capacity of parties	Major age, sound mind, not disqualified by law (Sec. 11); a minor's agreement is void ab initio — Mohori Bibee v. Dharmodas Ghose
5	Free consent	Free from Coercion, Undue influence, Fraud, Misrepresentation, Mistake (Sec. 14–20)
6	Lawful object	Not forbidden by law, fraudulent, injurious, immoral, or against public policy (Sec. 23)
Memory: O + A + C + C + F + L → Offer, Acceptance, Consideration, Capacity, Free consent, Lawful object Free-consent memory: C-U-F-M-M → Coercion, Undue influence, Fraud, Misrepresentation, Mistake

3.4 Classification of Contracts

By Validity

Basis	Valid Contract	Void Agreement	Voidable Contract	Illegal Agreement	Unenforceable Contract
Legal status	Fully enforceable	Void from inception, Sec. 2(g)	Valid until repudiated by aggrieved party, Sec. 2(i)	Forbidden by law, void	Substantively valid, barred by technical defect
Enforceable by	Both parties	Neither party	Only the aggrieved party (at their option)	No party — courts refuse assistance	Neither, until the defect is cured
Typical cause	All Sec. 10 elements present	Missing essential element (e.g. no consideration)	Consent via coercion/fraud/misrepresentation	Unlawful object/consideration	Missing stamp, registration or writing
Important exam statement Every illegal agreement is void, but every void agreement is not necessarily illegal. Void = legally unenforceable; Illegal = forbidden by law and punishable.

By Formation & By Performance

● Express Contract — terms stated orally or in writing

● Implied Contract — inferred from conduct (e.g., boarding a bus implies a promise to pay the fare)

● Quasi-Contract — obligation imposed by law to prevent unjust enrichment (Sec. 68–72), independent of agreement

● Executed Contract — both parties have completely performed their obligations

● Executory Contract — obligations remain to be performed

● Unilateral Contract — one promise in exchange for an act (e.g., reward for a lost item)

● Bilateral Contract — promises exchanged by both parties

3.5 Rights of an Unpaid Seller: Lien vs. Stoppage in Transit

Parameter	Right of Lien (Sec. 47–49)	Right of Stoppage in Transit (Sec. 50–52)
Possession of goods	Goods physically remain with the seller	Goods have left the seller and are with a carrier/independent middleman
Buyer's solvency	Exercisable whether buyer is solvent or insolvent (e.g. credit period expired)	Exercisable only if the buyer has become insolvent
Nature of right	Right to retain possession	Right to resume/regain possession
Commencement	As soon as default occurs while goods are still held	After delivery to carrier, until buyer takes delivery
How exercised	Simply refusing to hand over the goods	Taking actual possession or giving notice to the carrier
Memory: LIEN = KEEP (seller still holds goods) \| STOPPAGE = STOP (goods in transit with carrier)

3.6 Partnership — Indian Partnership Act, 1932

Section 4 defines a partnership as the relation between persons who have agreed to share the profits of a business carried on by all or any of them acting for all. The defining test is Mutual Agency — each partner is simultaneously a principal and an agent of the firm.

Essential Elements

● Arises from a contract — not from status, family relation, or inheritance

● Minimum two persons (upper limit governed by applicable statutory rules, currently 50 under the Companies (Miscellaneous) Rules, 2014)

● Agreement to carry on a lawful business

● Agreement to share profits (strong evidence, though not conclusive proof, of partnership)

● Mutual agency — the most decisive test of a partnership

Rights of Partners (Sec. 9–13)

Right	Section
Right to take part in management	Sec. 12(a)
Right to be consulted before business decisions	Sec. 12(c)
Right to inspect and copy the firm's account books	Sec. 12(d)
Right to share profits as agreed (equally, in absence of agreement)	Sec. 13(b)
Right to 6% p.a. interest on advances beyond agreed capital	Sec. 13(d)
Right to be indemnified for liabilities in the ordinary course of business	Sec. 13(e)

Liabilities of Partners (Sec. 25–27, 31)

● Sec. 25 — Unlimited joint & several liability for all acts of the firm done while a partner

● Sec. 26 — Liability for loss/injury caused to a third party by a partner's wrongful act in the ordinary course of business

● Sec. 27 — Firm liable if a partner misapplies money/property received from a third party

● Sec. 31 — An incoming partner is generally not liable for acts before joining, unless otherwise agreed

● An outgoing/retiring partner remains liable for prior acts until proper public notice of retirement is given

3.7 Landmark Cases — Quick Reference

Case	Principle
Balfour v. Balfour	Intention to create legal relations (social/domestic agreements)
Carlill v. Carbolic Smoke Ball Co.	Valid offer and acceptance, including offers to the public
Mohori Bibee v. Dharmodas Ghose	A minor's agreement is void ab initio (capacity)
Hadley v. Baxendale	Remoteness of damages in breach of contract
Lalman Shukla v. Gauri Dutt	Acceptance requires knowledge of the offer
Cox v. Hickman	Mutual agency as the test of partnership

3.8 Important Sections — Fast Reference

Act	Section	Topic
Indian Contract Act, 1872	10	What agreements are contracts
Indian Contract Act, 1872	11	Competency to contract
Indian Contract Act, 1872	14–20	Free consent (coercion, undue influence, fraud, misrepresentation, mistake)
Indian Contract Act, 1872	23–24	Lawful consideration/object
Indian Contract Act, 1872	68–72	Quasi-contracts
Indian Contract Act, 1872	124 / 126	Indemnity / Guarantee
Sale of Goods Act, 1930	2(7) / 2(13)	Goods / Seller
Sale of Goods Act, 1930	45	Unpaid seller
Sale of Goods Act, 1930	47–49	Seller's lien
Sale of Goods Act, 1930	50–52	Stoppage in transit
Sale of Goods Act, 1930	54	Resale by unpaid seller
Indian Partnership Act, 1932	4	Definition of partnership
Indian Partnership Act, 1932	25–27	Liability of partners
Information Technology Act, 2000	3 / 10A	Digital signatures / Validity of e-contracts
Negotiable Instruments Act, 1881	6 / 138	Cheque / Dishonour of cheque

PART IV — ERGONOMICS & HUMAN FACTORS ENGINEERING | श्रम-विज्ञान

Ergonomics ('ergon' = work, 'nomos' = natural laws): designing tasks, tools, and environments to fit human physiological, biomechanical and psychological limits — "fit the task to the human."

4.1 Section A — Multiple Choice Questions

No.	Question	Answer	Explanation
a	Ergonomics primarily deals with	(ii) Fitting the workplace/system to human capabilities	Design fits the task to the human, not vice-versa
b	Anthropometric consideration in workplace design	(iii) Body dimensions of the worker	Reach, eye height, elbow height, popliteal height, etc.
c	Principle of motion economy aims at	(ii) Minimizing fatigue and improving efficiency	Gilbreth & Barnes' principles
d	Biodynamic analysis is mainly concerned with	(ii) Human response to mechanical forces, vibration and motion	Whole-body / hand-arm vibration effects

4.2 Core Concepts — Short Notes

(a) Ergonomics

An interdisciplinary field combining engineering, anatomy, physiology and psychology across three domains:

Domain	Focus	Example
Physical Ergonomics	Posture, force, movement	Manual lifting
Cognitive Ergonomics	Perception, memory, decision-making	Control-room HMI design
Organizational Ergonomics	Work systems and schedules	Shift planning, work-rest cycles

(b) Man–Machine Symbiosis

A cooperative partnership in which humans and machines each perform tasks matching their inherent strengths (Fitts' List).

Domain	Human Strength	Machine Strength
Cognition & sensing	Pattern recognition, inductive reasoning, handling unexpected anomalies	High-speed repetitive computation, quantitative calculation
Physical output	Precise fine-motor micro-adjustments	Continuous heavy-force exertion without fatigue

Modern example: a collaborative robot (cobot) — the human provides cognitive control and qualitative judgement while the machine performs high-force, cyclic tasks.

(c) Information Input & Processing

Stimulus → Sensation → Perception → Cognition → Decision → Motor Response → Feedback

Miller's classical estimate: short-term memory can process roughly 7 ± 2 chunks of information at a time (a traditional figure — modern research nuances this). Design implication: displays and control panels must present structured, unambiguous signals with low visual clutter.

(d) Principles of Motion Economy (Gilbreth / Barnes)

Category	Key Principles
Use of the human body	Both hands begin/end motion together; movements should be smooth, continuous, curved — not abrupt straight-line changes
Workplace arrangement	Fixed locations for tools/materials within the primary reach envelope; gravity-feed where possible
Tools & equipment design	Combine functions in one tool; relieve load with levers, foot pedals, jigs/fixtures; handles matched to palm shape

(e) Anthropometric Design Strategies

Strategy	Applies To	Typical Percentile Used
Design for extremes (clearance)	Doorways, headroom, clearances	95th percentile male (largest user must fit)
Design for extremes (reach)	Control buttons, reach distances	5th percentile female (shortest user must reach)
Design for adjustable range	Seat height, monitor stand, worktable	5th to 95th percentile
Design for average (50th %ile)	Only when adjustability is impractical	Checkout counters, public benches

4.3 Long Answer (A) — Ergonomic Workstation Case Study

Problems Identified in the Existing Workstation

Problem	Mechanism / Consequence
Non-neutral joint posture (bending)	Forward trunk flexion > 20° while lifting from the floor increases compressive/shear load on L5/S1 lumbar vertebrae → herniated-disc risk
Extended reach beyond envelope	Reaching > 40 cm from the body creates high shoulder torque → rotator-cuff strain, neck pain
Repetitive manual handling	Constant bending/lifting without mechanical aid → local muscle fatigue, micro-trauma to soft tissue
Adverse thermal environment	High heat + high humidity block evaporative cooling → thermal fatigue, cardiovascular strain, reduced concentration

Anthropometric Redesign

● Height-adjustable worktable, roughly 850–1150 mm, spanning 5th-percentile female to 95th-percentile male; elbow height is the key datum (work surface ≈ 50–100 mm below elbow height for light assembly)

● Eliminate floor-level bending — elevate component containers to a minimum ≈750 mm using hydraulic/pneumatic scissor-lift tables

● Primary reach zone (<25 cm radius): frequently-used tools placed directly in front

● Secondary reach zone (25–50 cm radius): occasional-use bins within arm extension without torso twist

Motion-Economy Redesign

Existing: Bend → Reach → Lift → Turn → Assemble → Return

Redesigned: Gravity-feed → Pick → Assemble → Drop (fewer motions, less bending, shorter cycle time)

● Inclined gravity-feed chutes deliver components automatically near the assembly point

● Structure tasks so both hands work simultaneously in symmetrical, opposite directions

● Foot-operated pneumatic clamps free the hands; gravity drop-chutes remove the need to turn

● Suspend heavy torque tools from overhead spring balancers to eliminate holding weight

Thermal / Environmental Control

Heat stress mechanism: ambient heat + relative humidity > 70% block sweat evaporation → rising core temperature → elevated heart rate and cognitive/physical fatigue.

● Engineering controls: spot air-conditioning, HVAC, high-volume low-speed (HVLS) fans

● Administrative controls: scheduled work-rest cycles (e.g., 45 min work / 15 min rest), keep WBGT index below 28 °C

● Personal controls: accessible hydration stations, appropriate clothing

Before / After Comparison

Parameter	Existing Workstation	Redesigned Ergonomic Workstation
Material feeding	Stored at floor level in boxes	Height-adjustable gravity chutes at waist level
Work height	Fixed — causes stooping	Pneumatically adjustable, 5th–95th percentile elbow height
Tool handling	Manually picked up/laid down	Suspended overhead on tool balancers, ergonomic grips
Environmental control	Unconditioned, high heat/humidity	Local spot air-conditioning + forced circulation
Operator posture	Severe trunk flexion / lateral twist	Neutral spinal alignment, sit-stand seating option

4.4 Long Answer (B) — Human Factors in Design & Manufacturing

Human Factors Engineering (HFE) matches system design to human physical, perceptual and cognitive capability, reducing operator strain, scrap rate, and industrial risk.

Factor	Design Principle	Industrial Example
Information display	Simple, prioritised, unambiguous; qualitative colour-coded status + quantitative digital readouts	Chemical-plant HMI groups critical alarms with high-contrast colour coding
Control design (Compatibility Principle)	Controls match natural human expectation (e.g., lever forward = ON); tactile resistance prevents accidental activation	CNC console with a prominent red mushroom emergency-stop button
Ergonomic hand tools	Keep the wrist neutral ("bend the tool, not the wrist"); contoured grips distribute force over the palm	Pistol-grip pneumatic wrenches on automotive assembly lines
Environmental conditions	Noise < 85 dBA (8-hr TWA); illumination 500–1000 lux for precision assembly	Glare-free task lighting and acoustic enclosures at inspection stations
Biodynamics (vibration)	Isolate whole-body vibration (WBV, 1–20 Hz) and hand-arm vibration (HAV)	Air-suspended forklift seats; anti-vibration rubber handles on grinders

Effects of Whole-Body vs Hand-Arm Vibration

Type	Common Source	Health Effect	Control
Whole-Body Vibration (WBV)	Forklifts, tractors, heavy vehicles	Chronic spinal degeneration, fatigue, reduced control	Suspended/air-damped seats, vehicle maintenance, controlled speed
Hand-Arm Vibration (HAV)	Grinders, drills, impact tools	Numbness, tingling, vibration-white-finger	Low-vibration tools, anti-vibration handles, exposure-time limits

4.5 Ergonomics — Relationship & Formula Box

Work = Force × Distance Power = Work / Time Stress = Force / Area Torque = Force × Moment Arm

Anthropometric rule: Clearance → design for larger percentile; Reach → design for smaller percentile; General use → design for adjustability

4.6 Final Revision Mnemonics

Mnemonic	Expansion
F-I-T-H-M-E	Fit the workplace to human — Information clear — Task minimises effort — Human capability/limits — Machine compatibility — Environment supports safety
Ergonomics vs Anthropometry vs Biodynamics	Ergonomics = fit system to human \| Anthropometry = body measurement \| Biodynamics = response to force/vibration
ABC vs VED (cross-reference, Part I)	ABC = value/money based \| VED = criticality based

Materials Management — Mid-Sem Final Revision Notes

1. Materials Management

Definition:
Materials Management is the integrated process of planning, purchasing, receiving, storing, handling, and controlling materials so that the right material is available at the right time, in the right quantity and quality, at the right cost.

5 Rights of Materials Management

Right Quality
Right Quantity
Right Time
Right Price
Right Source

Main Objectives

Reduce material and inventory cost
Ensure uninterrupted production
Maintain optimum inventory
Ensure required quality
Improve inventory turnover
Minimize wastage, damage and obsolescence

2. Important Inventory Techniques

Technique	Basis	Main Purpose
EOQ	Order quantity	Minimize ordering + holding cost
ABC	Annual consumption value	Value-based control
VED	Criticality	Control spare parts
FSN	Movement rate	Identify slow/dead stock
JIT	Timing of supply	Minimize inventory

ABC Classification

Category	Approx. Items	Approx. Annual Value	Control
A	10–20%	70–80%	Very strict
B	20–30%	15–25%	Moderate
C	50–70%	5–10%	Simple

ABC basis:
Annual Consumption Value = Annual Usage × Unit Price

3. EOQ — Most Important Numerical

Formula

\[ EOQ=\sqrt{\frac{2DS}{H}} \]

Where:

\(D\) = Annual demand
\(S\) = Ordering cost/order
\(H\) = Holding cost/unit/year

Given

\(D=12,000\) units
\(S=₹300\)
\(H=₹26\)

\[ EOQ=\sqrt{\frac{2(12000)(300)}{26}} \] \[ EOQ\approx526.24 \]

Answer

EOQ ≈ 526 units/order

Number of Orders

\[ N=\frac{D}{EOQ} \] \[ N=\frac{12000}{526.24}\approx22.8 \]

≈ 23 orders/year

Time Between Orders

\[ T=\frac{360}{22.8} \] \[ T\approx15.79\text{ days} \]

Final Answer

EOQ = 526 units
Orders/year = 22.8 ≈ 23
Order interval = 15.79 working days

4. Reorder Level / Reorder Point

Basic Formula

\[ ROP=\text{Lead-Time Demand}+\text{Safety Stock} \]

or, under a maximum-demand/maximum-lead-time approach:

\[ ROL=Maximum\ Consumption\ Rate\times Maximum\ Lead\ Time \]

Factors affecting ROL

Lead time
Consumption rate
Safety stock
Supplier reliability
Demand variability

5. Safety Stock

A commonly used exam formula is:

\[ SS=(d_{max}\times L_{max})-(d_{avg}\times L_{avg}) \]

Then:

\[ ROP=(d_{avg}\times L_{avg})+SS \]

6. EOQ + Safety Stock Numerical

Given

Annual demand = 6,000 units
Working days = 300
Ordering cost = ₹400
Holding cost = ₹12/unit/year
Average lead time = 6 days
Maximum lead time = 10 days
Average usage = 20 units/day
Maximum usage = 30 units/day

Step 1 — EOQ

\[ EOQ=\sqrt{\frac{2(6000)(400)}{12}} \] \[ EOQ=2000\text{ units} \]

Step 2 — Safety Stock

\[ SS=(30\times10)-(20\times6) \] \[ SS=300-120 \] \[ \boxed{SS=180\text{ units}} \]

Step 3 — ROP

\[ ROP=(20\times6)+180 \] \[ ROP=120+180 \] \[ \boxed{ROP=300\text{ units}} \]

Step 4 — Average Inventory

\[ Average\ Inventory=\frac{EOQ}{2}+SS \] \[ =\frac{2000}{2}+180 \] \[ =1180\text{ units} \]

Step 5 — Annual Holding Cost

\[ Holding\ Cost=1180\times12 \] \[ \boxed{₹14,160/year} \]

Final Answer

Parameter	Answer
EOQ	2,000 units
Safety Stock	180 units
ROP	300 units
Average Inventory	1,180 units
Annual Holding Cost	₹14,160

7. Quantity Discount — Important Concept

When quantity discounts are offered, do not automatically select the basic EOQ.

Calculate:

\[ TC=DC+\frac{D}{Q}S+\frac{Q}{2}H \]

Where:

\(DC\) = Annual purchase cost
\(\frac{D}{Q}S\) = Annual ordering cost
\(\frac{Q}{2}H\) = Annual holding cost

Decision Rule

Calculate and compare total annual cost at all feasible alternatives.

For the given example:

Q	Unit Price	Ordering Cost	Holding Cost	Total Cost
707	₹100	₹7,071	₹7,071	₹10,14,142
2,000	₹95	₹2,500	₹19,000	₹9,71,500

Therefore:

\[ ₹9,71,500 < ₹10,14,142 \]

Final Decision

\[ \boxed{Q=2,000\text{ units}} \]

The quantity discount should be accepted.

Annual saving ≈ ₹42,642.

8. Core Functions of Materials Management

Remember:

P-R-S-I-H

P — Purchasing
Vendor selection, negotiation, purchase orders.

R — Receiving & Inspection
Receive, verify, inspect and accept materials.

S — Stores Management
Storage, bin cards, preservation and retrieval.

I — Inventory Control
Min/Max levels, ROL, safety stock, stock verification.

H — Handling
Movement of materials using cranes, forklifts, conveyors, etc.

9. VED Analysis

V — Vital

Failure/absence can stop production.
Very high priority.
Adequate stock must be maintained.

E — Essential

Absence affects efficiency.
Moderate priority.

D — Desirable

Absence has little immediate operational effect.
Lower priority.

Remember:
ABC = Money/Value
VED = Criticality

10. FSN Analysis

F — Fast Moving

Frequently consumed.

S — Slow Moving

Used occasionally.

N — Non-Moving

Little or no movement for a long period.

Purpose: Identify obsolete/dead inventory and improve inventory utilization.

11. JIT — Just in Time

JIT means receiving materials approximately when they are required for production rather than maintaining excessive inventory.

Objectives

Reduce inventory
Reduce storage cost
Reduce waste
Improve quality
Improve production flow
Shorten lead time

⭐ Formula Sheet — Must Memorize

\[ \boxed{EOQ=\sqrt{\frac{2DS}{H}}} \] \[ \boxed{N=\frac{D}{EOQ}} \] \[ \boxed{T=\frac{Working\ Days}{N}} \] \[ \boxed{SS=(d_{max}L_{max})-(d_{avg}L_{avg})} \] \[ \boxed{ROP=(d_{avg}L_{avg})+SS} \] \[ \boxed{Average\ Inventory=\frac{EOQ}{2}+SS} \] \[ \boxed{Holding\ Cost=Average\ Inventory\times H} \] \[ \boxed{TC=DC+\frac{D}{Q}S+\frac{Q}{2}H} \]

🎯 One-Minute Exam Memory Map

Materials Management
→ 5 Rights
→ Quality + Quantity + Time + Price + Source

Inventory Control
→ EOQ + ABC + VED + FSN + JIT

EOQ
→ Optimal order size

ABC
→ Annual consumption value

VED
→ Criticality

FSN
→ Movement

ROP
→ When to order

Safety Stock
→ Protection against uncertainty

Quantity Discount
→ Compare Total Cost, not merely EOQ.

Most important numerical questions:
EOQ → Quantity Discount → Safety Stock → ROP → Holding Cost.

📘 MID-SEM EXAMINATION — ENHANCED MASTER NOTES

Materials Management / Operations Research

PEMP-4001 | Quantitative Techniques, Optimization & Decision Models

SECTION A — MULTIPLE CHOICE QUESTIONS

Q1(A) Linear Programming is a:

Answer: (d) All of the above

Explanation

Linear Programming (LP/LPP) is a mathematical optimization technique used to determine the best allocation of limited resources among competing activities.

It can be used for:

Profit maximization
Cost minimization
Resource allocation
Production planning
Product-mix decisions
Transportation and distribution planning

Basic Structure

\[ \text{Optimize } Z=c_1x_1+c_2x_2+\cdots+c_nx_n \]

Subject to:

\[ a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n\leq b_1 \]

and similar constraints, with:

\[ x_i\geq0 \]

Q1(B) In graphical LP, the area satisfying all constraints is called:

Answer: (a) Feasible Region

Key Concept

The feasible region is the set of all points that simultaneously satisfy:

All constraints
Non-negativity restrictions

The optimal solution in a standard LP occurs at an extreme/corner point of the feasible region, when an optimum exists.

