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Study notes

Qwestrum Engineering360 · Industrial & Production · Operations Research

Transportation and Assignment Models

Transportation and assignment models allocate resources to destinations at minimum total cost.

Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

Dummy row/column balances unbalanced problem
Degeneracy in transportation basic cells
Assignment one-to-one allocation

Topic details

Introduction

These models are standard in B.Tech OR papers because they connect directly with plant-to-warehouse and machine-to-job allocation. Chase and Buffa present them as practical special LP structures.

Key relations & formulas

Formulas (Indian textbook notation)

$balanced transport: Σ supply = Σ demand$

Formulas (Indian textbook notation)

$VAM, MODI for initial feasible solution$

Formulas (Indian textbook notation)

$assignment: n jobs, n workers - Hungarian O(n^{3})$

Notation and sign conventions

Relation 1 —

balanced transport: Σ supply = Σ demand

Formulas (Indian textbook notation)

$balanced transport: Σ supply = Σ demand$

Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

VAM, MODI for initial feasible solution

Formulas (Indian textbook notation)

$VAM, MODI for initial feasible solution$

Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

assignment: n jobs, n workers - Hungarian O

Formulas (Indian textbook notation)

$assignment: n jobs, n workers - Hungarian O(n^{3})$

Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Transportation uses m+n-1 basic allocations in a balanced case and improves via MODI stepping-stone logic. Assignment is a one-to-one restricted transportation problem solved efficiently by Hungarian method. Groover production systems examples often include multi-plant shipping and labour assignment cases.

Assumptions and validity limits

State assumptions explicitly before using any relation for transportation and assignment models — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Operations Research viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Operations Research papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to transportation and assignment models.
4. Use equation 1:

balanced transport: Σ supply = Σ demand

.
5. Use equation 2:

VAM, MODI for initial feasible solution

.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Transportation and Assignment Models appears in logistics and planning. In Indian industrial curricula this topic is tested because it connects theory to mathematical decision models.

GATE and semester exams often combine transportation and assignment models with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use transportation and assignment models?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Typical mistakes: forgetting to add dummy source/destination for unbalanced data, and violating one-job-per-worker rule in assignment tables.

Quick revision checklist

Before attempting transportation and assignment models problems, confirm you can:

1. Dummy row/column balances unbalanced problem
2. Degeneracy in transportation basic cells
3. Assignment one-to-one allocation

Revise the solved examples in Operations Research — Hamdy Taha and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Balance check in transportation

Problem

Total supply is 120 units and total demand is 140 units. What preprocessing is needed before VAM?

Solution

Because demand exceeds supply by 20, add a dummy source with supply 20 and zero/penalty costs as instructed. Then solve the balanced table using VAM/MODI.

Conceptual check — Transportation and Assignment Models

Problem

In a Operations Research semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of transportation and assignment models." What should a complete answer include?

📖 Standard books (India)

Operations Research — Hamdy Taha
Read: Syllabus unit
LP, transportation, and simulation

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