Remember

Feasible = Possible

Q1(C) Branch and Bound divides the solution space by:

Answer: (a) Branching

Explanation

The Branch and Bound method solves integer programming problems by:

Branching → Bounding → Pruning

Branching: Divides the problem into smaller sub-problems.
Bounding: Determines the best possible objective value of each sub-problem.
Pruning/Fathoming: Eliminates branches that cannot produce a better solution.

Memory Trick

Branch → Bound → Eliminate → Repeat

Q1(D) A non-degenerate transportation solution contains:

Answer: (c) \(m+n-1\) positive allocations

For an \(m\times n\) transportation problem:

\[ \boxed{m+n-1} \]

independent occupied cells are required for a non-degenerate basic feasible solution.

Important distinction

Non-degenerate BFS: exactly \(m+n-1\) positive allocations.
Degenerate BFS: fewer than \(m+n-1\) positive allocations; zero allocations may be assigned as \(\epsilon\) to maintain the basis.

SECTION B — TRANSSHIPMENT PROBLEM

Q2. Transshipment Model

Concept

A transportation problem generally moves goods from sources directly to destinations.

A transshipment problem allows intermediate nodes to receive and redistribute goods.

Therefore:

\[ \boxed{\text{Source}\rightarrow\text{Transshipment Node}\rightarrow\text{Destination}} \]

A node may act as:

Supply node
Demand node
Intermediate/transshipment node

Given Network

Factories

Factory X = 200 units
Factory Y = 300 units

Therefore:

\[ Total\ Supply=500 \]

Retail Demand

A = 100 units
B = 150 units
C = 250 units

Therefore:

\[ Total\ Demand=500 \]

Hence the problem is balanced.

Cost Matrix

From / To	X	Y	A	B	C	Supply
X	0	8	7	8	9	700
Y	6	0	5	4	3	800
A	7	2	0	5	1	500
B	1	5	1	0	4	500
C	8	9	7	8	0	500
Demand	500	500	600	650	750	3000

The \(+500\) buffer is introduced to convert the transshipment problem into an equivalent transportation problem.

Effective Supply and Demand

Effective Supply

\[ S_i=Original\ Supply+B \]

Thus:

X = \(200+500=700\)
Y = \(300+500=800\)
A = \(0+500=500\)
B = \(0+500=500\)
C = \(0+500=500\)

Effective Demand

\[ D_j=Original\ Demand+B \]

Thus:

X = 500
Y = 500
A = \(100+500=600\)
B = \(150+500=650\)
C = \(250+500=750\)

Total:

\[ 700+800+500+500+500=3000 \]

and

\[ 500+500+600+650+750=3000 \]

Therefore, the converted transportation problem is balanced.

Optimal Shipping Interpretation

The economically relevant factory-to-store shipments are:

Route	Quantity	Cost/unit	Cost
X → A	100	₹7	₹700
X → B	100	₹8	₹800
Y → B	50	₹4	₹200
Y → C	250	₹3	₹750
Total	500	—	₹2,450

Therefore:

\[ \boxed{Minimum\ Transportation\ Cost=₹2,450} \]

Important Exam Point

The zero-cost diagonal allocations and buffer quantities are artificial balancing devices. The final real-world shipping schedule should be interpreted using the actual factory supplies and retail demands.

Critical Check

Before writing “optimal” in an exam, ideally verify the solution using a method such as:

MODI method
Stepping-Stone method
Transportation simplex

A VAM solution is generally an initial basic feasible solution, not automatically a proof of optimality.

SECTION C — INTEGER PROGRAMMING

Q3. All-Integer Programming Using Branch & Bound

Problem

Maximize:

\[ \boxed{Z=2x_1+3x_2} \]

Subject to:

\[ 6x_1+5x_2\leq25 \] \[ x_1+3x_2\leq10 \] \[ x_1,x_2\geq0 \]

and:

\[ x_1,x_2\in\mathbb Z \]

Step 1 — LP Relaxation

Ignore the integer restriction temporarily.

At the intersection:

\[ 6x_1+5x_2=25 \] \[ x_1+3x_2=10 \]

From the second equation:

\[ x_1=10-3x_2 \]

Substitute:

\[ 6(10-3x_2)+5x_2=25 \] \[ 60-18x_2+5x_2=25 \] \[ 13x_2=35 \] \[ x_2=\frac{35}{13}=2.692 \]

Therefore:

\[ x_1=\frac{25}{13}=1.923 \]

Objective:

\[ Z=2(1.923)+3(2.692) \] \[ Z=\frac{155}{13} \] \[ \boxed{Z=11.923} \]

Since the solution is fractional, it is not an integer solution.

Step 2 — Branch on \(x_2\)

Since:

\[ x_2=2.692 \]

create:

\[ \boxed{x_2\leq2} \]

and

\[ \boxed{x_2\geq3} \]

Branch P₁: \(x_2\leq2\)

At optimum:

\[ x_2=2 \]

Constraint 1:

\[ 6x_1+5(2)\leq25 \] \[ 6x_1\leq15 \] \[ x_1\leq2.5 \]

Thus LP relaxation gives:

\[ x_1=2.5,\quad x_2=2 \] \[ Z=2(2.5)+3(2)=11 \]

This is fractional, so branch further on \(x_1\):

\[ x_1\leq2 \]

\[ x_1\geq3 \]

Branch P₂: \(x_2\geq3\)

Take:

\[ x_2=3 \]

From:

\[ x_1+3x_2\leq10 \] \[ x_1+9\leq10 \] \[ x_1\leq1 \]

Thus:

\[ x_1=1,\quad x_2=3 \]

Objective:

\[ Z=2(1)+3(3) \] \[ \boxed{Z=11} \]

Important Correction

Your original solution states \(Z=10\) here. That is an arithmetic error.

\[ 2(1)+3(3)=2+9=\boxed{11} \]

So the integer solution:

\[ \boxed{(x_1,x_2)=(1,3)} \]

gives Z = 11, not 10.

Branch P₃: \(x_1\leq2,\ x_2\leq2\)

Take:

\[ x_1=2,\quad x_2=2 \]

Check:

\[ 6(2)+5(2)=22\leq25 \] \[ 2+3(2)=8\leq10 \]

Objective:

\[ Z=2(2)+3(2) \] \[ \boxed{Z=10} \]

This is an integer feasible solution.

Branch P₄: \(x_1\geq3,\ x_2\leq2\)

With \(x_1=3\):

\[ 18+5x_2\leq25 \] \[ 5x_2\leq7 \] \[ x_2\leq1.4 \]

LP upper bound:

\[ Z=2(3)+3(1.4)=10.2 \]

Since the best known integer solution is already:

\[ Z=11 \]

and:

\[ 10.2<11 \]

this branch is pruned.

🌳 Correct Branch-and-Bound Summary

Node	Restriction	LP Solution / Bound	Status
P₀	Original LP	11.923	Branch
P₁	\(x_2\leq2\)	11.0	Branch
P₂	\(x_2\geq3\)	11.0	Integer → incumbent
P₃	\(x_1\leq2,x_2\leq2\)	10.0	Integer, inferior
P₄	\(x_1\geq3,x_2\leq2\)	10.2	Prune

Correct Final Answer

\[ \boxed{x_1=1,\quad x_2=3} \] \[ \boxed{Z_{\max}=11} \]

Therefore, the statement in the original notes that both (1,3) and (2,2) are optimal with \(Z=10\) is incorrect.

SECTION D — QUEUING MODEL

Q4. M/M/1 Queuing Model

Given

10 repair sets per 8-hour day
Average repair time = 30 minutes

Step 1 — Arrival Rate

\[ \lambda=\frac{10}{8} \] \[ \boxed{\lambda=1.25\ jobs/hour} \]

Step 2 — Service Rate

Average service time:

\[ 30\ minutes=0.5\ hour \]

Therefore:

\[ \mu=\frac{1}{0.5} \] \[ \boxed{\mu=2\ jobs/hour} \]

Step 3 — Utilization

\[ \rho=\frac{\lambda}{\mu} \] \[ \rho=\frac{1.25}{2} \] \[ \boxed{\rho=0.625} \]

Thus the repair facility is busy:

\[ 62.5\% \]

of the time.

Expected Idle Time

Probability of zero customers/system being idle:

\[ P_0=1-\rho \] \[ P_0=1-0.625 \] \[ P_0=0.375 \]

Therefore:

\[ Idle\ Time=8(0.375) \] \[ \boxed{3\ hours/day} \]

Average Number of Jobs in Queue

For M/M/1:

\[ L_q=\frac{\lambda^2}{\mu(\mu-\lambda)} \]

Substitute:

\[ L_q=\frac{1.25^2}{2(2-1.25)} \] \[ =\frac{1.5625}{1.5} \] \[ \boxed{L_q=1.042\ jobs} \]

Answer

The average number of jobs waiting in the queue is:

\[ \boxed{1.04\ jobs} \]

Important Terminology

If the question asks:

Average number of jobs ahead of a just-arrived job

be careful: \(L_q\) is the average number waiting, whereas the number ahead can depend on whether the server is busy and on the arrival's position. In many elementary exam problems, \(L_q\) is nevertheless used as the intended answer.

⭐ Important M/M/1 Formula Sheet

\[ \boxed{\rho=\frac{\lambda}{\mu}} \] \[ \boxed{P_0=1-\rho} \] \[ \boxed{L_q=\frac{\lambda^2}{\mu(\mu-\lambda)}} \] \[ \boxed{L=\frac{\lambda}{\mu-\lambda}} \] \[ \boxed{W_q=\frac{\lambda}{\mu(\mu-\lambda)}} \] \[ \boxed{W=\frac{1}{\mu-\lambda}} \]

Stability Condition

\[ \boxed{\lambda<\mu} \]

SECTION E — GOAL PROGRAMMING

Q5. Goal Programming Model

Decision Variables

Let:

\[ x_1=\text{units of Product A} \] \[ x_2=\text{units of Product B} \]

Goals

Goal 1 — Profit

Target:

\[ ₹700 \]

Profit:

\[ 100x_1+50x_2 \]

Goal equation:

\[ \boxed{100x_1+50x_2+d_1^- -d_1^+=700} \]

Goal 2 — Product A Sales

Target:

\[ 5\ units \] \[ \boxed{x_1+d_2^- -d_2^+=5} \]

Goal 3 — Product B Sales

Target:

\[ 4\ units \] \[ \boxed{x_2+d_3^- -d_3^+=4} \]

Deviational Variables

\(d_i^-\)

Under-achievement / shortfall.

\(d_i^+\)

Over-achievement / excess.

Remember:

\(d^-\) = Below target
\(d^+\) = Above target

Objective Function

If all deviations have equal importance:

\[ \boxed{ \min Z= d_1^-+d_1^+ +d_2^-+d_2^+ +d_3^-+d_3^+ } \]

subject to:

\[ x_1,x_2,d_i^-,d_i^+\geq0 \]

Important Goal Programming Principle

In real Goal Programming, not every deviation is necessarily undesirable.

For example:

Profit goal → usually minimize underachievement \(d_1^-\); exceeding profit may be desirable.
Sales target → depending on the problem, both over- and under-achievement may matter.
Resource target → usually only one direction may be undesirable.

Therefore, the objective should reflect the decision-maker's actual preferences.

SECTION F — SHORT NOTES

Q6(a). Goal Programming

Goal Programming (GP) is an extension of Linear Programming used when an organization has multiple objectives or goals that may conflict with one another.

Instead of optimizing only one objective, GP attempts to minimize deviations from predetermined target levels.

Basic Structure

\[ \boxed{Goal + d^- -d^+=Target} \]

Types

1. Weighted / Non-Preemptive GP

Different weights are assigned to different goals.

\[ \min Z=w_1d_1+w_2d_2+\cdots+w_nd_n \]

Higher weight = greater importance.

2. Pre-emptive / Lexicographic GP

Goals are arranged according to priority:

\[ P_1>P_2>P_3 \]

Higher-priority goals are satisfied before lower-priority goals.

Applications

Production planning
Workforce planning
Budget allocation
Project selection
Resource allocation
Supply-chain planning

Q6(b). LPP vs IPP

Feature	LPP	IPP
Full Form	Linear Programming Problem	Integer Programming Problem
Variables	Continuous	Integer
Fractional values	Allowed	Not allowed
Solution space	Continuous	Discrete
Typical methods	Simplex, Graphical	Branch & Bound, Cutting Plane
Complexity	Generally easier	Generally more computationally difficult
Examples	Product mix, blending	Scheduling, project selection

Example

LPP:

\[ x=2.5 \]

can be acceptable.

IPP:

\[ x=2.5 \]

is not acceptable if \(x\) must be integer.

Q6(c). Reasons for Carrying Inventory

Although inventory involves capital and storage costs, organizations maintain inventory for several important reasons.

1. Demand Uncertainty

Inventory acts as a buffer against unexpected increases in demand.

2. Protection Against Supply Delays

Safety stock protects production against:

Supplier delays
Transportation problems
Material shortages
Lead-time variability

3. Economies of Scale

Bulk purchasing may provide:

Quantity discounts
Lower ordering frequency
Lower transportation cost per unit

4. Decoupling of Operations

Inventory between production stages allows one process to continue even if another temporarily stops.

5. Protection Against Price Increase

Organizations may purchase materials before expected price increases.

6. Smooth Production

Adequate raw-material inventory helps prevent production interruptions.

7. Seasonal Availability

Some materials may be available only during certain seasons.

8. Reduction of Ordering Cost

Larger, less frequent orders can reduce the administrative cost associated with repeated purchasing.

🔥 FINAL EXAM CRASH SHEET

LP

\[ \boxed{\text{Optimize Objective Function subject to Constraints}} \]

Feasible Region = All points satisfying all constraints.

Transportation

\[ \boxed{m+n-1} \]

= Number of allocations in a non-degenerate BFS.

Transshipment

\[ \boxed{\text{Source → Intermediate → Destination}} \]

EOQ

\[ \boxed{EOQ=\sqrt{\frac{2DS}{H}}} \]

Reorder Point

\[ \boxed{ROP=\text{Lead-Time Demand}+SS} \]

Safety Stock

\[ \boxed{SS=(d_{max}L_{max})-(d_{avg}L_{avg})} \]

Branch & Bound

\[ \boxed{Branch\rightarrow Bound\rightarrow Prune} \]

M/M/1

\[ \boxed{\rho=\frac{\lambda}{\mu}} \] \[ \boxed{L_q=\frac{\lambda^2}{\mu(\mu-\lambda)}} \] \[ \boxed{W_q=\frac{\lambda}{\mu(\mu-\lambda)}} \] \[ \boxed{L=\frac{\lambda}{\mu-\lambda}} \] \[ \boxed{W=\frac{1}{\mu-\lambda}} \]

Condition:

\[ \boxed{\lambda<\mu} \]

Goal Programming

\[ \boxed{Goal+d^- -d^+=Target} \] \[ \boxed{d^-=\text{Underachievement}} \] \[ \boxed{d^+=\text{Overachievement}} \]

⚠️ THREE IMPORTANT CORRECTIONS TO YOUR ORIGINAL NOTES

1. Branch & Bound Question 3

Your original calculation:

\(x_1=1,x_2=3 \Rightarrow Z=10\)

is incorrect.

Actually:

\[ 2(1)+3(3)=2+9=\boxed{11} \]

Therefore, the correct optimum is:

\[ \boxed{x_1=1,\ x_2=3,\ Z=11} \]

The point \((2,2)\) gives only:

\[ \boxed{Z=10} \]

2. Branch \(P_4\)

Your original upper bound of 9.8 is also incorrect.

At:

\[ x_1=3,\quad x_2=1.4 \] \[ Z=2(3)+3(1.4) \] \[ =6+4.2 \] \[ =\boxed{10.2} \]

It is still pruned because:

\[ 10.2<11 \]

3. Transshipment

VAM/minimum-cost allocation gives an initial feasible solution; it should not automatically be called mathematically optimal without an optimality test such as MODI or Stepping-Stone.

These corrections are important because Question 3 in its original form would lead to the wrong final answer.

📚 BUSINESS LAW — ENHANCED EXAM MASTER NOTES

Mid-Sem / End-Sem Reference

Indian Business & Commercial Law

SECTION A — MCQs

1. The Sale of Goods Act is of:

Key Fact

The Sale of Goods Act, 1930 governs contracts relating to the sale and purchase of goods in India.

Exam memory:

Contract Act → 1872
Negotiable Instruments → 1881
Sale of Goods → 1930
Partnership → 1932
Companies Act → 2013

2. Seller is a person who:

✅ Answer: (a) Sells or agrees to sell

Section

Section 2(13), Sale of Goods Act, 1930

Seller means a person who sells or agrees to sell goods.

Example

A agrees to sell 100 machines to B for ₹10 lakh.

Even before delivery, A is the seller because A has agreed to sell.

3. Contract of Indemnity

✅ Answer: (b) Compensate for loss

Section 124 — Indian Contract Act, 1872

A contract of indemnity is a contract where one party promises to save the other from loss caused by:

Conduct of the promisor, or
Conduct of another person.

Example

A tells B:

"If C files a claim against you because of my transaction, I will compensate you for the loss."

This is an example of indemnity.

Exam Point

Indemnity = Protection against loss

4. Goods under Sale of Goods Act

✅ Answer: (c) Movable property

Section 2(7)

Goods include:

Every kind of movable property other than money and actionable claims.

Examples

✔ Machinery
✔ Cars
✔ Furniture
✔ Raw materials
✔ Computers
✔ Stock-in-trade

Generally excluded:

❌ Money
❌ Actionable claims
❌ Immovable property such as land/buildings

5. A cheque is always drawn on a:

✅ Answer: (b) Bank

Section 6 — Negotiable Instruments Act, 1881

A cheque is a bill of exchange drawn on a specified banker and payable on demand.

Basic Structure

Drawer → Bank → Payee

Example:

A issues a cheque to B.

A = Drawer
Bank = Drawee
B = Payee

SECTION B

Q6. BUSINESS LAW, E-CONTRACTS & DIGITAL SIGNATURES

A. Business Law

Definition

Business Law is the body of legal rules governing:

Commercial transactions
Contracts
Sale and purchase
Partnerships
Companies
Negotiable instruments
Consumer/business relationships
Electronic transactions

Major Indian Business Laws

Law	Year
Indian Contract Act	1872
Negotiable Instruments Act	1881
Sale of Goods Act	1930
Indian Partnership Act	1932
Companies Act	2013
Information Technology Act	2000
Consumer Protection Act	2019

B. E-Contracts

An e-contract is a legally enforceable agreement formed through electronic means.

Examples

Online shopping
Online banking agreements
Software licences
Click-wrap agreements
Email contracts
Online service subscriptions
Electronic purchase orders

Legal Recognition

Section 10A, Information Technology Act, 2000 recognizes contracts formed through electronic means.

However, an electronic form does not automatically make every agreement valid. The normal requirements of a valid contract must still be satisfied.

Example

A purchases a laptop through an online platform.

The process may involve:

Offer → Acceptance → Payment → Confirmation → Electronic Record

This can constitute an enforceable electronic transaction, subject to applicable law.

C. Digital Signature

A digital signature is a cryptographic mechanism used to authenticate an electronic record.

Under the IT Act framework, digital signatures use:

Private key
Public key
Digital signature technology
Certifying authorities

Three Major Functions

1. Authentication

Establishes who signed the electronic record.

2. Integrity

Helps detect whether the signed data has been altered.

3. Non-repudiation

Provides evidence associated with the signatory's electronic signature, although the legal effect depends on the applicable circumstances and statutory framework.

Important Correction

Do not write simply:

"Digital signature encrypts the document."

A digital signature primarily provides authentication, integrity and evidentiary assurance; it is not the same thing as encrypting the entire document.

Example

A company digitally signs an electronic purchase order.

The recipient can verify:

Who signed it
Whether the signed data was altered
Whether the signature corresponds to the relevant key/certificate

Q7. ESSENTIAL ELEMENTS OF A VALID CONTRACT

Section 10 — Indian Contract Act, 1872

A valid contract generally requires:

\[ \boxed{\text{Agreement + Enforceability + Legal Requirements}} \]

Core Elements

Offer
Acceptance
Intention to create legal relations
Lawful consideration
Capacity
Free consent
Lawful object
Agreement not expressly declared void
Certainty of terms
Possibility of performance
Compliance with required legal formalities where applicable

1. Offer and Acceptance

There must be a valid proposal followed by valid acceptance.

Example

"I will sell my motorcycle to B for ₹80,000."

"I accept."

A valid agreement may arise if other legal requirements are satisfied.

Exam Case

Carlill v. Carbolic Smoke Ball Co.

Important for understanding offer and acceptance, particularly offers made to the public.

2. Intention to Create Legal Relations

The parties should intend their agreement to have legal consequences.

Example

A tells his friend:

"I'll give you ₹500 if you help me clean my room."

Whether a legally enforceable contract exists depends on the circumstances.

Social/domestic arrangements generally have a presumption against legal intention.

Landmark Case

Balfour v. Balfour

Commonly cited for the principle concerning domestic/social arrangements and intention to create legal relations.

3. Lawful Consideration

Consideration means something of value given in return for a promise.

Example

A supplies:

100 bags of cement.

B pays:

₹35,000.

Here:

A's consideration = cement
B's consideration = ₹35,000

Memory

Consideration = Something in return

4. Capacity of Parties

Section 11 requires parties to be competent to contract.

Generally, a competent person must:

Have attained majority
Be of sound mind
Not be disqualified by law

Minor

A minor's agreement is generally void ab initio.

Landmark Case

Mohori Bibee v. Dharmodas Ghose

Important examination case concerning a minor's contractual capacity.

5. Free Consent

Section 14

Consent is free when it is not caused by:

Coercion
Undue influence
Fraud
Misrepresentation
Mistake

Memory Trick

\[ \boxed{C-U-F-M-M} \]

Coercion
Undue influence
Fraud
Misrepresentation
Mistake

6. Lawful Object

The purpose of the agreement must be lawful.

An agreement cannot be based on an object that is:

Forbidden by law
Fraudulent
Injurious to person/property
Immoral
Opposed to public policy

Example

A agrees to pay B for committing an illegal act.

Such an agreement is not enforceable.

⭐ SECTION 7 — PERSONAL/MOVABLE PROPERTY

Important Terminology

In Indian commercial-law examination context, be careful with the expression personal property.

For the Sale of Goods Act, the key statutory concept is "goods", meaning movable property excluding money and actionable claims.

Tangible Movable Property

Physical items that can be possessed and moved.

Examples:

Machinery
Vehicles
Computers
Furniture
Raw materials
Finished goods

Intangible Property

Rights or interests that do not have ordinary physical form.

Examples:

Copyright
Patent rights
Trademark rights
Shares
Debts/actionable claims

Important Exam Caution

Do not automatically treat all intangible assets as "goods" under the Sale of Goods Act.

For exam purposes:

\[ \boxed{\text{Goods = Movable property − Money − Actionable Claims}} \]

SECTION C — LONG ANSWERS

Q10. CLASSIFICATION OF CONTRACTS

Contracts can be classified according to:

A. Validity

B. Formation

C. Performance

A. Classification According to Validity

1. Valid Contract

A contract enforceable by law.

Example

A agrees to sell a machine to B for ₹2 lakh, with lawful object, consideration, competent parties and free consent.

2. Void Agreement

Section 2(g)

An agreement not enforceable by law.

Example

An agreement with a person legally incapable of contracting may be void depending on the applicable rule.

3. Voidable Contract

Section 2(i)

A contract enforceable at the option of one party but not at the option of the other.

Example

A obtains B's consent through coercion.

B may have the right to rescind the contract.

4. Illegal Agreement

An agreement involving an unlawful object or consideration.

Example

Agreement to pay someone for committing a crime.

Important Distinction

\[ \boxed{\text{Every illegal agreement is void, but every void agreement is not necessarily illegal.}} \]

This is a very important exam statement.

5. Unenforceable Contract

The agreement may be otherwise valid, but cannot be enforced because of a procedural or technical legal defect.

Examples can include situations involving:

Required writing
Registration
Stamp requirements
Limitation

The exact consequence depends on the applicable statute.

📊 Valid vs Void vs Voidable vs Illegal

Basis	Valid	Void	Voidable	Illegal
Legal status	Enforceable	Not enforceable	Enforceable at aggrieved party's option	Unlawful and void
Consent	Free	May be absent/defective	Defective	May be irrelevant to illegality
Enforcement	Both parties	Neither	Aggrieved party can enforce/rescind	Court will not enforce illegal object
Example	Normal sale	Agreement prohibited/void under law	Coercion/fraud	Criminal transaction
Collateral effect	Generally valid	Depends	Generally not automatically affected	Collateral transactions may also be tainted

High-Value Exam Point

Do not write:

"Void agreement is always illegal."

Instead:

Void means legally unenforceable; illegal means forbidden by law.

Classification by Formation

1. Express Contract

Terms are explicitly stated.

Example

Written construction contract.

2. Implied Contract

Created through conduct or circumstances.

Example

A boards a public bus.

There is an implied obligation to pay the fare.

3. Quasi-Contract

Not actually created by agreement between parties.

It is an obligation imposed by law to prevent unjust enrichment.

Sections

Sections 68–72, Indian Contract Act

Example

A mistakenly delivers goods to B.

B cannot simply keep the benefit without legal consequences; the law may impose obligations depending on the circumstances.

Classification by Performance

Executed Contract

Obligations have been performed.

Example

A buys a product, pays immediately and receives the product.

Executory Contract

One or more obligations remain to be performed.

Example

A agrees today to deliver machinery next month.

Unilateral vs Bilateral

Unilateral

A promise is made in exchange for performance.

Example:

Reward offered for finding a lost item.

Bilateral

Promises are exchanged by both parties.

Example:

A promises to supply goods and B promises to pay.

Q11. LIEN VS STOPPAGE IN TRANSIT

This is a high-probability examination question.

Unpaid Seller

An unpaid seller may have important rights including:

Lien
Stoppage in transit
Resale
Other statutory remedies

A. Seller's Lien

Sections 47–49

The unpaid seller may retain possession of goods in certain circumstances.

When?

Generally where:

Goods are sold without credit.
Credit period has expired.
Buyer becomes insolvent.

Example

A sells machinery to B.

B has not paid.

A still possesses the machinery.

A may exercise lien where statutory conditions are satisfied.

B. Stoppage in Transit

Sections 50–52

If the seller has parted with possession and the goods are still in transit, an unpaid seller may, in specified circumstances, stop the goods when the buyer becomes insolvent.

Example

A sells goods to B.

A hands goods to a carrier.

Before delivery, B becomes insolvent.

A may have a right to stop the goods in transit, subject to statutory requirements.

⭐ Lien vs Stoppage

Basis	Lien	Stoppage in Transit
Seller's possession	Seller has possession	Seller has parted with possession
Goods	With seller	In transit
Buyer insolvency	Not always necessary	Generally essential
Main purpose	Retain goods	Stop goods before delivery
Key Sections	47–49	50–52
Ends	When possession is lost in relevant circumstances	When transit ends

Memory Trick

\[ \boxed{LIEN=KEEP} \] \[ \boxed{STOPPAGE=STOP} \]

Seller has goods → Lien

Carrier has goods → Stoppage

Q12. PARTNERSHIP — INDIAN PARTNERSHIP ACT, 1932

Section 4 — Definition

Partnership is the relationship between persons who have agreed to share the profits of a business carried on by all or any of them acting for all.

The Most Important Concept

\[ \boxed{\text{MUTUAL AGENCY}} \]

Each partner can be:

Principal + Agent

This is the real test of partnership.

Essential Elements

1. Agreement

Partnership arises from contract.

It does not arise merely from:

Family relationship
Status
Inheritance

2. Two or More Persons

There must be at least two persons.

Important Update

Your original note says:

"Maximum 50 as per Companies Act 2013."

For an exam, it is safer to state that the permissible number of partners is subject to the applicable statutory rules; the Companies (Miscellaneous) Rules, 2014 prescribe a limit of 50 persons for a partnership, subject to the relevant legal framework.

Avoid treating "50" as if it were contained in Section 4 of the Partnership Act.

3. Lawful Business

There must be an agreement to carry on a business.

4. Profit Sharing

Partners agree to share profits.

Important

Profit sharing is strong evidence of partnership, but profit sharing alone does not conclusively establish partnership.

5. Mutual Agency

This is the most important element.

\[ \boxed{\text{Mutual Agency = Partner acts for himself and as agent of other partners}} \]

Example

A, B and C operate a machine-parts business.

A purchases raw material for the firm.

B negotiates with customers.

C signs contracts on behalf of the firm.

Their acts within authority may bind the firm.

RIGHTS OF PARTNERS

Sections 9–13

1. Right to Participate

Every partner has a right to participate in business management, subject to the partnership agreement.

2. Right to Consultation

Partners have a right to be consulted in business matters.

3. Right to Inspect Books

Partners can inspect and copy firm accounts.

4. Right to Share Profits

Subject to agreement, partners generally share profits equally.

5. Interest on Advances

A partner is generally entitled to 6% per annum on advances beyond the agreed capital contribution under Section 13(d), subject to the Act/agreement.

Important distinction

Interest on advances ≠ interest on capital.

The Act provides different treatment for interest on advances and interest on capital.

6. Indemnity

A partner is entitled to indemnification by the firm for proper payments/liabilities incurred in the ordinary and proper conduct of business, subject to the Act.

LIABILITIES OF PARTNERS

1. Joint and Several Liability

Section 25

Every partner is liable jointly with the other partners and also severally for acts of the firm done while he is a partner.

Example

A and B are partners.

The firm owes ₹5 lakh to C.

Subject to applicable law, C can proceed against the partners according to the firm's liability rules.

2. Wrongful Acts

Section 26

Where loss or injury is caused to a third party by a partner's wrongful act or omission in the ordinary course of business or with authority, the firm may be liable.

Example

A partner negligently damages a customer's machinery while performing firm business.

The firm may be liable under the statutory conditions.

3. Misapplication of Money

Section 27

If a partner receives money/property from a third party in circumstances covered by the section and misapplies it, the firm may be liable.

4. Incoming Partner

Section 31

A newly admitted partner is generally not liable for acts of the firm done before joining, unless the legal arrangement/statutory position provides otherwise.

5. Retiring/Outgoing Partner

A retiring partner may remain liable to third parties for acts of the firm until the relevant statutory requirements, including public notice where applicable, are satisfied.

Exam Memory

\[ \boxed{\text{Incoming partner → Past liability generally NO}} \] \[ \boxed{\text{Outgoing partner → Public notice is important}} \]

🧠 LANDMARK CASES — EXAM EVIDENCE BANK

These cases can significantly improve a long-answer response.

Case	Principle/Topic
Balfour v. Balfour	Intention to create legal relations
Carlill v. Carbolic Smoke Ball Co.	Offer/acceptance
Mohori Bibee v. Dharmodas Ghose	Minor's agreement
Hadley v. Baxendale	Remoteness of damages
Lalman Shukla v. Gauri Dutt	Knowledge of offer
Mohori Bibee	Capacity/minor
CIT v. Dwarkadas Khetan & Co.	Partnership-related legal principles
Cox v. Hickman	Mutual agency/partnership principle

Exam Strategy

You do not need to insert a case into every answer.

For a 10–15 mark answer:

Definition → Section → Explanation → Example → Case → Conclusion

is an excellent structure.

⚖️ IMPORTANT SECTIONS TO MEMORIZE

Indian Contract Act, 1872

Section	Topic
2	Definitions
10	What agreements are contracts
11	Competency
14	Free consent
15	Coercion
16	Undue influence
17	Fraud
18	Misrepresentation
20	Bilateral mistake of fact
23	Lawful consideration/object
24	Agreements partly unlawful
25	Agreement without consideration
68–72	Quasi-contracts
124	Indemnity
126	Guarantee

🛒 SALE OF GOODS ACT, 1930

Section	Topic
2(7)	Goods
2(13)	Seller
12	Condition and warranty
15	Sale by description
16	Implied conditions as to quality/fitness
18–25	Transfer of property
26	Risk prima facie passes with property
27	Sale by person not owner
45	Unpaid seller
47–49	Seller's lien
50–52	Stoppage in transit
54	Resale by unpaid seller

🤝 INDIAN PARTNERSHIP ACT, 1932

Section	Topic
4	Definition of partnership
9	General duties
11	Rights/duties by contract
12	Conduct of business
13	Mutual rights/liabilities
18	Partner as agent of firm
25	Liability of partner for acts of firm
26	Wrongful acts
27	Misapplication
31	Introduction of partner
32	Retirement of partner
39	Dissolution of firm

💻 INFORMATION TECHNOLOGY ACT, 2000

Section	Topic
3	Digital signatures
4	Legal recognition of electronic records
5	Legal recognition of electronic signatures
10A	Validity of contracts formed through electronic means

🧾 NEGOTIABLE INSTRUMENTS ACT, 1881

Section	Topic
6	Cheque
13	Negotiable instrument
30	Liability of drawer
31	Liability of drawee bank
118	Presumptions
138	Dishonour of cheque in specified circumstances

🎯 HIGH-PROBABILITY EXAM QUESTIONS

Short Answer — 2–5 Marks

Define business law.
What is an e-contract?
What is a digital signature?
Define consideration.
What is free consent?
Define goods.
Who is an unpaid seller?
Define lien.
What is stoppage in transit?
Define partnership.
What is mutual agency?
What is indemnity?
Distinguish void and voidable contracts.
What is a quasi-contract?
What is an executory contract?

🔥 LONG-ANSWER QUESTIONS — 8–15 MARKS

Q1.

Explain the essential elements of a valid contract under Section 10 of the Indian Contract Act, 1872, with examples and relevant case laws.

Q2.

Explain and distinguish valid, void, voidable, illegal and unenforceable agreements.

Q3.

Explain the rights of an unpaid seller with special reference to lien and stoppage in transit.

Q4.

Define partnership under Section 4 and explain its essential elements.

Q5.

Explain the rights and liabilities of partners under the Indian Partnership Act, 1932.

Q6.

Explain e-contracts and digital signatures and discuss their legal recognition in India.

Q7.

Explain the classification of contracts according to validity, formation and performance.

🧠 ULTRA-FAST MEMORY SYSTEM

CONTRACT

\[ \boxed{O+A+C+C+F+L} \]

Offer
Acceptance
Consideration
Capacity
Free Consent
Lawful Object

FREE CONSENT

\[ \boxed{C-U-F-M-M} \]

Coercion → Undue Influence → Fraud → Misrepresentation → Mistake

PARTNERSHIP

\[ \boxed{A+B+P+M} \]

Agreement + Business + Profit Sharing + Mutual Agency

Most important:

\[ \boxed{\text{MUTUAL AGENCY}} \]

UNPAID SELLER

\[ \boxed{\text{LIEN → STOPPAGE → RESALE}} \]

Possession with seller → Goods in transit → Resale under conditions

E-CONTRACT

\[ \boxed{\text{Electronic Offer + Electronic Acceptance + Valid Contract Requirements}} \]

⭐ HOW TO WRITE A HIGH-SCORING LAW ANSWER

For a 10–15 mark question, use this fixed structure:

1. Definition

Quote/mention the statutory definition where relevant.

2. Section

Write the relevant section number.

3. Explanation

Explain the principle in simple language.

4. Essential Elements

Use numbered headings.

5. Example

Give a practical business example.

6. Case Law

Add one relevant landmark case where appropriate.

7. Comparison Table

For "difference between" questions.

8. Conclusion

End with 2–3 lines connecting the law to business practice.

Example concluding style:

Thus, the rule provides a legal framework for protecting commercial interests while ensuring that business transactions are conducted with certainty, fairness and enforceability.

This structure will make your answers more systematic, evidence-based and examiner-friendly, rather than merely listing definitions.

ERGONOMICS & HUMAN FACTORS ENGINEERING

Enhanced Mid-Sem Examination Reference Notes

SECTION A — MULTIPLE CHOICE QUESTIONS

1. Ergonomics primarily deals with:

Answer: (ii) Fitting the workplace and system to human capabilities

Explanation

Ergonomics is the scientific discipline concerned with understanding interactions between humans and other elements of a system, and applying theory, principles, data and methods to design systems that optimize:

Human well-being
Safety
Comfort
Performance
Productivity
Reliability

Key phrase for examination

“Fit the task to the human, not the human to the task.”

Industrial Example

An adjustable workstation allows workers of different heights to work without excessive bending or stretching.

Remember

Ergonomics = Human + Machine + Task + Environment + Organization

2. Anthropometric consideration in workplace design

Answer: (iii) Body dimensions of the worker

Explanation

Anthropometry is the measurement and study of human body dimensions.

Important measurements include:

Standing height
Sitting height
Eye height
Shoulder height
Elbow height
Knee height
Popliteal height
Arm reach
Hand length
Foot dimensions

Industrial Example

An adjustable operator chair should accommodate workers from approximately the 5th to 95th percentile, rather than being designed only around an average worker.

Exam Keyword

Anthropometry = Human body measurement for design.

3. Principle of Motion Economy

Answer: (ii) Minimizing fatigue and improving efficiency

Explanation

Motion economy aims to:

Eliminate unnecessary movements
Reduce fatigue
Reduce cycle time
Improve productivity
Improve workplace organization
Reduce operator effort

Historical Contributors

Frank B. Gilbreth
Lillian M. Gilbreth
Ralph M. Barnes

Industrial Example

Instead of repeatedly bending to pick components from the floor, components are supplied through gravity-fed bins positioned near the operator.

4. Biodynamic Analysis

Answer: (ii) Human response to mechanical forces, vibration and motion

Explanation

Biodynamics studies the interaction between:

Mechanical force → Human body → Tissue/organ response

Important applications include:

Whole-body vibration (WBV)
Hand-arm vibration (HAV)
Shock
Impact
Repeated mechanical loading
Vehicle vibration

Example

Forklift operators experience whole-body vibration, while workers using grinders may experience hand-arm vibration.

SECTION B — SHORT ANSWER QUESTIONS

5. Ergonomics

Definition

Ergonomics is the scientific discipline concerned with designing jobs, tools, machines, workplaces and systems according to human physical and cognitive capabilities and limitations.

Major Domains

Domain	Focus	Example
Physical Ergonomics	Posture, force, movement	Lifting
Cognitive Ergonomics	Perception, memory, decision-making	Control-room HMI
Organizational Ergonomics	Work systems and schedules	Shift planning

Objectives

Reduce occupational injuries.
Reduce Musculoskeletal Disorders (MSDs).
Reduce fatigue.
Improve productivity.
Improve quality.
Improve human-machine interaction.
Reduce human error.
Improve worker satisfaction.
Improve system reliability.

Industrial Example

An automotive assembly workstation uses:

Adjustable table + gravity bins + ergonomic tools + proper lighting

to reduce bending, reaching and repetitive strain.

6. Man-Machine Symbiosis

Definition

Man-machine symbiosis means designing a system where humans and machines work cooperatively, with each performing tasks according to their relative strengths.

Basic Concept

Human

→ Judgment
→ Creativity
→ Pattern recognition
→ Adaptability
→ Ethical decisions
→ Handling unexpected situations

Machine

→ Calculation
→ Repetition
→ High-speed processing
→ Heavy force
→ Precision
→ Continuous operation

Comparison

Human	Machine
Flexible	Consistent
Creative	Computational
Good judgment	High-speed calculation
Handles uncertainty	Handles repetitive work
Learns from context	High precision
Social interaction	High endurance

Modern Example

Collaborative Robot (Cobot)

Human:

Selects appropriate components
Handles exceptions
Performs inspection

Robot:

Lifts components
Performs repetitive movement
Maintains positioning accuracy

Exam Conclusion

Effective industrial design does not necessarily replace humans with machines; it combines human intelligence with machine capability.

7. Information Input and Processing

Human information processing can be represented as:

Stimulus → Sensation → Perception → Cognition → Decision → Motor Response → Feedback

Example

A machine alarm occurs:

Alarm sound → Operator detects → Identifies abnormal condition → Decides response → Presses emergency control

Major Information Channels

Visual
Auditory
Tactile
Proprioceptive

Important Cognitive Factors

Attention
Perception
Memory
Decision-making
Mental workload
Reaction time

Miller's 7±2 Rule

A classical cognitive psychology concept suggests that immediate memory capacity was traditionally described as approximately 7 ± 2 chunks, although modern research gives a more nuanced view of working-memory capacity.

Design Principle

Avoid:

Excessive information
Ambiguous displays
Unnecessary alarms
Poor contrast
Complex control layouts

Prefer:

Clear symbols
Consistent controls
Hierarchical displays
Appropriate alarm prioritization
Immediate feedback

8. Principles of Motion Economy

Motion economy is traditionally organized into three major groups.

A. Use of Human Body

Both hands should begin and finish their motions simultaneously where practical.
Avoid unnecessary movements.
Use smooth and continuous motions.
Use natural body rhythms.
Prefer smaller muscle groups only where appropriate.
Avoid unnecessary bending and twisting.

B. Workplace Arrangement

Frequently used tools should be within the normal working area.
Materials should have fixed locations.
Gravity-feed bins should be used where appropriate.
Tools should be arranged according to sequence of use.
Work surfaces should be at appropriate heights.

C. Tools and Equipment

Combine functions where practical.
Use fixtures and jigs.
Use power-assisted tools.
Use foot controls where appropriate.
Suspend heavy tools.
Design handles according to grip requirements.

Example

Traditional:

Floor box → bending → lifting → turning → assembly

Ergonomic:

Gravity bin → reach → pick → assembly

Result:

Less movement + Less fatigue + Shorter cycle time + Better productivity

9. Anthropometric Considerations

Definition

Anthropometry deals with the measurement and variation of human body dimensions.

Human dimensions vary according to:

Age
Sex
Population
Nutrition
Occupation
Genetics
Body posture

Therefore, designing exclusively around the "average person" can be inappropriate.

Three Major Design Strategies

1. Design for Extremes

For clearance, design for the larger user.

Example:

Door height
Legroom
Head clearance

Typically consider a high percentile such as the 95th percentile.

For reach, design for the smaller user.

Example:

Emergency button
Control lever
Shelf height

Typically consider a low percentile such as the 5th percentile.

2. Design for Adjustability

Best approach where possible.

Examples:

Adjustable chairs
Adjustable desks
Adjustable monitor
Adjustable footrests
Adjustable worktables

3. Design for Average

Used only where:

Adjustability is impractical
Extreme dimensions are not critical
Cost or engineering constraints exist

SECTION C — LONG ANSWER

QUESTION 10(A): ERGONOMIC WORKSTATION CASE STUDY

Introduction

An ergonomic workstation should integrate:

Human → Task → Machine → Material → Environment → Organization

The objective is to optimize both:

Human Outcomes

Safety
Comfort
Health
Reduced fatigue

System Outcomes

Productivity
Quality
Reliability
Reduced downtime
Reduced cost

1. Problems in Existing Workstation

Problem 1 — Excessive Bending

Parts are stored on the floor.

This causes:

Bending → trunk flexion → increased spinal loading → fatigue → injury risk

Problem 2 — Excessive Reach

Frequently used materials are placed outside the primary reach zone.

Consequences:

Shoulder loading
Neck strain
Trunk twisting
Longer cycle time

Problem 3 — Repetitive Motion

Repeated:

Reaching
Gripping
Lifting
Turning
Assembly

may contribute to fatigue and MSD risk.

Problem 4 — Poor Work Height

A fixed work surface may be unsuitable for workers with different body dimensions.

Problem 5 — Heat and Humidity

High heat and humidity can cause:

Dehydration
Fatigue
Reduced concentration
Increased physiological strain
Increased error probability

2. Anthropometric Redesign

Recommended Design Philosophy

Adjustability > Average-size design

Workstation

Height-adjustable workstation

Possible design range should be determined from actual task requirements and the target worker population rather than using a universal number.

Important Anthropometric Datums

Elbow height
Eye height
Shoulder height
Sitting height
Popliteal height
Reach distance

Working Height

For light precision assembly, the working surface is commonly positioned relative to elbow height, with the exact height determined by task precision, force requirements and posture.

3. Reach Envelope

Primary Reach Zone

Frequently used components and tools should be positioned close to the operator.

Secondary Reach Zone

Less frequently used materials can be placed farther away but still within comfortable reach.

Design Rule

Frequency of use should determine location.

Frequently used:

Closest

Occasionally used:

Farther

Rarely used:

Outside immediate working zone

4. Motion Economy Redesign

Existing Process

Bend → Reach → Lift → Turn → Assemble → Return

Improved Process

Gravity Feed → Pick → Assemble → Drop

This reduces:

Number of motions
Travel distance
Bending
Twisting
Cycle time
Fatigue

5. Ergonomic Tools

Use:

Tool balancers
Torque-controlled screwdrivers
Pneumatic tools
Ergonomic handles
Jigs and fixtures
Foot-operated controls

Example

A suspended pneumatic screwdriver:

Reduces tool weight carried by the worker → reduces wrist/shoulder loading.

6. Environmental Ergonomics

Important factors:

Temperature

High temperature increases thermal strain.

Humidity

High humidity can reduce sweat evaporation.

Noise

Excessive noise can cause:

Hearing risk
Communication difficulty
Fatigue
Reduced concentration

Lighting

Insufficient or excessive/glare-producing lighting can cause:

Eye strain
Visual errors
Reduced inspection accuracy

Vibration

Can affect:

Hands
Arms
Spine
Musculoskeletal system

7. Heat Stress Control

A better engineering approach is to assess heat exposure using an appropriate WBGT (Wet Bulb Globe Temperature) assessment rather than relying on temperature or relative humidity alone.

Controls include:

Engineering Controls

Ventilation
Air conditioning
Local cooling
HVLS fans
Heat shielding

Administrative Controls

Work-rest cycles
Acclimatization
Scheduling heavy work during cooler periods
Worker training

Personal/Work Practice Controls

Hydration
Appropriate clothing
Rest in cool areas

8. Existing vs Redesigned Workstation

Parameter	Existing	Redesigned
Material storage	Floor level	Waist/appropriate working level
Work height	Fixed	Adjustable
Tools	Manually handled	Suspended/ergonomic
Reach	Excessive	Optimized
Posture	Bending/twisting	Neutral posture
Material movement	Manual	Gravity-assisted
Environment	Poorly controlled	Ventilated/cooled
Fatigue	High	Reduced
Productivity	Lower	Higher
Quality	More errors	Better consistency

QUESTION 10(B): HUMAN FACTORS IN DESIGN & MANUFACTURING

1. Introduction

Human Factors Engineering (HFE) applies knowledge of human capabilities and limitations to the design of:

Machines
Tools
Workplaces
Software
Control systems
Manufacturing processes
Safety systems

Main Objective

Optimize total system performance while protecting human safety and well-being.

2. Human Factors System Model

A useful exam framework is:

HUMAN

↓

TASK

↓

MACHINE

↓

ENVIRONMENT

↓

ORGANIZATION

↓

PERFORMANCE & SAFETY

3. Information Display Design

Displays should be:

Simple
Consistent
Readable
Prioritized
Unambiguous
Appropriate to operator needs

Example

A process-control system can distinguish:

Normal → Warning → Critical

rather than presenting every alarm with equal visual prominence.

Important Principle

Critical information should be detected and interpreted quickly.

4. Control Design

Controls should follow the principle of compatibility.

Examples

Logical direction of movement
Clear labels
Appropriate resistance
Proper spacing
Prevention of accidental activation
Feedback after activation

Emergency Stop

An emergency stop should be:

Prominent
Easily identifiable
Accessible
Protected from accidental activation where appropriate
Designed according to applicable machinery safety requirements

5. Ergonomic Hand Tools

Design Principles

A good hand tool should:

Maintain neutral wrist posture
Distribute pressure
Reduce grip force
Reduce vibration
Match the task
Minimize repetitive strain

Example

Instead of forcing the wrist to bend:

Tool geometry changes → wrist remains closer to neutral.

Key Phrase

“Bend the tool, not the wrist.”

6. Environmental Ergonomics

Major factors include:

Noise

Excessive noise affects hearing and communication.

Illumination

Appropriate lighting improves visual performance.

Temperature

Extreme heat/cold affects physical and cognitive performance.

Vibration

Continuous vibration can contribute to discomfort and injury risk.

Air Quality

Poor ventilation can affect health, comfort and concentration.

7. Biodynamic Considerations

Whole-Body Vibration — WBV

Common sources:

Forklifts
Tractors
Heavy machinery
Earth-moving equipment
Industrial vehicles

Potential effects:

Discomfort
Fatigue
Reduced control
Musculoskeletal stress

Controls

Seat suspension
Vibration isolation
Vehicle maintenance
Appropriate operating speed
Improved road/surface conditions

8. Hand-Arm Vibration — HAV

Sources:

Grinders
Drills
Impact tools
Pneumatic tools
Cutting equipment

Potential effects include:

Numbness
Tingling
Reduced grip sensation
Hand-arm vibration-related disorders

Controls

Engineering controls are preferred, such as:

Low-vibration tools
Vibration isolation
Tool maintenance
Process redesign

Administrative controls can supplement engineering controls.

IMPORTANT ERGONOMIC PRINCIPLES FOR EXAMINATION

Remember the acronym:

F-I-T-H-M-E

F — Fit the workplace to human

I — Information must be clear

T — Task should minimize unnecessary effort

H — Human capabilities and limitations

M — Machine compatibility

E — Environment should support safe performance

IMPORTANT FORMULAS / RELATIONSHIPS

Work

\[ Work = Force \times Distance \]

Mechanical Power

\[ Power = \frac{Work}{Time} \]

Mechanical Stress

\[ Stress=\frac{Force}{Area} \]

Torque

\[ Torque=Force\times Moment\ Arm \]

Reach Design

For frequently used components:

\[ \text{Shorter Reach Distance} \rightarrow \text{Lower Motion Demand} \]

Anthropometric Design

Clearance → larger percentile

Reach → smaller percentile

Adjustability → broad user population

IMPORTANT INDUSTRIAL EXAMPLES

1. Automobile Assembly

Problem:

Repeated overhead work.

Solution:

Adjustable fixtures
Tool balancers
Rotating workstations
Ergonomic tools

Result:

Reduced shoulder loading + improved productivity

2. CNC Machine

Human:

Programming
Monitoring
Inspection
Troubleshooting

Machine:

Cutting
Automatic tool movement
Repetitive machining

This demonstrates man-machine symbiosis.

3. Warehouse

Problem:

Workers repeatedly lift heavy boxes from floor level.

Solutions:

Pallet positioning
Lift tables
Conveyors
Adjustable platforms
Mechanical handling

Result:

Reduced manual handling + lower injury risk + faster movement

4. Forklift

Main ergonomic issue:

Whole-body vibration

Controls:

Suspended seat
Proper tire maintenance
Smooth operating surfaces
Appropriate speed
Operator training

5. Grinding Station

Main issue:

Hand-arm vibration

Controls:

Low-vibration grinder
Anti-vibration features
Tool maintenance
Process redesign
Exposure management

VERY IMPORTANT EXAM DISTINCTIONS

Concept	Meaning
Ergonomics	Fit work/system to humans
Anthropometry	Human body measurements
Biodynamics	Human response to force/vibration/motion
Motion Economy	Minimize unnecessary movements
Human Factors	Human capabilities/limitations in system design
Man-Machine Symbiosis	Humans and machines complement each other
Physical Ergonomics	Body, posture, force, movement
Cognitive Ergonomics	Perception, memory, decision-making
Organizational Ergonomics	Work schedules, communication, systems

LIKELY EXAM QUESTIONS

Short Answer — 2–5 Marks

Define ergonomics.
What is anthropometry?
Define biodynamics.
Explain motion economy.
What is man-machine symbiosis?
Explain human information processing.
What is the importance of ergonomic workstation design?
Explain WBV and HAV.
Explain the 5th and 95th percentile concept.
What are physical, cognitive and organizational ergonomics?

Long Answer — 10–15 Marks

Explain the principles of ergonomic workstation design with an industrial example.
Discuss anthropometric considerations in workplace design.
Explain the principles of motion economy with suitable examples.
Discuss human factors in manufacturing system design.
Explain man-machine symbiosis with industrial examples.
Explain the effects of heat, noise, illumination and vibration on human performance.
Design an ergonomic workstation for an assembly operation.
Explain biodynamic considerations in industrial workplace design.
Discuss the role of ergonomics in productivity and occupational safety.
Explain how human factors engineering reduces human error in manufacturing.

HIGH-VALUE ANSWER STRUCTURE FOR LONG QUESTIONS

For a 10/15-mark answer, use this sequence:

1. Definition

Give a precise technical definition.

2. Objective

Explain why the concept is important.

3. Principles

Give 4–8 structured points.

4. Diagram

Draw a simple system/workstation diagram.

5. Industrial Example

Use automotive, CNC, warehouse, construction or process industry.

6. Benefits

Mention:

Safety
Productivity
Quality
Comfort
Reduced fatigue
Reduced errors
Reduced cost

7. Conclusion

End with:

“An ergonomically designed system improves both human well-being and overall system performance by matching work demands with human capabilities and limitations.”

FINAL ONE-PAGE REVISION MAP

                  ERGONOMICS
                      │
        ┌─────────────┼─────────────┐
        │             │             │
     PHYSICAL      COGNITIVE   ORGANIZATIONAL
        │             │             │
     Posture       Memory       Work Schedule
     Force         Decision     Shift System
     Movement      Perception   Communication
        │             │             │
        └─────────────┼─────────────┘
                      │
              HUMAN FACTORS
                      │
       ┌──────────────┼──────────────┐
       │              │              │
 Anthropometry   Biodynamics   Motion Economy
       │              │              │
 Body Size       Vibration      Less Motion
 Reach            Shock          Less Fatigue
 Clearance        Force          More Efficiency
       │              │              │
       └──────────────┼──────────────┘
                      │
             MAN–MACHINE SYSTEM
                      │
         ┌────────────┼────────────┐
         │            │            │
       HUMAN       MACHINE     ENVIRONMENT
         │            │            │
     Judgment      Precision     Heat
     Creativity    Repetition    Noise
     Adaptability  Strength      Light
                                  Vibration
                      │
                      ↓
          SAFETY + QUALITY + PRODUCTIVITY

⭐ Most Important Points to Memorize

1. Ergonomics: Fit the system to the human.

2. Anthropometry: Measurement of human body dimensions.

3. Biodynamics: Human response to mechanical forces and vibration.

4. Motion Economy: Eliminate unnecessary movement.

5. Anthropometric design:
Clearance → large percentile
Reach → small percentile
Adjustability → broad population

6. Man-machine symbiosis:
Human = judgment/adaptability
Machine = speed/precision/repetition

7. Information processing:
Stimulus → Perception → Cognition → Decision → Response

8. Ergonomic workstation:
Correct height + optimized reach + neutral posture + appropriate tools + suitable environment

9. Vibration:
WBV → whole body
HAV → hand and arm

10. Final objective:
Human well-being + Safety + Quality + Productivity + System Performance.

Sub section 1.2

Materials Management (PEMP-4001).

SECTION A: Multiple Choice Questions

1. The main objective of Materials Management is to:

Correct Answer: b) Ensure the right material at the right time and cost
Key Concept: Materials Management focuses on the "5 Rights": Right Quality, Right Quantity, Right Time, Right Price, and Right Source.

2. EOQ stands for:

Correct Answer: a) Economic Order Quantity
Key Concept: EOQ is the ideal order quantity that minimizes the total cost of ordering and holding inventory.

3. ABC analysis is based mainly on:

Correct Answer: b) Annual consumption value
Key Concept: It follows Pareto's 80/20 Rule, categorizing inventory items based on their annual financial usage value (\text{Annual Usage} \times \text{Unit Cost}).

4. The point at which a new order should be placed is called:

Correct Answer: b) Reorder level
Key Concept: The Reorder Level (ROL) triggers a purchase requisition to replenish stock before running into a shortage.

5. Which of the following is a function of Materials Management?

Correct Answer: d) All of the above
Key Concept: Materials Management oversees the end-to-end material flow, including procurement (purchasing), tracking/monitoring (inventory control), and warehousing (stores management).

SECTION B: Short Answer Type Questions

6. Definition and Objectives of Materials Management

Materials Management is an integrated management approach responsible for planning, acquiring, storing, moving, and controlling materials to ensure optimal production flow at minimal cost.

Main Objectives:

Cost Reduction: Minimizing overall material costs through effective purchasing and low inventory holding costs.
Uninterrupted Production: Ensuring materials are available on time so manufacturing line stoppages do not occur.
Inventory Optimization: Balancing stock levels to avoid overstocking (capital tie-up) or stockouts.
Quality Maintenance: Procuring raw materials that meet strict quality specifications.
High Inventory Turnover: Increasing the turnover ratio to maximize capital efficiency.

7. ABC Analysis and Classification

ABC Analysis is an inventory control technique based on Pareto's Law (80/20 rule), which divides inventory items into three distinct categories based on their annual consumption value:
+-------------------------------------------------------------+ | Category | % of Total Items | % of Annual Usage Value | +-------------------------------------------------------------+ | A Items | 10% – 20% | 70% – 80% | | B Items | 20% – 30% | 15% – 25% | | C Items | 50% – 70% | 5% – 10% | +-------------------------------------------------------------+

Category A: High-value items requiring strict inventory control, tight safety stocks, and frequent monitoring by top management.
Category B: Moderate-value items requiring intermediate control, periodic ordering, and moderate safety stocks.
Category C: Low-value items managed with simple, decentralized controls, bulk ordering, and minimum monitoring effort.

8. Reorder Level (ROL) and Influencing Factors

Reorder Level (ROL) is the predetermined inventory threshold at which a purchase order must be placed to replenish stock before it runs out.
\text{Reorder Level (ROL)} = (\text{Maximum Consumption Rate} \times \text{Maximum Lead Time})
(Or \text{ROL} = \text{Average Lead Time Consumption} + \text{Safety Stock})

Factors Affecting Determination of ROL:

Lead Time: The total time taken between placing an order and receiving the goods. Longer lead time requires a higher ROL.
Rate of Consumption: How quickly raw materials are consumed on the shop floor per day/week.
Safety Stock (Buffer Stock): Reserve stock kept to cushion against demand spikes or supplier delays.
Supplier Reliability: Dependability of suppliers regarding delivery schedules and quality compliance.

SECTION C: Long Answer Type Questions & Calculations

9. Core Functions of Materials Management

Purchasing (Procurement):

Vendor selection, price negotiation, issuing Purchase Orders (PO), and establishing long-term contract agreements.

Receiving & Inspection:

Receiving: Verification of incoming goods against Delivery Challans/POs, unloading, and logging inbound register entries.
Inspection: Quality assurance check against technical specifications before accepting delivery into main storage.

Storage & Stores Management:

Safe warehousing, bin card updates, preventing damage/pilferage, and maintaining layout for easy retrieval.

Inventory Control:

Setting stock levels (Max, Min, ROL), conducting periodic stock auditing, and optimizing holding vs. ordering costs.

Material Handling:

Moving items efficiently within the shop floor using forklifts, overhead cranes, or conveyer belts to minimize internal transit time and damage.

10. Key Inventory Control Techniques

EOQ (Economic Order Quantity): Mathematical model to determine optimal batch size by minimizing total holding and ordering costs.
ABC Analysis (Value-based): Prioritizes control focus based on monetary usage (A > B > C).
VED Analysis (Vital, Essential, Desirable): Categorizes spare parts based on criticality to production failure:
- Vital (V): Absence stops production immediately. Must always be stocked.
- Essential (E): Absence leads to operational inefficiency or minor downtime.
- Desirable (D): Non-availability does not affect immediate operations.
FSN Analysis (Fast, Slow, Non-moving): Categorizes items by movement rate/turnover frequency to clear dead stock.
Just-in-Time (JIT): Japanese inventory philosophy (Toyota Production System) aiming to eliminate inventory by receiving materials only when needed in production.

11. Step-by-Step Calculation: EOQ Problem

Given Data:

Annual Demand (D): 12{,}000\text{ units/year}
Ordering Cost (S): ₹300\text{ per order}
Annual Carrying Cost (H): ₹26\text{ per unit/year}
Working Days per Year: 360\text{ days}

Step 1: Calculate Economic Order Quantity (EOQ)

\text{EOQ} = \sqrt{\frac{2 \cdot D \cdot S}{H}} \text{EOQ} = \sqrt{\frac{2 \times 12000 \times 300}{26}} \text{EOQ} = \sqrt{\frac{7200000}{26}} \approx \sqrt{276923.077} \approx 526.235\text{ units}
Rounding to the nearest whole integer yields 526\text{ units}.

Step 2: Calculate Number of Orders per Year (N)

N = \frac{D}{\text{EOQ}} N = \frac{12000}{526.235} \approx 22.80\text{ orders/year}
Rounding to practical order frequency yields 22.8\text{ orders} (or \approx 23\text{ orders}).

Step 3: Calculate Time Between Two Consecutive Orders (T)

T = \frac{\text{Working Days per Year}}{N} T = \frac{360}{22.80} \approx 15.789\text{ days}

Final Exam Summary Table for Q11

+--------------------------------------------------------------------+ | Parameter | Value | +----------------------------------------+---------------------------+ | (a) Economic Order Quantity (EOQ) | 526 units (approx 526.24) | | (b) Number of orders per year (N) | 22.8 orders (~23 orders) | | (c) Time between consecutive orders (T) | ~15.79 working days | +----------------------------------------+---------------------------+
Here are step-by-step numerical examples covering EOQ with Quantity Discounts and EOQ with Safety Stock / Reorder Level (ROL) calculations.

Example 1: EOQ with Quantity Discounts

When a supplier offers a price discount for ordering in larger quantities, the basic EOQ formula alone is insufficient. You must compare the Total Annual Cost (TAC) at the standard EOQ level against the discount threshold levels.
\text{Total Cost (TC)} = \text{Purchase Cost} + \text{Ordering Cost} + \text{Carrying Cost} \text{TC} = (D \times C) + \left(\frac{D}{Q} \times S\right) + \left(\frac{Q}{2} \times H\right)
Where:

D = Annual Demand
C = Unit Purchase Price
S = Cost per Order
H = Holding/Carrying Cost per unit per year (often expressed as a percentage I of unit price C, so H = I \times C)
Q = Order Quantity

Problem Statement

A manufacturing firm has an annual requirement of 10,000 units of a raw material.

Ordering cost per order (S) = ₹500
Base unit purchase price (C) = ₹100
Inventory carrying cost rate (I) = 20% per year (0.20 \times C)

The supplier offers the following price discount schedule:

Tier 1 (0 \le Q < 2,000): No discount (C_1 = ₹100)
Tier 2 (Q \ge 2,000): 5% discount on all units (C_2 = ₹95)

Determine the most economical order quantity.

Step-by-Step Solution

Step 1: Calculate the standard EOQ for Tier 1 (No Discount)

For C_1 = ₹100:
H_1 = 20\% \text{ of } ₹100 = ₹20\text{ per unit/year} \text{EOQ}_1 = \sqrt{\frac{2 \cdot D \cdot S}{H_1}} = \sqrt{\frac{2 \times 10000 \times 500}{20}} = \sqrt{\frac{10000000}{20}} = \sqrt{500000} \approx 707.1\text{ units}
Since 707 units falls in the bracket 0 \le Q < 2000, this standard EOQ is feasible.

Step 2: Calculate Total Annual Cost for Option 1 (Q = 707\text{ units})

\text{TC}_1 = (10000 \times 100) + \left(\frac{10000}{707.1} \times 500\right) + \left(\frac{707.1}{2} \times 20\right) \text{TC}_1 = 1,000,000 + 7,071.07 + 7,071.00 = \mathbf{₹1,014,142.07}

Step 3: Check the Discount Threshold (Tier 2: Q = 2,000\text{ units})

For C_2 = ₹95:
H_2 = 20\% \text{ of } ₹95 = ₹19\text{ per unit/year} \text{EOQ}_2 = \sqrt{\frac{2 \times 10000 \times 500}{19}} = \sqrt{526315.79} \approx 725.48\text{ units}
Note: 725.48 units is not feasible for Tier 2 because the discount requires ordering at least 2,000 units. Therefore, the minimum order quantity to qualify for the discount is Q = 2,000\text{ units}.

Step 4: Calculate Total Annual Cost for Option 2 (Q = 2,000\text{ units})

\text{TC}_2 = (10000 \times 95) + \left(\frac{10000}{2000} \times 500\right) + \left(\frac{2000}{2} \times 19\right) \text{TC}_2 = 950,000 + 2,500 + 19,000 = \mathbf{₹971,500.00}

Step 5: Cost Comparison & Final Recommendation

+------------------------------------------------------------------------------------+ | Quantity Option | Unit Price | Ordering Cost | Holding Cost | Total Annual Cost | +------------------+------------+---------------+--------------+---------------------+ | Q = 707 units | ₹100 | ₹7,071.07 | ₹7,071.00 | ₹1,014,142.07 | | Q = 2,000 units | ₹95 | ₹2,500.00 | ₹19,000.00 | ₹971,500.00 | +------------------+------------+---------------+--------------+---------------------+

Annual Savings: ₹1,014,142.07 - ₹971,500.00 = \mathbf{₹42,642.07}
Verdict: The company should accept the discount and order 2,000 units per batch, despite the higher inventory holding cost, because the purchase price savings far outweigh the additional holding cost.

Example 2: EOQ with Safety Stock & Reorder Point (ROP)

When demand during lead time varies or lead time itself fluctuates, safety stock is added to prevent stockouts.

Relevant Formulas:

Safety Stock (SS): \text{SS} = (d_{\text{max}} \times L_{\text{max}}) - (d_{\text{avg}} \times L_{\text{avg}}) (Or using standard deviation under probabilistic demand: \text{SS} = Z \times \sigma_L)
Reorder Point (ROP): \text{ROP} = (d_{\text{avg}} \times L_{\text{avg}}) + \text{SS}
Average Inventory with Safety Stock: \text{Average Inventory} = \frac{\text{EOQ}}{2} + \text{SS}

Problem Statement

A firm operates 300 working days a year and consumes an annual total of 6,000 units of a critical spare part.

Ordering cost per order (S) = ₹400
Annual carrying cost per unit (H) = ₹12
Average lead time (L_{\text{avg}}) = 6 days
Maximum lead time (L_{\text{max}}) = 10 days
Average daily usage (d_{\text{avg}}) = \frac{6000}{300} = 20 units/day
Maximum daily usage (d_{\text{max}}) = 30 units/day

Calculate:

Economic Order Quantity (EOQ)
Safety Stock (SS) required
Reorder Point (ROP)
Total Annual Inventory Holding Cost (including safety stock)

Step-by-Step Solution

Step 1: Calculate EOQ

\text{EOQ} = \sqrt{\frac{2 \cdot D \cdot S}{H}} = \sqrt{\frac{2 \times 6000 \times 400}{12}} = \sqrt{\frac{4800000}{12}} = \sqrt{400000} = \mathbf{2,000\text{ units}}

Step 2: Calculate Safety Stock (SS)

\text{Safety Stock} = (\text{Max Daily Usage} \times \text{Max Lead Time}) - (\text{Avg Daily Usage} \times \text{Avg Lead Time}) \text{SS} = (30 \times 10) - (20 \times 6) = 300 - 120 = \mathbf{180\text{ units}}

Step 3: Calculate Reorder Point (ROP)

\text{Normal Lead Time Usage} = 20 \text{ units/day} \times 6 \text{ days} = 120\text{ units} \text{ROP} = \text{Normal Lead Time Usage} + \text{Safety Stock} \text{ROP} = 120 + 180 = \mathbf{300\text{ units}}
Interpretation: When the stock level drops to 300 units, a fresh order of 2,000 units should be placed immediately.

Step 4: Calculate Total Annual Carrying Cost

With safety stock included, the average inventory level rises from \frac{\text{EOQ}}{2} to \frac{\text{EOQ}}{2} + \text{SS}.
\text{Average Inventory} = \frac{2000}{2} + 180 = 1000 + 180 = 1,180\text{ units} \text{Total Carrying Cost} = \text{Average Inventory} \times H = 1180 \times 12 = \mathbf{₹14,160}

Key Takeaways for Examinations

+-----------------------------------------------------------------------------------------+ | Topic | Key Formula / Rule to Remember | +------------------------+----------------------------------------------------------------+ | Quantity Discount | Always calculate TC at EOQ, then check TC at each discount | | | break point (Q_min). Compare total costs, not just EOQ. | +------------------------+----------------------------------------------------------------+ | Reorder Point (ROP) | ROP = Lead Time Demand + Safety Stock | +------------------------+----------------------------------------------------------------+ | Carrying Cost with SS | Total Holding Cost = (EOQ / 2 + Safety Stock) * H | +------------------------+----------------------------------------------------------------+

Question 1: Multiple Choice Questions

A) Linear programming is a

Answer: (d) all of the above
Explanation: Linear Programming (LP) is a mathematical technique used for the economic allocation of limited resources to achieve optimization (maximizing profit or minimizing cost) under given constraints.

B) While solving a LP model graphically, the area bounded by the constraints is called

Answer: (a) feasible region
Explanation: The feasible region is the set of all possible points (solutions) that satisfy all given constraints simultaneously in a graphical linear programming problem.

C) Branch and Bound method divides the feasible solution space into smaller parts by

Answer: (a) branching
Explanation: The process of dividing the feasible region into smaller sub-problems is known as branching. Bounding is used to calculate upper/lower limits to eliminate non-optimal sub-problems.

D) The solution to a transportation problem with m-rows (supplies) and n-columns (destinations) is feasible if number of positive allocations are

Answer: (c) m+n-1
Explanation: A non-degenerate feasible solution to an m \times n transportation problem must have exactly m + n - 1 independent allocations (occupied cells).

Question 2: Trans-shipment Problem

1. Problem Formulation

In a trans-shipment problem with m sources and n destinations, every point (factories and retail stores) can act as both a supply node and a demand node.

Let the total buffer quantity be B = \text{Total Supply} = 200 + 300 = 500 units.

Nodes: Factories (X, Y), Retail Stores (A, B, C) — total 5 nodes.
Effective Supply (S_i):
- Factory X: 200 + B = 700
- Factory Y: 300 + B = 800
- Store A: 0 + B = 500
- Store B: 0 + B = 500
- Store C: 0 + B = 500
Effective Demand (D_j):
- Factory X: 0 + B = 500
- Factory Y: 0 + B = 500
- Store A: 100 + B = 600
- Store B: 150 + B = 650
- Store C: 250 + B = 750

Cost Matrix Table (with Buffer Quantities)

From \ To
X
Y
A
B
C
Supply (S_i)

Factory X
0
8
7
8
9
700

Factory Y
6
0
5
4
3
800

Store A
7
2
0
5
1
500

Store B
1
5
1
0
4
500

Store C
8
9
7
8
0
500

Demand (D_j)
500
500
600
650
750
3000

2. Initial Feasible Solution (Vogel's Approximation Method / Minimum Cost Allocation)

Allocating units using minimum cost paths and shortest trans-shipment paths:

Direct vs Trans-shipment Cost Analysis:

X \to A: Direct cost = 7. Trans-shipment via B: X \to B \to A = 8 + 1 = 9. Direct is optimal (7).
X \to B: Direct cost = 8.
X \to C: Direct cost = 9. Trans-shipment via A: X \to A \to C = 7 + 1 = 8. (Cheaper via A)
Y \to A: Direct cost = 5.
Y \to B: Direct cost = 4.
Y \to C: Direct cost = 3.

Allocations:

Allocate 500 units on self-trans-shipment diagonals (X,X), (Y,Y), (A,A), (B,B), (C,C) at 0 cost.
Remaining Net Supplies: Factory X = 200, Factory Y = 300.
Remaining Net Demands: Store A = 100, Store B = 150, Store C = 250.
Allocate 300 units from Factory Y:
- Y \to C: 250 units at cost ₹3
- Y \to B: 50 units at cost ₹4
Allocate 200 units from Factory X:
- X \to B: 100 units at cost ₹8
- X \to A: 100 units at cost ₹7

3. Optimal Shipping Schedule & Total Cost

Route
Units Shipped
Cost per Unit (₹)
Total Cost (₹)

Factory X \to Store A
100
7
700

Factory X \to Store B
100
8
800

Factory Y \to Store B
50
4
200

Factory Y \to Store C
250
3
750

Total Minimum Cost
₹ 2,450

Question 3: All-Integer Programming (Branch and Bound Method)

\text{Maximize } Z = 2x_1 + 3x_2
Subject to constraints:

6x_1 + 5x_2 \le 25
x_1 + 3x_2 \le 10
x_1, x_2 \ge 0 \text{ and integers}

Step 1: Solve Continuous LP Relaxation (Sub-problem \ P_0)

Convert inequalities to equalities to find intersection of boundaries:

Equation (1): 6x_1 + 5x_2 = 25
Equation (2): x_1 + 3x_2 = 10 \implies x_1 = 10 - 3x_2

Substitute x_1 in (1):
6(10 - 3x_2) + 5x_2 = 25 60 - 18x_2 + 5x_2 = 25 \implies 13x_2 = 35 \implies x_2 = \frac{35}{13} \approx 2.69 x_1 = 10 - 3(2.69) = \frac{25}{13} \approx 1.92 \text{Objective Value } Z_0 = 2\left(\frac{25}{13}\right) + 3\left(\frac{35}{13}\right) = \frac{50 + 105}{13} = \frac{155}{13} \approx 11.92
Since x_1 and x_2 are non-integers, branch on x_2 (x_2 \le 2 or x_2 \ge 3).

Step 2: Branching Tree

                   [P0] Z = 11.92                     x1 = 1.92, x2 = 2.69                          /        \              x2 <= 2    /          \    x2 >= 3                        /            \                    [P1]              [P2]              Z = 11.0              Z = 10.0           x1 = 2.5, x2 = 2     x1 = 1.0, x2 = 3                /      \          (INTEGER SOLUTION)    x1 <= 2    /        \ x1 >= 3              /          \          [P3]            [P4]        Z = 10.0         Z = 9.8     x1=2, x2=2       x1=3, x2=1.4 (INTEGER SOLUTION)

Sub-problem P_1 (Add constraint x_2 \le 2):

From x_1 + 3x_2 \le 10 \implies with x_2 = 2, x_1 \le 4.
From 6x_1 + 5x_2 \le 25 \implies 6x_1 + 5(2) \le 25 \implies 6x_1 \le 15 \implies x_1 \le 2.5.
Max x_1 = 2.5, x_2 = 2 \implies Z_1 = 2(2.5) + 3(2) = 11.0.

Sub-problem P_2 (Add constraint x_2 \ge 3):

From x_1 + 3(3) \le 10 \implies x_1 \le 1.
Check 6(1) + 5(3) = 21 \le 25 (Valid).
Max x_1 = 1, x_2 = 3 \implies Z_2 = 2(1) + 3(3) = 10.0.
This is an Integer Feasible Solution with Z = 10.0.

Branching further on P_1 (Branch on x_1: x_1 \le 2 and x_1 \ge 3):

Sub-problem P_3 (x_1 \le 2, x_2 \le 2):
- Best integer values: x_1 = 2, x_2 = 2.
- Check constraints: 6(2)+5(2) = 22 \le 25 and 2+3(2)=8 \le 10.
- Z_3 = 2(2) + 3(2) = 10.0 (Integer Solution).
Sub-problem P_4 (x_1 \ge 3, x_2 \le 2):
- From 6(3) + 5x_2 \le 25 \implies 5x_2 \le 7 \implies x_2 \le 1.4.
- Max x_1 = 3, x_2 = 1.4 \implies Z_4 = 2(3) + 3(1.4) = 9.8 (Lower than current best integer solution Z = 10.0, so prune).

Optimal Integer Solution

There are two alternative optimal integer solutions:

x_1 = 1, x_2 = 3 with Maximum Z = 10
x_1 = 2, x_2 = 2 with Maximum Z = 10

Question 4: Queuing Model (M/M/1)

Given Data

Service Rate (\mu): Average repair time = 30\text{ minutes} = 0.5\text{ hours}. \mu = \frac{1}{0.5} = 2 \text{ jobs/hour}
Arrival Rate (\lambda): 10 sets per 8-hour day. \lambda = \frac{10}{8} = 1.25 \text{ jobs/hour}

Part 1: Expected Idle Time Each Day

Traffic Intensity / Utilization Factor (\rho): \rho = \frac{\lambda}{\mu} = \frac{1.25}{2} = 0.625 \text{ (or } 62.5\%\text{)}
Proportion of Idle Time (P_0): P_0 = 1 - \rho = 1 - 0.625 = 0.375 \text{ (or } 37.5\%\text{)}
Expected Idle Time in an 8-Hour Day: \text{Idle Time} = 8 \text{ hours} \times 0.375 = 3 \text{ hours}

Part 2: Average Number of Jobs Ahead of a Just-Arrived Set

The number of jobs ahead of a new arrival is equivalent to the average length of the queue (L_q):
L_q = \frac{\lambda^2}{\mu(\mu - \lambda)}
Substitute the values:
L_q = \frac{(1.25)^2}{2(2 - 1.25)} = \frac{1.5625}{2(0.75)} = \frac{1.5625}{1.5} \approx 1.0417 \text{ jobs}

Expected Idle Time: 3 hours per day
Average Jobs Ahead: 1.04 jobs (or approximately 1 job)

Question 5: Goal Programming Model Formulation

1. Decision Variables

x_1: Number of units of Product A produced next week
x_2: Number of units of Product B produced next week

2. Deviational Variables

d_1^-, d_1^+: Under-achievement and over-achievement of the total profit goal (₹700)
d_2^-, d_2^+: Under-achievement and over-achievement of product A sales goal (5 units)
d_3^-, d_3^+: Under-achievement and over-achievement of product B sales goal (4 units)

3. Goal Constraints

Profit Goal: 100x_1 + 50x_2 + d_1^- - d_1^+ = 700
Sales Volume Goal for Product A: x_1 + d_2^- - d_2^+ = 5
Sales Volume Goal for Product B: x_2 + d_3^- - d_3^+ = 4

4. Objective Function

Since the decision-maker wants total profit to be exactly ₹700, both under-achievement (d_1^-) and over-achievement (d_1^+) must be minimized. For sales goals to be close to target volumes, both negative and positive deviations are minimized:
\text{Minimize } Z = (d_1^- + d_1^+) + (d_2^- + d_2^+) + (d_3^- + d_3^+)
(Non-negativity constraint: x_1, x_2, d_1^-, d_1^+, d_2^-, d_2^+, d_3^-, d_3^+ \ge 0)

Question 6: Short Notes

a) Goal Programming

Goal Programming (GP) is an extension of Linear Programming designed to handle multiple, often conflicting operational goals simultaneously.

Key Concept: Instead of optimizing a single objective function (like maximizing total profit or minimizing total cost), Goal Programming seeks to minimize the unwanted deviations (d^- and d^+) from target goal levels.
Types:
1. Non-preemptive (Weighted) Goal Programming: All goals have assigned numerical weights reflecting their relative importance.
2. Preemptive (Lexicographic) Goal Programming: Goals are ranked in order of priority (P_1 > P_2 > P_3), and higher-priority goals must be satisfied before lower-priority goals are considered.

b) Difference between LPP & IPP

Feature
Linear Programming Problem (LPP)
Integer Programming Problem (IPP)

Variable Constraints
Decision variables can take any real continuous value (fractions/decimals allowed).
Decision variables are strictly restricted to integer values.

Feasible Region
Continuous convex region with infinite solution points.
Discrete set of points within the constrained region.

Solution Method
Simplex Method, Graphical Method.
Branch and Bound Method, Cutting Plane Method (Gomory's).

Computational Complexity
Solvable in polynomial time (relatively fast).
NP-hard problem; computationally expensive for large systems.

Practical Application
Blending problems, general resource allocation.
Capital budgeting, scheduling, project selection (yes/no decisions).

c) Reasons for Carrying Inventory

Maintaining inventory requires holding costs, but organizations hold inventory for strategic operational reasons:

Meeting Fluctuating Demand: Ensures continuous customer satisfaction by acting as a buffer against unexpected surges in market demand.
Protection Against Supply Delays: Mitigates risks associated with supplier lead-time variability, transportation delays, or material shortages.
Economies of Scale (Quantity Discounts): Allows firms to purchase raw materials in bulk, reducing unit purchasing costs and shipping expenses.
Decoupling Operations: Separates consecutive production processes so that a breakdown in one machine or station does not halt the entire manufacturing line.
Hedging Against Price Inflation: Helps hedge against anticipated increases in raw material prices or raw material scarcity in volatile markets."

SECTION A

1. Multiple Choice Questions

1. The Sale of Goods Act is of:

Answer: (c) 1930
Explanation: The Sale of Goods Act in India was enacted on 1st July 1930, separating sales law from the Indian Contract Act, 1872.

2. Seller is a person who:

Answer: (a) Sells or agrees to sell
Explanation: As per Section 2(13) of the Sale of Goods Act, 1930, a seller is defined as a person who sells or agrees to sell goods.

3. A contract of indemnity is primarily a contract to:

Answer: (b) Compensate for loss
Explanation: As per Section 124 of the Indian Contract Act, 1872, a contract of indemnity is one by which one party promises to save the other from loss caused to him by the conduct of the promisor himself, or by the conduct of any other person.

4. Under Sale of Goods Act, goods refers to:

Answer: (c) Movable property
Explanation: Section 2(7) defines goods as every kind of movable property other than actionable claims and money.

5. A cheque is always drawn on a:

Answer: (b) Bank
Explanation: Under Section 6 of the Negotiable Instruments Act, 1881, a cheque is defined as a bill of exchange drawn on a specified banker and payable on demand.

SECTION B (Short Answer Questions)

6. Business Law, E-Contracts, and Digital Signatures

Business Law

Business Law (also known as Commercial Law) refers to the body of law that governs business entities, commercial transactions, trade, and industrial activities. It provides a structured framework within which enterprises operate, ensuring fairness, transparency, and dispute resolution mechanisms. Key acts under Indian business law include the Indian Contract Act (1872), Sale of Goods Act (1930), Negotiable Instruments Act (1881), and Companies Act (2013).

E-Contracts (Electronic Contracts)

An e-contract is a contract modeled, executed, and enacted by a software system or digital platform. Instead of paper, the offer and acceptance are communicated electronically through emails, web forms, or click-wrap agreements. Under Section 10A of the Information Technology Act, 2000, e-contracts are legally valid and enforceable in India provided essential contract elements are met.

Digital Signatures

A digital signature is a mathematical scheme used to demonstrate the authenticity of digital messages or documents. Recognized under Section 3 of the Information Technology Act, 2000:

It uses asymmetric cryptosystems (a key pair consisting of a private key and a public key) to encrypt and verify signature data.
It ensures authentication (identifying the signatory), non-repudiation (the signatory cannot deny creating the signature), and data integrity (proving the document was not altered post-signing).

7. Essential Elements of a Valid Contract

According to Section 10 of the Indian Contract Act, 1872, all agreements are contracts if they are made by the free consent of parties competent to contract, for a lawful consideration and with a lawful object, and are not expressly declared to be void.
+-------------------------------------------------------------------------------+ | ESSENTIAL ELEMENTS OF A VALID CONTRACT | +-------------------------------------------------------------------------------+ | 1. Offer & Acceptance ---> Two distinct parties with a clear proposal/consent| | 2. Intention to Create ---> Legal relationship intended (e.g., Balfour v. | | Legal Obligations Balfour) | | 3. Lawful Consideration ---> Quid Pro Quo ("something in return") | | 4. Capacity of Parties ---> Major age, sound mind, not disqualified | | 5. Free Consent ---> Free from coercion, undue influence, fraud, etc. | | 6. Lawful Object ---> Not forbidden by law or opposed to public policy | +-------------------------------------------------------------------------------+

Proper Offer and Acceptance: There must be at least two parties — one making a definite offer and another accepting it unconditionally.

Example: A offers to sell his car to B for ₹3,00,000, and B accepts the offer as is.

Intention to Create Legal Relations: The parties must intend to enter into a legally binding obligation. Social or domestic agreements are generally not contracts.

Example: A promises to take his spouse out for dinner; failure to do so does not give rise to legal action (Balfour v. Balfour).

Lawful Consideration: Consideration is quid pro quo ("something in return"). It must be real and lawful.

Example: A promises to deliver 100 bags of cement to B, and B promises to pay ₹35,000 upon delivery.

Capacity of Parties: Parties must be competent — major age (18+), of sound mind, and not disqualified by any law.

Example: A contract entered into by a 15-year-old minor is void ab initio (Mohori Bibee v. Dharmodas Ghose).

Free Consent: Consent must be given freely without Coercion (Sec 15), Undue Influence (Sec 16), Fraud (Sec 17), Misrepresentation (Sec 18), or Mistake (Sec 20).
Lawful Object: The purpose of the agreement must not be illegal, immoral, or opposed to public policy.

8. Personal Property and Its Types

Definition

Personal property (also called personalty or movable property) encompasses all property that is not real property (land, buildings, and permanent structures attached to the earth).

Types of Personal Property

                          PERSONAL PROPERTY                                      |              +-----------------------+-----------------------+              |                                               |      Tangible Personal                               Intangible Personal       Property (Chattels)                            Property (Choses in Action)              |                                               |      +-------+-------+                              +--------+--------+      |               |                              |                 |   Corpreal        Perishable                    Intellectual       Financial   Goods           Goods                         Property           Assets (Vehicles,      (Food items,                  (Patents,          (Shares, Machinery)       Crops)                        Trademarks)        Debts)

Tangible Personal Property (Corporeal Chattels):

Physical items that can be touched, moved, and felt.
Examples: Motor vehicles, machinery, laptops, furniture, raw materials.

Intangible Personal Property (Incorporeal Chattels / Choses in Action):

Property that represents value or rights but lacks physical substance.
Examples:
- Intellectual Property: Patents, copyrights, trademarks, design registrations.
- Financial Assets & Legal Claims: Shares, bonds, bank accounts, actionable claims, goodwill.

SECTION C (Long Answer Questions)

10. Classification of Contracts & Distinction between Agreements

Contracts can be classified based on Validity/Enforceability, Formation, and Performance:
TYPES OF CONTRACTS | +----------------------------------+----------------------------------+ | | | By Validity By Formation By Performance * Valid * Express * Executed * Void Agreement * Implied * Executory * Voidable * Quasi-contract * Unilateral * Illegal * E-Contract * Bilateral * Unenforceable

Detailed Classification

By Validity / Enforceability:

Valid Contract: Meets all Section 10 criteria and is legally enforceable.
Void Agreement: Void ab initio (from the start); has no legal force (Sec 2(g)).
Voidable Contract: Enforceable at the option of one party (the aggrieved party) but not the other (Sec 2(i)).
Illegal Agreement: Forbidden by law or involves criminal activity.
Unenforceable Contract: Substantively valid but unenforceable due to a technical defect (e.g., lack of stamp, signature, or written form).

By Formation:

Express Contract: Terms stated orally or in writing.
Implied Contract: Formed by the conduct/action of parties (e.g., getting into a bus creates an implied contract to pay the fare).
Quasi-Contract: Imposed by law to prevent unjust enrichment, independent of party agreement (Sec 68-72).

By Performance:

Executed: Both parties have fulfilled their obligations.
Executory: Obligations remain to be performed in the future.

Comparative Analysis: Valid, Void, Voidable, Illegal & Unenforceable Agreements

Basis of Comparison
Valid Contract
Void Agreement
Voidable Contract
Illegal Agreement
Unenforceable Contract

Legal Status
Fully valid and legally binding.
Completely void from inception (void ab initio).
Valid until repudiated by the aggrieved party.
Void and explicitly prohibited by law.
Substantively valid, but barred by procedural defects.

Enforceability
Enforceable by both parties.
Enforceable by neither party.
Enforceable only at the option of the injured party.
Not enforceable by any court.
Unenforceable until procedural defect is cured.

Cause
All Section 10 elements present.
Lacks an essential element (e.g., minor, no consideration).
Consent obtained via coercion, fraud, misrepresentation.
Purpose/object is illegal, criminal, or immoral.
Absence of registration, stamps, or written proof.

Collateral Transactions
Valid and enforceable.
Collateral agreements remain valid (unless illegal).
Collateral transactions remain valid.
Collateral transactions are also void.
Collateral transactions remain unaffected.

Restitution / Remedies
Damages, specific performance available.
Restitution available under Sec 65 in certain cases.
Aggrieved party can rescind and claim damages.
No court assistance; In pari delicto applies.
Remedy available once procedural error is rectified.

11. Lien vs. Stoppage in Transit

Concept of Lien

A Lien is the right of an unpaid seller to retain possession of goods sold until the full purchase price is paid or tendered. Under Section 47 of the Sale of Goods Act, 1930, the unpaid seller in possession can exercise a lien when:

Goods were sold without credit terms.
Goods were sold on credit, but the credit period has expired.
The buyer becomes insolvent.

Key Differences: Lien vs. Stoppage in Transit

               POSSESSION & TRANSIT STATUS                       [Seller's Custody]  =======>  [Carrier / Transit]  =======>  [Buyer's Custody]    |                 |           |                 |           |               |    +--- RIGHT OF ----+           +--- RIGHT OF ----+           +-- POSSESSION -+    |       LIEN      |           |    STOPPAGE     |           |   TRANSFERRED |    |   (Sec 47-49)   |           |    IN TRANSIT   |           |   (Lien Lost) |    |                 |           |   (Sec 50-52)   |           |               |

Parameter
Right of Lien (Sec 47–49)
Right of Stoppage in Transit (Sec 50–52)

Location / Possession of Goods
Goods are in the actual physical possession of the seller.
Goods have left the seller's possession and are with an independent carrier/middleman in transit.

Solvency of Buyer
Can be exercised whether the buyer is solvent or insolvent (e.g., expired credit term).
Can ONLY be exercised if the buyer has become insolvent.

Nature of Right
Right to retain possession.
Right to regain/resume possession.

Point of Commencement
Begins as soon as default occurs while goods are still held by the seller.
Begins after the seller delivers goods to a carrier and ends when the buyer takes delivery.

How Exercised
By simply refusing to hand over goods to the buyer.
By taking actual possession or giving notice to the carrier/bailee.

12. Partnership under the Indian Partnership Act, 1932

Formation of a Partnership

Under Section 4 of the Indian Partnership Act, 1932, Partnership is the relation between persons who have agreed to share the profits of a business carried on by all or any of them acting for all.

Essentials for Formation:

Contractual Relationship: Must arise from a contract, not from status or inheritance.
Two or More Persons: Minimum 2 members; maximum 50 (as per Companies Act 2013).
Business: Agreement must be to carry on a lawful business/trade.
Sharing of Profits: Agreement to share profits (and losses) of the business.

Mutual Agency: Business must be carried on by all or any of them acting for all (each partner is both principal and agent).

                PARTNERSHIP STRUCTURE (SEC 4)                                      |     +--------------------------------+--------------------------------+     |                                |                                | Contractual Origin            Mutual Agency                    Profit Sharing (Not by Status/Birth)    (Principal <---> Agent)              (Agreement required)

Rights of Partners (Sec 9–13)

Right to Take Part in Management: Right to participate in the conduct of the business (Sec 12(a)).
Right to be Consulted: Right to express opinions before business decisions are made (Sec 12(c)).
Right to Access Books: Right to inspect and copy any of the account books of the firm (Sec 12(d)).
Right to Share Profits: Right to share equally (or as agreed) in the profits generated (Sec 13(b)).
Right to Interest on Capital & Advances: Right to 6% per annum interest on advances made beyond capital contribution (Sec 13(d)).
Right to Indemnity: Right to be indemnified by the firm for liabilities incurred in the ordinary course of business (Sec 13(e)).

Liabilities of Partners (Sec 25–27)

Unlimited Joint & Several Liability: Every partner is jointly and severally liable for all acts of the firm done while they are a partner (Sec 25).
Liability for Wrongful Acts / Torts: Firm and partners are liable for loss or injury caused to third parties due to a partner's wrongful act in the ordinary course of business (Sec 26).
Liability for Misapplication of Money: If a partner receives third-party funds and misapplies them, the firm is liable to make good the loss (Sec 27).
Liability of Incoming and Outgoing Partners: An incoming partner is not liable for acts done before joining unless agreed upon; an outgoing partner remains liable for acts prior to retirement until public notice is given."

📘 MID-SEM EXAMINATION — ENHANCED MASTER NOTES

Materials Management / Operations Research

PEMP-4001 | Quantitative Techniques, Optimization & Decision Models

SECTION A — MULTIPLE CHOICE QUESTIONS

Q1(A) Linear Programming is a:

Answer: (d) All of the above

Explanation

Linear Programming (LP/LPP) is a mathematical optimization technique used to determine the best allocation of limited resources among competing activities.

It can be used for:

Profit maximization
Cost minimization
Resource allocation
Production planning
Product-mix decisions
Transportation and distribution planning

Basic Structure

\[ \text{Optimize } Z=c_1x_1+c_2x_2+\cdots+c_nx_n \]

Subject to:

\[ a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n\leq b_1 \]

and similar constraints, with:

\[ x_i\geq0 \]

Q1(B) In graphical LP, the area satisfying all constraints is called:

Answer: (a) Feasible Region

Key Concept

The feasible region is the set of all points that simultaneously satisfy:

All constraints
Non-negativity restrictions

The optimal solution in a standard LP occurs at an extreme/corner point of the feasible region, when an optimum exists.

Remember

Feasible = Possible

Q1(C) Branch and Bound divides the solution space by:

Answer: (a) Branching

Explanation

The Branch and Bound method solves integer programming problems by:

Branching → Bounding → Pruning

Branching: Divides the problem into smaller sub-problems.
Bounding: Determines the best possible objective value of each sub-problem.
Pruning/Fathoming: Eliminates branches that cannot produce a better solution.

Memory Trick

Branch → Bound → Eliminate → Repeat

Q1(D) A non-degenerate transportation solution contains:

Answer: (c) \(m+n-1\) positive allocations

For an \(m\times n\) transportation problem:

\[ \boxed{m+n-1} \]

independent occupied cells are required for a non-degenerate basic feasible solution.

Important distinction

Non-degenerate BFS: exactly \(m+n-1\) positive allocations.
Degenerate BFS: fewer than \(m+n-1\) positive allocations; zero allocations may be assigned as \(\epsilon\) to maintain the basis.

SECTION B — TRANSSHIPMENT PROBLEM

Q2. Transshipment Model

Concept

A transportation problem generally moves goods from sources directly to destinations.

A transshipment problem allows intermediate nodes to receive and redistribute goods.

Therefore:

\[ \boxed{\text{Source}\rightarrow\text{Transshipment Node}\rightarrow\text{Destination}} \]

A node may act as:

Supply node
Demand node
Intermediate/transshipment node

Given Network

Factories

Factory X = 200 units
Factory Y = 300 units

Therefore:

\[ Total\ Supply=500 \]

Retail Demand

A = 100 units
B = 150 units
C = 250 units

Therefore:

\[ Total\ Demand=500 \]

Hence the problem is balanced.

Cost Matrix

From / To	X	Y	A	B	C	Supply
X	0	8	7	8	9	700
Y	6	0	5	4	3	800
A	7	2	0	5	1	500
B	1	5	1	0	4	500
C	8	9	7	8	0	500
Demand	500	500	600	650	750	3000

The \(+500\) buffer is introduced to convert the transshipment problem into an equivalent transportation problem.

Effective Supply and Demand

Effective Supply

\[ S_i=Original\ Supply+B \]

Thus:

X = \(200+500=700\)
Y = \(300+500=800\)
A = \(0+500=500\)
B = \(0+500=500\)
C = \(0+500=500\)

Effective Demand

\[ D_j=Original\ Demand+B \]

Thus:

X = 500
Y = 500
A = \(100+500=600\)
B = \(150+500=650\)
C = \(250+500=750\)

Total:

\[ 700+800+500+500+500=3000 \]

and

\[ 500+500+600+650+750=3000 \]

Therefore, the converted transportation problem is balanced.

Optimal Shipping Interpretation

The economically relevant factory-to-store shipments are:

Route	Quantity	Cost/unit	Cost
X → A	100	₹7	₹700
X → B	100	₹8	₹800
Y → B	50	₹4	₹200
Y → C	250	₹3	₹750
Total	500	—	₹2,450

Therefore:

\[ \boxed{Minimum\ Transportation\ Cost=₹2,450} \]

Important Exam Point

Critical Check

Before writing “optimal” in an exam, ideally verify the solution using a method such as:

MODI method
Stepping-Stone method
Transportation simplex

A VAM solution is generally an initial basic feasible solution, not automatically a proof of optimality.

SECTION C — INTEGER PROGRAMMING

Q3. All-Integer Programming Using Branch & Bound

Problem

Maximize:

\[ \boxed{Z=2x_1+3x_2} \]

Subject to:

\[ 6x_1+5x_2\leq25 \] \[ x_1+3x_2\leq10 \] \[ x_1,x_2\geq0 \]

and:

\[ x_1,x_2\in\mathbb Z \]

Step 1 — LP Relaxation

Ignore the integer restriction temporarily.

At the intersection:

\[ 6x_1+5x_2=25 \] \[ x_1+3x_2=10 \]

From the second equation:

\[ x_1=10-3x_2 \]

Substitute:

\[ 6(10-3x_2)+5x_2=25 \] \[ 60-18x_2+5x_2=25 \] \[ 13x_2=35 \] \[ x_2=\frac{35}{13}=2.692 \]

Therefore:

\[ x_1=\frac{25}{13}=1.923 \]

Objective:

\[ Z=2(1.923)+3(2.692) \] \[ Z=\frac{155}{13} \] \[ \boxed{Z=11.923} \]

Since the solution is fractional, it is not an integer solution.

Step 2 — Branch on \(x_2\)

Since:

\[ x_2=2.692 \]

create:

\[ \boxed{x_2\leq2} \]

and

\[ \boxed{x_2\geq3} \]

Branch P₁: \(x_2\leq2\)

At optimum:

\[ x_2=2 \]

Constraint 1:

\[ 6x_1+5(2)\leq25 \] \[ 6x_1\leq15 \] \[ x_1\leq2.5 \]

Thus LP relaxation gives:

\[ x_1=2.5,\quad x_2=2 \] \[ Z=2(2.5)+3(2)=11 \]

This is fractional, so branch further on \(x_1\):

\[ x_1\leq2 \]

\[ x_1\geq3 \]

Branch P₂: \(x_2\geq3\)

Take:

\[ x_2=3 \]

From:

\[ x_1+3x_2\leq10 \] \[ x_1+9\leq10 \] \[ x_1\leq1 \]

Thus:

\[ x_1=1,\quad x_2=3 \]

Objective:

\[ Z=2(1)+3(3) \] \[ \boxed{Z=11} \]

Important Correction

Your original solution states \(Z=10\) here. That is an arithmetic error.

\[ 2(1)+3(3)=2+9=\boxed{11} \]

So the integer solution:

\[ \boxed{(x_1,x_2)=(1,3)} \]

gives Z = 11, not 10.

Branch P₃: \(x_1\leq2,\ x_2\leq2\)

Take:

\[ x_1=2,\quad x_2=2 \]

Check:

\[ 6(2)+5(2)=22\leq25 \] \[ 2+3(2)=8\leq10 \]

Objective:

\[ Z=2(2)+3(2) \] \[ \boxed{Z=10} \]

This is an integer feasible solution.

Branch P₄: \(x_1\geq3,\ x_2\leq2\)

With \(x_1=3\):

\[ 18+5x_2\leq25 \] \[ 5x_2\leq7 \] \[ x_2\leq1.4 \]

LP upper bound:

\[ Z=2(3)+3(1.4)=10.2 \]

Since the best known integer solution is already:

\[ Z=11 \]

and:

\[ 10.2<11 \]

this branch is pruned.

🌳 Correct Branch-and-Bound Summary

Node	Restriction	LP Solution / Bound	Status
P₀	Original LP	11.923	Branch
P₁	\(x_2\leq2\)	11.0	Branch
P₂	\(x_2\geq3\)	11.0	Integer → incumbent
P₃	\(x_1\leq2,x_2\leq2\)	10.0	Integer, inferior
P₄	\(x_1\geq3,x_2\leq2\)	10.2	Prune

Correct Final Answer

\[ \boxed{x_1=1,\quad x_2=3} \] \[ \boxed{Z_{\max}=11} \]

Therefore, the statement in the original notes that both (1,3) and (2,2) are optimal with \(Z=10\) is incorrect.

SECTION D — QUEUING MODEL

Q4. M/M/1 Queuing Model

Given

10 repair sets per 8-hour day
Average repair time = 30 minutes

Step 1 — Arrival Rate

\[ \lambda=\frac{10}{8} \] \[ \boxed{\lambda=1.25\ jobs/hour} \]

Step 2 — Service Rate

Average service time:

\[ 30\ minutes=0.5\ hour \]

Therefore:

\[ \mu=\frac{1}{0.5} \] \[ \boxed{\mu=2\ jobs/hour} \]

Step 3 — Utilization

\[ \rho=\frac{\lambda}{\mu} \] \[ \rho=\frac{1.25}{2} \] \[ \boxed{\rho=0.625} \]

Thus the repair facility is busy:

\[ 62.5\% \]

of the time.

Expected Idle Time

Probability of zero customers/system being idle:

\[ P_0=1-\rho \] \[ P_0=1-0.625 \] \[ P_0=0.375 \]

Therefore:

\[ Idle\ Time=8(0.375) \] \[ \boxed{3\ hours/day} \]

Average Number of Jobs in Queue

For M/M/1:

\[ L_q=\frac{\lambda^2}{\mu(\mu-\lambda)} \]

Substitute:

\[ L_q=\frac{1.25^2}{2(2-1.25)} \] \[ =\frac{1.5625}{1.5} \] \[ \boxed{L_q=1.042\ jobs} \]

Answer

The average number of jobs waiting in the queue is:

\[ \boxed{1.04\ jobs} \]

Important Terminology

If the question asks:

Average number of jobs ahead of a just-arrived job

⭐ Important M/M/1 Formula Sheet

Stability Condition

\[ \boxed{\lambda<\mu} \]

SECTION E — GOAL PROGRAMMING

Q5. Goal Programming Model

Decision Variables

Let:

\[ x_1=\text{units of Product A} \] \[ x_2=\text{units of Product B} \]

Goals

Goal 1 — Profit

Target:

\[ ₹700 \]

Profit:

\[ 100x_1+50x_2 \]

Goal equation:

\[ \boxed{100x_1+50x_2+d_1^- -d_1^+=700} \]

Goal 2 — Product A Sales

Target:

\[ 5\ units \] \[ \boxed{x_1+d_2^- -d_2^+=5} \]

Goal 3 — Product B Sales

Target:

\[ 4\ units \] \[ \boxed{x_2+d_3^- -d_3^+=4} \]

Deviational Variables

\(d_i^-\)

Under-achievement / shortfall.

\(d_i^+\)

Over-achievement / excess.

Remember:

\(d^-\) = Below target
\(d^+\) = Above target

Objective Function

If all deviations have equal importance:

\[ \boxed{ \min Z= d_1^-+d_1^+ +d_2^-+d_2^+ +d_3^-+d_3^+ } \]

subject to:

\[ x_1,x_2,d_i^-,d_i^+\geq0 \]

Important Goal Programming Principle

In real Goal Programming, not every deviation is necessarily undesirable.

For example:

Profit goal → usually minimize underachievement \(d_1^-\); exceeding profit may be desirable.
Sales target → depending on the problem, both over- and under-achievement may matter.
Resource target → usually only one direction may be undesirable.

Therefore, the objective should reflect the decision-maker's actual preferences.

SECTION F — SHORT NOTES

Q6(a). Goal Programming

Goal Programming (GP) is an extension of Linear Programming used when an organization has multiple objectives or goals that may conflict with one another.

Instead of optimizing only one objective, GP attempts to minimize deviations from predetermined target levels.

Basic Structure

\[ \boxed{Goal + d^- -d^+=Target} \]

Types

1. Weighted / Non-Preemptive GP

Different weights are assigned to different goals.

\[ \min Z=w_1d_1+w_2d_2+\cdots+w_nd_n \]

Higher weight = greater importance.

2. Pre-emptive / Lexicographic GP

Goals are arranged according to priority:

\[ P_1>P_2>P_3 \]

Higher-priority goals are satisfied before lower-priority goals.

Applications

Production planning
Workforce planning
Budget allocation
Project selection
Resource allocation
Supply-chain planning

Q6(b). LPP vs IPP

Feature	LPP	IPP
Full Form	Linear Programming Problem	Integer Programming Problem
Variables	Continuous	Integer
Fractional values	Allowed	Not allowed
Solution space	Continuous	Discrete
Typical methods	Simplex, Graphical	Branch & Bound, Cutting Plane
Complexity	Generally easier	Generally more computationally difficult
Examples	Product mix, blending	Scheduling, project selection

Example

LPP:

\[ x=2.5 \]

can be acceptable.

IPP:

\[ x=2.5 \]

is not acceptable if \(x\) must be integer.

Q6(c). Reasons for Carrying Inventory

Although inventory involves capital and storage costs, organizations maintain inventory for several important reasons.

1. Demand Uncertainty

Inventory acts as a buffer against unexpected increases in demand.

2. Protection Against Supply Delays

Safety stock protects production against:

Supplier delays
Transportation problems
Material shortages
Lead-time variability

3. Economies of Scale

Bulk purchasing may provide:

Quantity discounts
Lower ordering frequency
Lower transportation cost per unit

4. Decoupling of Operations

Inventory between production stages allows one process to continue even if another temporarily stops.

5. Protection Against Price Increase

Organizations may purchase materials before expected price increases.

6. Smooth Production

Adequate raw-material inventory helps prevent production interruptions.

7. Seasonal Availability

Some materials may be available only during certain seasons.

8. Reduction of Ordering Cost

Larger, less frequent orders can reduce the administrative cost associated with repeated purchasing.

🔥 FINAL EXAM CRASH SHEET

LP

\[ \boxed{\text{Optimize Objective Function subject to Constraints}} \]

Feasible Region = All points satisfying all constraints.

Transportation

\[ \boxed{m+n-1} \]

= Number of allocations in a non-degenerate BFS.

Transshipment

\[ \boxed{\text{Source → Intermediate → Destination}} \]

EOQ

\[ \boxed{EOQ=\sqrt{\frac{2DS}{H}}} \]

Reorder Point

\[ \boxed{ROP=\text{Lead-Time Demand}+SS} \]

Safety Stock

\[ \boxed{SS=(d_{max}L_{max})-(d_{avg}L_{avg})} \]

Branch & Bound

\[ \boxed{Branch\rightarrow Bound\rightarrow Prune} \]

M/M/1

Condition:

\[ \boxed{\lambda<\mu} \]

Goal Programming

\[ \boxed{Goal+d^- -d^+=Target} \] \[ \boxed{d^-=\text{Underachievement}} \] \[ \boxed{d^+=\text{Overachievement}} \]

⚠️ THREE IMPORTANT CORRECTIONS TO YOUR ORIGINAL NOTES

1. Branch & Bound Question 3

Your original calculation:

\(x_1=1,x_2=3 \Rightarrow Z=10\)

is incorrect.

Actually:

\[ 2(1)+3(3)=2+9=\boxed{11} \]

Therefore, the correct optimum is:

\[ \boxed{x_1=1,\ x_2=3,\ Z=11} \]

The point \((2,2)\) gives only:

\[ \boxed{Z=10} \]

2. Branch \(P_4\)

Your original upper bound of 9.8 is also incorrect.

At:

\[ x_1=3,\quad x_2=1.4 \] \[ Z=2(3)+3(1.4) \] \[ =6+4.2 \] \[ =\boxed{10.2} \]

It is still pruned because:

\[ 10.2<11 \]

3. Transshipment

VAM/minimum-cost allocation gives an initial feasible solution; it should not automatically be called mathematically optimal without an optimality test such as MODI or Stepping-Stone.

These corrections are important because Question 3 in its original form would lead to the wrong final answer.

Materials Management — Mid-Sem Final Revision Notes

1. Materials Management

5 Rights of Materials Management

Right Quality
Right Quantity
Right Time
Right Price
Right Source

Main Objectives

Reduce material and inventory cost
Ensure uninterrupted production
Maintain optimum inventory
Ensure required quality
Improve inventory turnover
Minimize wastage, damage and obsolescence

2. Important Inventory Techniques

Technique	Basis	Main Purpose
EOQ	Order quantity	Minimize ordering + holding cost
ABC	Annual consumption value	Value-based control
VED	Criticality	Control spare parts
FSN	Movement rate	Identify slow/dead stock
JIT	Timing of supply	Minimize inventory

ABC Classification

Category	Approx. Items	Approx. Annual Value	Control
A	10–20%	70–80%	Very strict
B	20–30%	15–25%	Moderate
C	50–70%	5–10%	Simple

ABC basis:
Annual Consumption Value = Annual Usage × Unit Price

3. EOQ — Most Important Numerical

Formula

\[ EOQ=\sqrt{\frac{2DS}{H}} \]

Where:

\(D\) = Annual demand
\(S\) = Ordering cost/order
\(H\) = Holding cost/unit/year

Given

\(D=12,000\) units
\(S=₹300\)
\(H=₹26\)

\[ EOQ=\sqrt{\frac{2(12000)(300)}{26}} \] \[ EOQ\approx526.24 \]

Answer

EOQ ≈ 526 units/order

Number of Orders

\[ N=\frac{D}{EOQ} \] \[ N=\frac{12000}{526.24}\approx22.8 \]

≈ 23 orders/year

Time Between Orders

\[ T=\frac{360}{22.8} \] \[ T\approx15.79\text{ days} \]

Final Answer

EOQ = 526 units
Orders/year = 22.8 ≈ 23
Order interval = 15.79 working days

4. Reorder Level / Reorder Point

Basic Formula

\[ ROP=\text{Lead-Time Demand}+\text{Safety Stock} \]

or, under a maximum-demand/maximum-lead-time approach:

\[ ROL=Maximum\ Consumption\ Rate\times Maximum\ Lead\ Time \]

Factors affecting ROL

Lead time
Consumption rate
Safety stock
Supplier reliability
Demand variability

5. Safety Stock

A commonly used exam formula is:

\[ SS=(d_{max}\times L_{max})-(d_{avg}\times L_{avg}) \]

Then:

\[ ROP=(d_{avg}\times L_{avg})+SS \]

6. EOQ + Safety Stock Numerical

Given

Annual demand = 6,000 units
Working days = 300
Ordering cost = ₹400
Holding cost = ₹12/unit/year
Average lead time = 6 days
Maximum lead time = 10 days
Average usage = 20 units/day
Maximum usage = 30 units/day

Step 1 — EOQ

\[ EOQ=\sqrt{\frac{2(6000)(400)}{12}} \] \[ EOQ=2000\text{ units} \]

Step 2 — Safety Stock

\[ SS=(30\times10)-(20\times6) \] \[ SS=300-120 \] \[ \boxed{SS=180\text{ units}} \]

Step 3 — ROP

\[ ROP=(20\times6)+180 \] \[ ROP=120+180 \] \[ \boxed{ROP=300\text{ units}} \]

Step 4 — Average Inventory

\[ Average\ Inventory=\frac{EOQ}{2}+SS \] \[ =\frac{2000}{2}+180 \] \[ =1180\text{ units} \]

Step 5 — Annual Holding Cost

\[ Holding\ Cost=1180\times12 \] \[ \boxed{₹14,160/year} \]

Final Answer

Parameter	Answer
EOQ	2,000 units
Safety Stock	180 units
ROP	300 units
Average Inventory	1,180 units
Annual Holding Cost	₹14,160

7. Quantity Discount — Important Concept

When quantity discounts are offered, do not automatically select the basic EOQ.

Calculate:

\[ TC=DC+\frac{D}{Q}S+\frac{Q}{2}H \]

Where:

\(DC\) = Annual purchase cost
\(\frac{D}{Q}S\) = Annual ordering cost
\(\frac{Q}{2}H\) = Annual holding cost

Decision Rule

Calculate and compare total annual cost at all feasible alternatives.

For the given example:

Q	Unit Price	Ordering Cost	Holding Cost	Total Cost
707	₹100	₹7,071	₹7,071	₹10,14,142
2,000	₹95	₹2,500	₹19,000	₹9,71,500

Therefore:

\[ ₹9,71,500 < ₹10,14,142 \]

Final Decision

\[ \boxed{Q=2,000\text{ units}} \]

The quantity discount should be accepted.

Annual saving ≈ ₹42,642.

8. Core Functions of Materials Management

Remember:

P-R-S-I-H

P — Purchasing
Vendor selection, negotiation, purchase orders.

R — Receiving & Inspection
Receive, verify, inspect and accept materials.

S — Stores Management
Storage, bin cards, preservation and retrieval.

I — Inventory Control
Min/Max levels, ROL, safety stock, stock verification.

H — Handling
Movement of materials using cranes, forklifts, conveyors, etc.

9. VED Analysis

V — Vital

Failure/absence can stop production.
Very high priority.
Adequate stock must be maintained.

E — Essential

Absence affects efficiency.
Moderate priority.

D — Desirable

Absence has little immediate operational effect.
Lower priority.

Remember:
ABC = Money/Value
VED = Criticality

10. FSN Analysis

F — Fast Moving

Frequently consumed.

S — Slow Moving

Used occasionally.

N — Non-Moving

Little or no movement for a long period.

Purpose: Identify obsolete/dead inventory and improve inventory utilization.

11. JIT — Just in Time

JIT means receiving materials approximately when they are required for production rather than maintaining excessive inventory.

Objectives

Reduce inventory
Reduce storage cost
Reduce waste
Improve quality
Improve production flow
Shorten lead time

⭐ Formula Sheet — Must Memorize

🎯 One-Minute Exam Memory Map

Materials Management
→ 5 Rights
→ Quality + Quantity + Time + Price + Source

Inventory Control
→ EOQ + ABC + VED + FSN + JIT

EOQ
→ Optimal order size

ABC
→ Annual consumption value

VED
→ Criticality

FSN
→ Movement

ROP
→ When to order

Safety Stock
→ Protection against uncertainty

Quantity Discount
→ Compare Total Cost, not merely EOQ.

Most important numerical questions:
EOQ → Quantity Discount → Safety Stock → ROP → Holding Cost.

Sub section 2.0

Here are the complete solutions and explanatory notes for your Mid-Sem Examination in Materials Management (PEMP-4001).

SECTION A: Multiple Choice Questions

1. The main objective of Materials Management is to:

Correct Answer: b) Ensure the right material at the right time and cost
Key Concept: Materials Management focuses on the "5 Rights": Right Quality, Right Quantity, Right Time, Right Price, and Right Source.

2. EOQ stands for:

Correct Answer: a) Economic Order Quantity
Key Concept: EOQ is the ideal order quantity that minimizes the total cost of ordering and holding inventory.

3. ABC analysis is based mainly on:

Correct Answer: b) Annual consumption value
Key Concept: It follows Pareto's 80/20 Rule, categorizing inventory items based on their annual financial usage value (\text{Annual Usage} \times \text{Unit Cost}).

4. The point at which a new order should be placed is called:

Correct Answer: b) Reorder level
Key Concept: The Reorder Level (ROL) triggers a purchase requisition to replenish stock before running into a shortage.

5. Which of the following is a function of Materials Management?

Correct Answer: d) All of the above
Key Concept: Materials Management oversees the end-to-end material flow, including procurement (purchasing), tracking/monitoring (inventory control), and warehousing (stores management).

SECTION B: Short Answer Type Questions

6. Definition and Objectives of Materials Management

Materials Management is an integrated management approach responsible for planning, acquiring, storing, moving, and controlling materials to ensure optimal production flow at minimal cost.

Main Objectives:

Cost Reduction: Minimizing overall material costs through effective purchasing and low inventory holding costs.
Uninterrupted Production: Ensuring materials are available on time so manufacturing line stoppages do not occur.
Inventory Optimization: Balancing stock levels to avoid overstocking (capital tie-up) or stockouts.
Quality Maintenance: Procuring raw materials that meet strict quality specifications.
High Inventory Turnover: Increasing the turnover ratio to maximize capital efficiency.

7. ABC Analysis and Classification

Category A: High-value items requiring strict inventory control, tight safety stocks, and frequent monitoring by top management.
Category B: Moderate-value items requiring intermediate control, periodic ordering, and moderate safety stocks.
Category C: Low-value items managed with simple, decentralized controls, bulk ordering, and minimum monitoring effort.

8. Reorder Level (ROL) and Influencing Factors

Factors Affecting Determination of ROL:

Lead Time: The total time taken between placing an order and receiving the goods. Longer lead time requires a higher ROL.
Rate of Consumption: How quickly raw materials are consumed on the shop floor per day/week.
Safety Stock (Buffer Stock): Reserve stock kept to cushion against demand spikes or supplier delays.
Supplier Reliability: Dependability of suppliers regarding delivery schedules and quality compliance.

SECTION C: Long Answer Type Questions & Calculations

9. Core Functions of Materials Management

Purchasing (Procurement):

Vendor selection, price negotiation, issuing Purchase Orders (PO), and establishing long-term contract agreements.

Receiving & Inspection:

Receiving: Verification of incoming goods against Delivery Challans/POs, unloading, and logging inbound register entries.
Inspection: Quality assurance check against technical specifications before accepting delivery into main storage.

Storage & Stores Management:

Safe warehousing, bin card updates, preventing damage/pilferage, and maintaining layout for easy retrieval.

Inventory Control:

Setting stock levels (Max, Min, ROL), conducting periodic stock auditing, and optimizing holding vs. ordering costs.

Material Handling:

Moving items efficiently within the shop floor using forklifts, overhead cranes, or conveyer belts to minimize internal transit time and damage.

10. Key Inventory Control Techniques

EOQ (Economic Order Quantity): Mathematical model to determine optimal batch size by minimizing total holding and ordering costs.
ABC Analysis (Value-based): Prioritizes control focus based on monetary usage (A > B > C).
VED Analysis (Vital, Essential, Desirable): Categorizes spare parts based on criticality to production failure:
- Vital (V): Absence stops production immediately. Must always be stocked.
- Essential (E): Absence leads to operational inefficiency or minor downtime.
- Desirable (D): Non-availability does not affect immediate operations.
FSN Analysis (Fast, Slow, Non-moving): Categorizes items by movement rate/turnover frequency to clear dead stock.
Just-in-Time (JIT): Japanese inventory philosophy (Toyota Production System) aiming to eliminate inventory by receiving materials only when needed in production.

11. Step-by-Step Calculation: EOQ Problem

Given Data:

Annual Demand (D): 12{,}000\text{ units/year}
Ordering Cost (S): ₹300\text{ per order}
Annual Carrying Cost (H): ₹26\text{ per unit/year}
Working Days per Year: 360\text{ days}

Step 1: Calculate Economic Order Quantity (EOQ)

Step 2: Calculate Number of Orders per Year (N)

N = \frac{D}{\text{EOQ}} N = \frac{12000}{526.235} \approx 22.80\text{ orders/year}
Rounding to practical order frequency yields 22.8\text{ orders} (or \approx 23\text{ orders}).

Step 3: Calculate Time Between Two Consecutive Orders (T)

T = \frac{\text{Working Days per Year}}{N} T = \frac{360}{22.80} \approx 15.789\text{ days}

Final Exam Summary Table for Q11

Example 1: EOQ with Quantity Discounts

D = Annual Demand
C = Unit Purchase Price
S = Cost per Order
H = Holding/Carrying Cost per unit per year (often expressed as a percentage I of unit price C, so H = I \times C)
Q = Order Quantity

Problem Statement

A manufacturing firm has an annual requirement of 10,000 units of a raw material.

Ordering cost per order (S) = ₹500
Base unit purchase price (C) = ₹100
Inventory carrying cost rate (I) = 20% per year (0.20 \times C)

The supplier offers the following price discount schedule:

Tier 1 (0 \le Q < 2,000): No discount (C_1 = ₹100)
Tier 2 (Q \ge 2,000): 5% discount on all units (C_2 = ₹95)

Determine the most economical order quantity.

Step-by-Step Solution

Step 1: Calculate the standard EOQ for Tier 1 (No Discount)

Step 2: Calculate Total Annual Cost for Option 1 (Q = 707\text{ units})

\text{TC}_1 = (10000 \times 100) + \left(\frac{10000}{707.1} \times 500\right) + \left(\frac{707.1}{2} \times 20\right) \text{TC}_1 = 1,000,000 + 7,071.07 + 7,071.00 = \mathbf{₹1,014,142.07}

Step 3: Check the Discount Threshold (Tier 2: Q = 2,000\text{ units})

Step 4: Calculate Total Annual Cost for Option 2 (Q = 2,000\text{ units})

\text{TC}_2 = (10000 \times 95) + \left(\frac{10000}{2000} \times 500\right) + \left(\frac{2000}{2} \times 19\right) \text{TC}_2 = 950,000 + 2,500 + 19,000 = \mathbf{₹971,500.00}

Step 5: Cost Comparison & Final Recommendation

Annual Savings: ₹1,014,142.07 - ₹971,500.00 = \mathbf{₹42,642.07}
Verdict: The company should accept the discount and order 2,000 units per batch, despite the higher inventory holding cost, because the purchase price savings far outweigh the additional holding cost.

Example 2: EOQ with Safety Stock & Reorder Point (ROP)

When demand during lead time varies or lead time itself fluctuates, safety stock is added to prevent stockouts.

Relevant Formulas:

Safety Stock (SS): \text{SS} = (d_{\text{max}} \times L_{\text{max}}) - (d_{\text{avg}} \times L_{\text{avg}}) (Or using standard deviation under probabilistic demand: \text{SS} = Z \times \sigma_L)
Reorder Point (ROP): \text{ROP} = (d_{\text{avg}} \times L_{\text{avg}}) + \text{SS}
Average Inventory with Safety Stock: \text{Average Inventory} = \frac{\text{EOQ}}{2} + \text{SS}

Problem Statement

A firm operates 300 working days a year and consumes an annual total of 6,000 units of a critical spare part.

Ordering cost per order (S) = ₹400
Annual carrying cost per unit (H) = ₹12
Average lead time (L_{\text{avg}}) = 6 days
Maximum lead time (L_{\text{max}}) = 10 days
Average daily usage (d_{\text{avg}}) = \frac{6000}{300} = 20 units/day
Maximum daily usage (d_{\text{max}}) = 30 units/day

Calculate:

Economic Order Quantity (EOQ)
Safety Stock (SS) required
Reorder Point (ROP)
Total Annual Inventory Holding Cost (including safety stock)

Step-by-Step Solution

Step 1: Calculate EOQ

\text{EOQ} = \sqrt{\frac{2 \cdot D \cdot S}{H}} = \sqrt{\frac{2 \times 6000 \times 400}{12}} = \sqrt{\frac{4800000}{12}} = \sqrt{400000} = \mathbf{2,000\text{ units}}

Step 2: Calculate Safety Stock (SS)

Step 3: Calculate Reorder Point (ROP)

Step 4: Calculate Total Annual Carrying Cost

Key Takeaways for Examinations

Question 1: Multiple Choice Questions

A) Linear programming is a

Answer: (d) all of the above
Explanation: Linear Programming (LP) is a mathematical technique used for the economic allocation of limited resources to achieve optimization (maximizing profit or minimizing cost) under given constraints.

B) While solving a LP model graphically, the area bounded by the constraints is called

Answer: (a) feasible region
Explanation: The feasible region is the set of all possible points (solutions) that satisfy all given constraints simultaneously in a graphical linear programming problem.

C) Branch and Bound method divides the feasible solution space into smaller parts by

Answer: (a) branching
Explanation: The process of dividing the feasible region into smaller sub-problems is known as branching. Bounding is used to calculate upper/lower limits to eliminate non-optimal sub-problems.

D) The solution to a transportation problem with m-rows (supplies) and n-columns (destinations) is feasible if number of positive allocations are

Answer: (c) m+n-1
Explanation: A non-degenerate feasible solution to an m \times n transportation problem must have exactly m + n - 1 independent allocations (occupied cells).

Question 2: Trans-shipment Problem

1. Problem Formulation

In a trans-shipment problem with m sources and n destinations, every point (factories and retail stores) can act as both a supply node and a demand node.

Let the total buffer quantity be B = \text{Total Supply} = 200 + 300 = 500 units.

Nodes: Factories (X, Y), Retail Stores (A, B, C) — total 5 nodes.
Effective Supply (S_i):
- Factory X: 200 + B = 700
- Factory Y: 300 + B = 800
- Store A: 0 + B = 500
- Store B: 0 + B = 500
- Store C: 0 + B = 500
Effective Demand (D_j):
- Factory X: 0 + B = 500
- Factory Y: 0 + B = 500
- Store A: 100 + B = 600
- Store B: 150 + B = 650
- Store C: 250 + B = 750

Cost Matrix Table (with Buffer Quantities)

From \ To
X
Y
A
B
C
Supply (S_i)

Factory X
0
8
7
8
9
700

Factory Y
6
0
5
4
3
800

Store A
7
2
0
5
1
500

Store B
1
5
1
0
4
500

Store C
8
9
7
8
0
500

Demand (D_j)
500
500
600
650
750
3000

2. Initial Feasible Solution (Vogel's Approximation Method / Minimum Cost Allocation)

Allocating units using minimum cost paths and shortest trans-shipment paths:

Direct vs Trans-shipment Cost Analysis:

X \to A: Direct cost = 7. Trans-shipment via B: X \to B \to A = 8 + 1 = 9. Direct is optimal (7).
X \to B: Direct cost = 8.
X \to C: Direct cost = 9. Trans-shipment via A: X \to A \to C = 7 + 1 = 8. (Cheaper via A)
Y \to A: Direct cost = 5.
Y \to B: Direct cost = 4.
Y \to C: Direct cost = 3.

Allocations:

Allocate 500 units on self-trans-shipment diagonals (X,X), (Y,Y), (A,A), (B,B), (C,C) at 0 cost.
Remaining Net Supplies: Factory X = 200, Factory Y = 300.
Remaining Net Demands: Store A = 100, Store B = 150, Store C = 250.
Allocate 300 units from Factory Y:
- Y \to C: 250 units at cost ₹3
- Y \to B: 50 units at cost ₹4
Allocate 200 units from Factory X:
- X \to B: 100 units at cost ₹8
- X \to A: 100 units at cost ₹7

3. Optimal Shipping Schedule & Total Cost

Route
Units Shipped
Cost per Unit (₹)
Total Cost (₹)

Factory X \to Store A
100
7
700

Factory X \to Store B
100
8
800

Factory Y \to Store B
50
4
200

Factory Y \to Store C
250
3
750

Total Minimum Cost
₹ 2,450

Question 3: All-Integer Programming (Branch and Bound Method)

\text{Maximize } Z = 2x_1 + 3x_2
Subject to constraints:

6x_1 + 5x_2 \le 25
x_1 + 3x_2 \le 10
x_1, x_2 \ge 0 \text{ and integers}

Step 1: Solve Continuous LP Relaxation (Sub-problem \ P_0)

Convert inequalities to equalities to find intersection of boundaries:

Equation (1): 6x_1 + 5x_2 = 25
Equation (2): x_1 + 3x_2 = 10 \implies x_1 = 10 - 3x_2

Step 2: Branching Tree

                   [P0] Z = 11.92                     x1 = 1.92, x2 = 2.69                          /        \              x2 <= 2    /          \    x2 >= 3                        /            \                    [P1]              [P2]              Z = 11.0              Z = 10.0           x1 = 2.5, x2 = 2     x1 = 1.0, x2 = 3                /      \          (INTEGER SOLUTION)    x1 <= 2    /        \ x1 >= 3              /          \          [P3]            [P4]        Z = 10.0         Z = 9.8     x1=2, x2=2       x1=3, x2=1.4 (INTEGER SOLUTION)

Sub-problem P_1 (Add constraint x_2 \le 2):

From x_1 + 3x_2 \le 10 \implies with x_2 = 2, x_1 \le 4.
From 6x_1 + 5x_2 \le 25 \implies 6x_1 + 5(2) \le 25 \implies 6x_1 \le 15 \implies x_1 \le 2.5.
Max x_1 = 2.5, x_2 = 2 \implies Z_1 = 2(2.5) + 3(2) = 11.0.

Sub-problem P_2 (Add constraint x_2 \ge 3):

From x_1 + 3(3) \le 10 \implies x_1 \le 1.
Check 6(1) + 5(3) = 21 \le 25 (Valid).
Max x_1 = 1, x_2 = 3 \implies Z_2 = 2(1) + 3(3) = 10.0.
This is an Integer Feasible Solution with Z = 10.0.

Branching further on P_1 (Branch on x_1: x_1 \le 2 and x_1 \ge 3):

Sub-problem P_3 (x_1 \le 2, x_2 \le 2):
- Best integer values: x_1 = 2, x_2 = 2.
- Check constraints: 6(2)+5(2) = 22 \le 25 and 2+3(2)=8 \le 10.
- Z_3 = 2(2) + 3(2) = 10.0 (Integer Solution).
Sub-problem P_4 (x_1 \ge 3, x_2 \le 2):
- From 6(3) + 5x_2 \le 25 \implies 5x_2 \le 7 \implies x_2 \le 1.4.
- Max x_1 = 3, x_2 = 1.4 \implies Z_4 = 2(3) + 3(1.4) = 9.8 (Lower than current best integer solution Z = 10.0, so prune).

Optimal Integer Solution

There are two alternative optimal integer solutions:

x_1 = 1, x_2 = 3 with Maximum Z = 10
x_1 = 2, x_2 = 2 with Maximum Z = 10

Question 4: Queuing Model (M/M/1)

Given Data

Service Rate (\mu): Average repair time = 30\text{ minutes} = 0.5\text{ hours}. \mu = \frac{1}{0.5} = 2 \text{ jobs/hour}
Arrival Rate (\lambda): 10 sets per 8-hour day. \lambda = \frac{10}{8} = 1.25 \text{ jobs/hour}

Part 1: Expected Idle Time Each Day

Traffic Intensity / Utilization Factor (\rho): \rho = \frac{\lambda}{\mu} = \frac{1.25}{2} = 0.625 \text{ (or } 62.5\%\text{)}
Proportion of Idle Time (P_0): P_0 = 1 - \rho = 1 - 0.625 = 0.375 \text{ (or } 37.5\%\text{)}
Expected Idle Time in an 8-Hour Day: \text{Idle Time} = 8 \text{ hours} \times 0.375 = 3 \text{ hours}

Part 2: Average Number of Jobs Ahead of a Just-Arrived Set

Expected Idle Time: 3 hours per day
Average Jobs Ahead: 1.04 jobs (or approximately 1 job)

Question 5: Goal Programming Model Formulation

1. Decision Variables

x_1: Number of units of Product A produced next week
x_2: Number of units of Product B produced next week

2. Deviational Variables

d_1^-, d_1^+: Under-achievement and over-achievement of the total profit goal (₹700)
d_2^-, d_2^+: Under-achievement and over-achievement of product A sales goal (5 units)
d_3^-, d_3^+: Under-achievement and over-achievement of product B sales goal (4 units)

3. Goal Constraints

Profit Goal: 100x_1 + 50x_2 + d_1^- - d_1^+ = 700
Sales Volume Goal for Product A: x_1 + d_2^- - d_2^+ = 5
Sales Volume Goal for Product B: x_2 + d_3^- - d_3^+ = 4

4. Objective Function

Question 6: Short Notes

a) Goal Programming

Goal Programming (GP) is an extension of Linear Programming designed to handle multiple, often conflicting operational goals simultaneously.

Key Concept: Instead of optimizing a single objective function (like maximizing total profit or minimizing total cost), Goal Programming seeks to minimize the unwanted deviations (d^- and d^+) from target goal levels.
Types:
1. Non-preemptive (Weighted) Goal Programming: All goals have assigned numerical weights reflecting their relative importance.
2. Preemptive (Lexicographic) Goal Programming: Goals are ranked in order of priority (P_1 > P_2 > P_3), and higher-priority goals must be satisfied before lower-priority goals are considered.

b) Difference between LPP & IPP

Feature
Linear Programming Problem (LPP)
Integer Programming Problem (IPP)

Variable Constraints
Decision variables can take any real continuous value (fractions/decimals allowed).
Decision variables are strictly restricted to integer values.

Feasible Region
Continuous convex region with infinite solution points.
Discrete set of points within the constrained region.

Solution Method
Simplex Method, Graphical Method.
Branch and Bound Method, Cutting Plane Method (Gomory's).

Computational Complexity
Solvable in polynomial time (relatively fast).
NP-hard problem; computationally expensive for large systems.

Practical Application
Blending problems, general resource allocation.
Capital budgeting, scheduling, project selection (yes/no decisions).

c) Reasons for Carrying Inventory

Maintaining inventory requires holding costs, but organizations hold inventory for strategic operational reasons:

Meeting Fluctuating Demand: Ensures continuous customer satisfaction by acting as a buffer against unexpected surges in market demand.
Protection Against Supply Delays: Mitigates risks associated with supplier lead-time variability, transportation delays, or material shortages.
Economies of Scale (Quantity Discounts): Allows firms to purchase raw materials in bulk, reducing unit purchasing costs and shipping expenses.
Decoupling Operations: Separates consecutive production processes so that a breakdown in one machine or station does not halt the entire manufacturing line.
Hedging Against Price Inflation: Helps hedge against anticipated increases in raw material prices or raw material scarcity in volatile markets

SECTION A

1. Multiple Choice Questions

1. The Sale of Goods Act is of:

Answer: (c) 1930
Explanation: The Sale of Goods Act in India was enacted on 1st July 1930, separating sales law from the Indian Contract Act, 1872.

2. Seller is a person who:

Answer: (a) Sells or agrees to sell
Explanation: As per Section 2(13) of the Sale of Goods Act, 1930, a seller is defined as a person who sells or agrees to sell goods.

3. A contract of indemnity is primarily a contract to:

Answer: (b) Compensate for loss
Explanation: As per Section 124 of the Indian Contract Act, 1872, a contract of indemnity is one by which one party promises to save the other from loss caused to him by the conduct of the promisor himself, or by the conduct of any other person.

4. Under Sale of Goods Act, goods refers to:

Answer: (c) Movable property
Explanation: Section 2(7) defines goods as every kind of movable property other than actionable claims and money.

5. A cheque is always drawn on a:

Answer: (b) Bank
Explanation: Under Section 6 of the Negotiable Instruments Act, 1881, a cheque is defined as a bill of exchange drawn on a specified banker and payable on demand.

SECTION B (Short Answer Questions)

6. Business Law, E-Contracts, and Digital Signatures

Business Law

E-Contracts (Electronic Contracts)

Digital Signatures

A digital signature is a mathematical scheme used to demonstrate the authenticity of digital messages or documents. Recognized under Section 3 of the Information Technology Act, 2000:

It uses asymmetric cryptosystems (a key pair consisting of a private key and a public key) to encrypt and verify signature data.
It ensures authentication (identifying the signatory), non-repudiation (the signatory cannot deny creating the signature), and data integrity (proving the document was not altered post-signing).

7. Essential Elements of a Valid Contract

Proper Offer and Acceptance: There must be at least two parties — one making a definite offer and another accepting it unconditionally.

Example: A offers to sell his car to B for ₹3,00,000, and B accepts the offer as is.

Intention to Create Legal Relations: The parties must intend to enter into a legally binding obligation. Social or domestic agreements are generally not contracts.

Example: A promises to take his spouse out for dinner; failure to do so does not give rise to legal action (Balfour v. Balfour).

Lawful Consideration: Consideration is quid pro quo ("something in return"). It must be real and lawful.

Example: A promises to deliver 100 bags of cement to B, and B promises to pay ₹35,000 upon delivery.

Capacity of Parties: Parties must be competent — major age (18+), of sound mind, and not disqualified by any law.

Example: A contract entered into by a 15-year-old minor is void ab initio (Mohori Bibee v. Dharmodas Ghose).

Free Consent: Consent must be given freely without Coercion (Sec 15), Undue Influence (Sec 16), Fraud (Sec 17), Misrepresentation (Sec 18), or Mistake (Sec 20).
Lawful Object: The purpose of the agreement must not be illegal, immoral, or opposed to public policy.

8. Personal Property and Its Types

Definition

Personal property (also called personalty or movable property) encompasses all property that is not real property (land, buildings, and permanent structures attached to the earth).

Types of Personal Property

                          PERSONAL PROPERTY                                      |              +-----------------------+-----------------------+              |                                               |      Tangible Personal                               Intangible Personal       Property (Chattels)                            Property (Choses in Action)              |                                               |      +-------+-------+                              +--------+--------+      |               |                              |                 |   Corpreal        Perishable                    Intellectual       Financial   Goods           Goods                         Property           Assets (Vehicles,      (Food items,                  (Patents,          (Shares, Machinery)       Crops)                        Trademarks)        Debts)

Tangible Personal Property (Corporeal Chattels):

Physical items that can be touched, moved, and felt.
Examples: Motor vehicles, machinery, laptops, furniture, raw materials.

Intangible Personal Property (Incorporeal Chattels / Choses in Action):

Property that represents value or rights but lacks physical substance.
Examples:
- Intellectual Property: Patents, copyrights, trademarks, design registrations.
- Financial Assets & Legal Claims: Shares, bonds, bank accounts, actionable claims, goodwill.

SECTION C (Long Answer Questions)

10. Classification of Contracts & Distinction between Agreements

Detailed Classification

By Validity / Enforceability:

Valid Contract: Meets all Section 10 criteria and is legally enforceable.
Void Agreement: Void ab initio (from the start); has no legal force (Sec 2(g)).
Voidable Contract: Enforceable at the option of one party (the aggrieved party) but not the other (Sec 2(i)).
Illegal Agreement: Forbidden by law or involves criminal activity.
Unenforceable Contract: Substantively valid but unenforceable due to a technical defect (e.g., lack of stamp, signature, or written form).

By Formation:

Express Contract: Terms stated orally or in writing.
Implied Contract: Formed by the conduct/action of parties (e.g., getting into a bus creates an implied contract to pay the fare).
Quasi-Contract: Imposed by law to prevent unjust enrichment, independent of party agreement (Sec 68-72).

By Performance:

Executed: Both parties have fulfilled their obligations.
Executory: Obligations remain to be performed in the future.

Comparative Analysis: Valid, Void, Voidable, Illegal & Unenforceable Agreements

Basis of Comparison
Valid Contract
Void Agreement
Voidable Contract
Illegal Agreement
Unenforceable Contract

11. Lien vs. Stoppage in Transit

Concept of Lien

Goods were sold without credit terms.
Goods were sold on credit, but the credit period has expired.
The buyer becomes insolvent.

Key Differences: Lien vs. Stoppage in Transit

               POSSESSION & TRANSIT STATUS                       [Seller's Custody]  =======>  [Carrier / Transit]  =======>  [Buyer's Custody]    |                 |           |                 |           |               |    +--- RIGHT OF ----+           +--- RIGHT OF ----+           +-- POSSESSION -+    |       LIEN      |           |    STOPPAGE     |           |   TRANSFERRED |    |   (Sec 47-49)   |           |    IN TRANSIT   |           |   (Lien Lost) |    |                 |           |   (Sec 50-52)   |           |               |

Parameter
Right of Lien (Sec 47–49)
Right of Stoppage in Transit (Sec 50–52)

Location / Possession of Goods
Goods are in the actual physical possession of the seller.
Goods have left the seller's possession and are with an independent carrier/middleman in transit.

Solvency of Buyer
Can be exercised whether the buyer is solvent or insolvent (e.g., expired credit term).
Can ONLY be exercised if the buyer has become insolvent.

Nature of Right
Right to retain possession.
Right to regain/resume possession.

Point of Commencement
Begins as soon as default occurs while goods are still held by the seller.
Begins after the seller delivers goods to a carrier and ends when the buyer takes delivery.

How Exercised
By simply refusing to hand over goods to the buyer.
By taking actual possession or giving notice to the carrier/bailee.

12. Partnership under the Indian Partnership Act, 1932

Formation of a Partnership

Essentials for Formation:

Contractual Relationship: Must arise from a contract, not from status or inheritance.
Two or More Persons: Minimum 2 members; maximum 50 (as per Companies Act 2013).
Business: Agreement must be to carry on a lawful business/trade.
Sharing of Profits: Agreement to share profits (and losses) of the business.

Mutual Agency: Business must be carried on by all or any of them acting for all (each partner is both principal and agent).

                PARTNERSHIP STRUCTURE (SEC 4)                                      |     +--------------------------------+--------------------------------+     |                                |                                | Contractual Origin            Mutual Agency                    Profit Sharing (Not by Status/Birth)    (Principal <---> Agent)              (Agreement required)

Rights of Partners (Sec 9–13)

Right to Take Part in Management: Right to participate in the conduct of the business (Sec 12(a)).
Right to be Consulted: Right to express opinions before business decisions are made (Sec 12(c)).
Right to Access Books: Right to inspect and copy any of the account books of the firm (Sec 12(d)).
Right to Share Profits: Right to share equally (or as agreed) in the profits generated (Sec 13(b)).
Right to Interest on Capital & Advances: Right to 6% per annum interest on advances made beyond capital contribution (Sec 13(d)).
Right to Indemnity: Right to be indemnified by the firm for liabilities incurred in the ordinary course of business (Sec 13(e)).

Liabilities of Partners (Sec 25–27)

Unlimited Joint & Several Liability: Every partner is jointly and severally liable for all acts of the firm done while they are a partner (Sec 25).
Liability for Wrongful Acts / Torts: Firm and partners are liable for loss or injury caused to third parties due to a partner's wrongful act in the ordinary course of business (Sec 26).
Liability for Misapplication of Money: If a partner receives third-party funds and misapplies them, the firm is liable to make good the loss (Sec 27).
Liability of Incoming and Outgoing Partners: An incoming partner is not liable for acts done before joining unless agreed upon; an outgoing partner remains liable for acts prior to retirement until public notice is given.

Question 1: Multiple Choice Questions

a) Ergonomics primarily deals with:

Answer: ii) Fitting the workplace and system to human capabilities
Explanation: Ergonomics (or Human Factors Engineering) is derived from the Greek words ergon (work) and nomos (natural laws). Its fundamental goal is to design tasks, tools, systems, and environments so that they fit the physiological, biomechanical, and psychological limits of human operators ("fitting the task to the human", rather than forcing the human to fit the task).

b) Which of the following is an anthropometric consideration in workplace design?

Answer: iii) Body dimensions of the worker
Explanation: Anthropometry is the branch of ergonomics dealing with physical measurements of the human body (e.g., reach envelope, eye height, elbow height, sitting popliteal height). Temperature, humidity, and illumination fall under environmental ergonomics.

c) The principle of motion economy aims primarily at:

Answer: ii) Minimizing fatigue and improving efficiency
Explanation: Developed by Frank and Lillian Gilbreth and refined by Ralph M. Barnes, motion economy principles aim to eliminate redundant or awkward movements, utilize natural body rhythms, and reduce physiological weariness while maximizing productive output.

d) Biodynamic analysis is mainly concerned with:

Answer: ii) Human response to mechanical forces, vibration and motion
Explanation: Biodynamics studies how physical energy, impact, shock waves, whole-body vibration (WBV), and hand-arm vibration (HAV) interact with human musculoskeletal structures and internal organs.

Question 2: Short Notes (Any Four)

a) Ergonomics

Ergonomics is an interdisciplinary field combining engineering, anatomy, physiology, and psychology.

Core Domains: Physical (posture, materials handling, repetitive strain), Cognitive (mental workload, decision-making, human-computer interaction), and Organizational (work-rest cycles, shift schedules).
Objective: Enhance human safety, operational comfort, and system effectiveness while eliminating occupational hazards like Musculoskeletal Disorders (MSDs).

b) Man-Machine Symbiosis

Man-Machine Symbiosis refers to a cooperative partnership where humans and machines perform complementary functions based on their inherent strengths (often categorized using Fitts' List):

Domain
Human Strengths
Machine Strengths

Cognition & Sensing
Pattern recognition, inductive reasoning, handling unexpected anomalies.
High-speed repetitive computation, quantitative calculations.

Physical Output
Precise fine-motor micro-adjustments.
Continuous heavy force exertion without physical fatigue.

In modern manufacturing (e.g., Collaborative Robots / Cobots), the human provides cognitive control and qualitative decision-making, while the machine handles high-force lifting and precise cyclic tasks.

c) Information Input and Processing

Information input and processing models explain how operators process environmental cues to take physical action:
\text{Sensory Input (Visual/Auditory)} \longrightarrow \text{Perceptive Filtering} \longrightarrow \text{Cognitive Processing (Memory \& Decision)} \longrightarrow \text{Motor Response Output}

Information Channel Limit: Human short-term cognitive memory can process approximately 7 \pm 2 chunks of information at a time (Miller's Law).
Key Design Takeaway: To prevent cognitive overload, control panels and visual displays must present structured, unambiguous signals with low visual noise.

e) Principles of Motion Economy

Rules used to optimize manual assembly tasks, categorized into three operational areas:
PRINCIPLES OF MOTION ECONOMY | +-------------------------+-------------------------+ | | | Use of Human Body Workplace Arrangement Design of Tools & Equipment (Symmetrical, continuous (Fixed bins within reach (Combine tools, ratchets, curved arm motions) envelope, gravity feed) handles matching palm)

Use of the Human Body: Both hands should begin and end movements simultaneously; arm motions should be continuous, smooth, and curved rather than straight-line with abrupt directional changes.
Workplace Arrangement: Materials and tools should be positioned in a fixed zone within the primary reach envelope.
Design of Tools & Equipment: Multi-functional tools should be used where possible, and loads should be relieved by levers, foot pedals, or mechanical fixtures.

f) Anthropometric Condition

Anthropometric conditions refer to the statistical variations in human body dimensions across target populations.

Design applications use three fundamental statistical principles:

Design for Extreme Individuals:
- 95th Percentile Male: Doorway heights, clearance dimensions (ensures the largest people fit).
- 5th Percentile Female: Reach distances, control button layouts (ensures the shortest reach can operate).
Design for Adjustable Range: Seat heights, monitor stands (typically covers 5th to 95th percentile).
Design for Average (50th Percentile): Used only when adjustability is technically impractical (e.g., checkout counters, public benches).

Question 3: Long Answer Option (a) Workstation Ergonomic Case Study

1. Ergonomic Problems Identified in Existing Workstation

Non-Neutral Joint Postures (Awkward Bending): Frequent forward trunk flexion (>20^\circ) when lifting components from the floor increases compressive shear forces on the L_5/S_1 lumbar vertebrae, drastically elevating the risk of lower back injury (herniated discs).
Extended Reach Beyond Normal Envelope: Reaching beyond the primary reach zone (>40\text{ cm} from body) creates high mechanical torque around the shoulder joints, leading to rotator cuff strain and neck pain.
Repetitive Manual Material Handling: Constant bending and lifting without mechanical assistance causes local muscle fatigue, localized ischemia, and micro-trauma to soft tissues.
Adverse Thermal Environment: High ambient temperatures combined with high humidity restrict the body's natural evaporative cooling (sweating), raising the core body temperature and inducing thermal fatigue, increased cardiovascular strain, and reduced concentration.

2. Application of Anthropometric Principles to Workstation Redesign

                    REDESIGNED WORKSPACE LAYOUT +-----------------------------------------------------------------------+ |                                                                       | |   [ Tool Balancer ]        [ Vertical Gravity Bins ]                  | |          |                            |                               | |          v                            v                               | |    +------------+           +------------------+                      | |    | Assembly   |           |  Component Drop  |                      | |    | Jig Area   |           |  (Height Adjust) |                      | |    +------------+           +------------------+                      | |          ^                                                            | |          |                                                            | |     (Operator) ---> Footrest & Height-Adjustable Pneumatic Chair       | |                                                                       | +-----------------------------------------------------------------------+

Height-Adjustable Work Surface: Work table height should be adjustable between 850 mm to 1150 mm to accommodate standing/sitting work between the 5th percentile female and 95th percentile male. Elbow height serves as the key datum (work level 50–100 mm below elbow height for light assembly).
Elimination of Floor-Level Bending: Containers carrying parts must be elevated to a minimum height of 750 mm using hydraulic/pneumatic scissor-lift tables.
Reach Envelope Optimization:
- Primary Reach Zone (<25\text{ cm} radius): Frequently used assembly tools placed directly in front of the operator.
- Secondary Reach Zone (25\text{--}50\text{ cm} radius): Intermittently used component supply bins placed within normal arm extension without twisting the torso.

3. Principles of Motion Economy for Efficiency and Fatigue Reduction

Eliminate Floor Bending & Reaching: Supply component bins using inclined gravity-feed chutes so raw materials drop automatically close to the assembly point.
Symmetrical Symmetrical Two-Hand Motions: Structure assembly steps so both hands work simultaneously in opposite, symmetrical directions (reduces asymmetric muscular loading).
Drop Chutes and Foot Controls: Use gravity drop chutes for finished components so operators release finished parts without turning. Utilize foot-operated pneumatic clamps to free up hands.
Suspended Power Tools: Suspend heavy torque screwdrivers and assembly tools from overhead spring-tool balancers to eliminate holding weight.

4. Thermal & Environmental Effects on Performance

Heat Stress Mechanisms: High ambient temperatures paired with high relative humidity (>70%) prevent sweat evaporation. Core temperature increases, causing elevated cardiac strain (heart rate spikes to pump blood to skin capillaries for cooling rather than to working muscles).
Performance Impact:
- Physiological: Loss of electrolytes, dehydration, muscle cramps, physical exhaustion.
- Psychological: Cognitive impairment, slowed reaction times, increased visual error rate, irritability, and higher accident frequency.
Mitigation Strategies: Maintain Wet Bulb Globe Temperature (WBGT) index below 28^\circ\text{C} using localized spot-cooling air ducts, ambient HVAC conditioning, high-volume low-speed (HVLS) fans, scheduled work-rest cycles (e.g., 45 min work / 15 min rest in cool break areas), and accessible hydration stations.

5. Improved Workstation Layout Comparison

Parameter
Existing Workstation
Redesigned Ergonomic Workstation

Material Feeding
Parts stored on floor level in boxes.
Parts delivered via height-adjustable gravity chutes at waist level.

Work Height
Fixed height causing operator stooping.
Pneumatically adjustable table matching 5th–95th percentile elbow height.

Tool Handling
Tools picked up and laid down on bench manually.
Suspended overhead with tool balancers and ergonomic grips.

Environmental Control
Unconditioned, high humidity/heat environment.
Localized spot air-conditioning diffusers and forced air circulation.

Operator Posture
Severe trunk flexion and lateral twisting.
Neutral spinal alignment with dynamic sit-stand seating option.

Question 3: Long Answer Option (b) Human Factors in Design & Manufacturing

Overview

Human Factors Engineering ensures systems match human physical, perceptual, and cognitive capabilities. Integrating human factors prevents operator strain, lowers scrap rates, and minimizes industrial risks.
HUMAN FACTORS SYSTEM | +-----------------------------+-----------------------------+ | | | Cognitive Processing Physical Interactions Environmental Factors (Displays, Controls) (Tools, Motor Skills) (Microclimate, Vibration)

Core Ergonomic Factors & Industrial Implementation

1. Information Processing & Visual Display Design

Principles: Displays must present information intuitively without clutter. Use qualitative displays (e.g., color-coded red/yellow/green zones) for quick status checks and quantitative displays (digital readouts) for precise numerical parameters.
Industrial Example: Control room Human-Machine Interfaces (HMIs) in chemical plants group critical alarms using high-contrast color coding to prevent cognitive overload during emergency shutdowns.

2. Motor Skills & Human Control of Systems

Principles: Controls should match natural human expectations (Compatibility Principle). For instance, moving a lever forward or pushing a button in should turn a machine ON, while clockwise rotation should increase output. Controls must also incorporate tactile resistance to avoid accidental activation.
Industrial Example: CNC machine control consoles feature distinct button shapes (emergency stop is a prominent red mushroom head) and directionally consistent dual-hand control switches.

3. Ergonomic Hand Tools

Principles: Hand tools should keep the wrist in a neutral, straight position ("bend the tool, not the wrist"). Handles should feature pistol grips or contoured shapes that distribute force over the large palmar surface to prevent focal nerve compression (Carpal Tunnel Syndrome).
Industrial Example: Pistol-grip pneumatic assembly wrenches in automotive assembly lines ensure operators maintain a straight wrist alignment when securing vertical fasteners.

4. Environmental Conditions

Principles: Environmental factors like noise (target <85\text{ dBA} over an 8-hour TWA), illumination (500\text{--}1000\text{ lux} for precision assembly), and microclimate affect human alertness and precision.
Industrial Example: Quality inspection stations in electronic assembly plants use glare-free task lighting and sound-dampening acoustic enclosures to preserve concentration and visual accuracy.

5. Biodynamic Considerations (Vibration & Shock)

Principles: Exposure to whole-body vibration (WBV) from industrial vehicles leads to chronic spinal degeneration, while hand-arm vibration (HAV) from grinding tools causes vibration white finger (VWF) syndrome.
Industrial Example: Heavy equipment like forklift trucks incorporate air-suspended operator seats with built-in dampers to isolate low-frequency vibration (1\text{--}20\text{ Hz}). Grinding tools utilize anti-vibration rubber handles and dampened drive couplings.

Sunday, 30 August 2026

2nd mead term PEM in JUT 2026

TABLE OF CONTENTS | विषय सूची

PART I — MATERIALS MANAGEMENT | सामग्री प्रबंधन

1.1 Definition & the 5 Rights | परिभाषा एवं पाँच अधिकार

1.2 Objectives of Materials Management

1.3 Core Functions — Mnemonic P-R-S-I-H

1.4 Inventory Control Techniques — Overview

ABC Analysis — Classification (Pareto 80/20 Rule)

VED Analysis — Criticality

1.5 Reorder Level (ROL) / Reorder Point (ROP)

1.6 EOQ — Core Formula and Solved Numerical

1.7 Worked Example — EOQ with Safety Stock & ROP

1.8 Worked Example — EOQ with Quantity Discount

1.9 Reasons for Carrying Inventory

1.10 Materials Management — Formula Sheet

1.11 Section A — Multiple Choice Questions (Materials Management)

PART II — OPERATIONS RESEARCH & QUANTITATIVE TECHNIQUES | संक्रिया अनुसंधान

2.1 Section A — Multiple Choice Questions

2.2 Transshipment Problem — Full Solution

Cost Matrix (with buffer-adjusted supply/demand)

Optimal Shipping Schedule

2.3 Integer Programming — Branch & Bound Method

Step 1 — Continuous LP Relaxation (P₀)

Step 2 — Branch Tree (corrected)

2.4 Queuing Model — M/M/1 (Single Server)

2.5 Goal Programming — Model Formulation

2.6 Short Notes

(a) Goal Programming

(b) LPP vs. IPP

2.7 Operations Research — Formula Sheet

PART III — BUSINESS LAW | वाणिज्यिक विधि

3.1 Section A — Multiple Choice Questions

3.2 Business Law, E-Contracts & Digital Signatures

E-Contracts

Digital Signatures

3.3 Essential Elements of a Valid Contract — Sec. 10, Indian Contract Act 1872

3.4 Classification of Contracts

By Validity

By Formation & By Performance

3.5 Rights of an Unpaid Seller: Lien vs. Stoppage in Transit

3.6 Partnership — Indian Partnership Act, 1932

Essential Elements

Rights of Partners (Sec. 9–13)

Liabilities of Partners (Sec. 25–27, 31)

3.7 Landmark Cases — Quick Reference

3.8 Important Sections — Fast Reference

PART IV — ERGONOMICS & HUMAN FACTORS ENGINEERING | श्रम-विज्ञान

4.1 Section A — Multiple Choice Questions

4.2 Core Concepts — Short Notes

(a) Ergonomics

(b) Man–Machine Symbiosis

(c) Information Input & Processing

(d) Principles of Motion Economy (Gilbreth / Barnes)

(e) Anthropometric Design Strategies

4.3 Long Answer (A) — Ergonomic Workstation Case Study

Problems Identified in the Existing Workstation

Anthropometric Redesign

Motion-Economy Redesign

Thermal / Environmental Control

Before / After Comparison

4.4 Long Answer (B) — Human Factors in Design & Manufacturing

Effects of Whole-Body vs Hand-Arm Vibration

4.5 Ergonomics — Relationship & Formula Box

4.6 Final Revision Mnemonics

Materials Management — Mid-Sem Final Revision Notes

1. Materials Management

5 Rights of Materials Management

Main Objectives

2. Important Inventory Techniques

ABC Classification

3. EOQ — Most Important Numerical

Formula

Given

Answer

Number of Orders

Time Between Orders

Final Answer

4. Reorder Level / Reorder Point

Basic Formula