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Unit 1 of 4 · MBA Sem 3

Unit 1: Introduction to operations research

Operation Research Applications notes · PTU syllabus (MBA 952-18)

3 min read6 topics10 exam questions
On this page
  1. Unit summary
  2. Origin and historical development of OR
  3. Managerial applications of optimisation
  4. Classical and advanced optimisation techniques
  5. General approach to solving OR problems
  6. Classification of mathematical models
  7. Decision-making environments
  8. Key terms
  9. Quick revision
  10. Important questions

Unit summary

Operations research gives managers mathematical tools to find the best decision under constraints. This unit covers the historical development and origin of OR, managerial applications of optimisation, classical and advanced optimisation techniques, the general approach to solving OR problems, the classification of mathematical models and decision-making environments.

After this unit you can

  • Trace the origin and development of OR
  • Explain managerial applications of optimisation
  • Distinguish classical and advanced optimisation techniques
  • Classify OR models and decision-making environments

PTU syllabus topics

  • Historical development
  • managerial applications of optimization
  • classical and advanced optimization techniques
  • origin of OR
  • general approach for solving OR problems
  • classification of mathematical models and decision-making environments
ProcessThe OR approach
  1. 1

    Formulate the problem

  2. 2

    Build a mathematical model

  3. 3

    Collect data

  4. 4

    Solve the model

  5. 5

    Validate the solution

  6. 6

    Implement and monitor

1

Topic 1

Origin and historical development of OR

Operations research is the application of scientific methods, techniques and tools to problems involving the operations of systems, to provide optimal solutions (Churchman, Ackoff and Arnoff). Evolution: began in Britain during World War II for radar deployment and convoy routing; after the war it spread to industry and government.

ProcessThe OR approach
  1. 1Formulate the problem
  2. 2Build a mathematical model
  3. 3Derive a solution
  4. 4Test the model and solution
  5. 5Implement and control

Techniques: linear programming, transportation and assignment, game theory, sequencing, queuing, inventory models, PERT/CPM, simulation and decision theory. Applications: production planning, product mix, distribution, scheduling, finance and marketing.

ProcessMilestones in OR
  1. 1

    1930s–1945

    British and US military OR teams — radar, convoys, bombing (Blackett's circus)

  2. 2

    1947

    George Dantzig develops the simplex method

  3. 3

    1950s

    Game theory, dynamic programming (Bellman), queuing and inventory models spread to industry

  4. 4

    1958

    PERT (US Navy, Polaris) and CPM (DuPont)

  5. 5

    1960s–80s

    Computers enable large models; integer and network programming

  6. 6

    1990s onward

    Supply chain optimisation, metaheuristics, analytics and AI-based optimisation

2

Topic 2

Managerial applications of optimisation

AreaOptimisation application
ProductionProduct mix, blending, scheduling, capacity planning
LogisticsTransportation, vehicle routing, warehouse location
FinancePortfolio selection, capital budgeting, cash management
MarketingMedia selection, sales territory allocation, pricing
HRStaff scheduling, assignment of people to jobs
ProjectsScheduling with PERT and CPM, crashing
ServicesQueue management in banks, hospitals, call centres

Example

Indian Railways and airlines use optimisation models for crew and fleet scheduling; quick-commerce firms use routing models to deliver within minutes.

3

Topic 3

Classical and advanced optimisation techniques

ComparisonOptimisation techniques
Classical
Advanced

Basis

Differential calculus

Mathematical programming and computing

Methods

Unconstrained maxima and minima, Lagrange multipliers for equality constraints

Linear, integer, non-linear, dynamic and goal programming; network models; heuristics and metaheuristics (genetic algorithms, simulated annealing)

Problems suited

Smooth continuous functions, few variables

Large problems with many variables and inequality constraints

Limitation

Cannot handle inequality constraints easily

May need software; heuristics give near-optimal solutions

4

Topic 4

General approach to solving OR problems

Operations research (OR) is the application of scientific methods, techniques and tools to problems involving the operations of a system so as to provide those in control with optimum solutions (Churchman, Ackoff and Arnoff). It originated in military operations during World War II.

ProcessPhases of OR
  1. 1

    Formulate the problem

  2. 2

    Construct a mathematical model

  3. 3

    Derive a solution

  4. 4

    Test the model and solution

  5. 5

    Establish controls

  6. 6

    Implement

  • Scope: production planning, inventory, transportation and logistics, finance (portfolio), marketing (media selection), HR (assignment), project scheduling.
  • Objectives: optimise (maximise profit or minimise cost) under constraints; improve decision quality.
  • Limitations: models simplify reality; data may be unavailable; costly; managers may not understand models; non-quantifiable factors ignored.
5

Topic 5

Classification of mathematical models

ClassificationClassification of OR models
OR models

  • By structure

    Iconic (scale models), analogue (graphs, flow charts), symbolic (mathematical equations)

  • By purpose

    Descriptive (queuing, simulation), predictive, prescriptive or optimisation (LP)

  • By certainty

    Deterministic (LP, EOQ) and probabilistic or stochastic (queuing, PERT)

  • By time

    Static (single period) and dynamic (multi-period)

  • By method of solution

    Analytical (exact formulas) and simulation (experiments on models)

6

Topic 6

Decision-making environments

ComparisonDecision environments
Knowledge of outcomes
Typical tools

Certainty

Outcome of each action is known

Linear programming, transportation, assignment

Risk

Probabilities of outcomes are known

Expected monetary value, decision trees, PERT

Uncertainty

Probabilities unknown

Maximin, maximax, minimax regret, Hurwicz, Laplace criteria

Conflict

Outcome depends on an opponent's choices

Game theory

Key terms

Operations research
Scientific approach to optimal decisions in systems
Symbolic model
Model expressed in mathematical equations
Deterministic model
Model in which all values are known with certainty
Metaheuristic
General search strategy giving near-optimal solutions
Decision under risk
Decision where outcome probabilities are known

Quick revision

  • Origin in World War II; Dantzig's simplex (1947); PERT and CPM (1958).
  • Applications in production, logistics, finance, marketing, HR, projects, services.
  • Classical (calculus, Lagrange) vs advanced (LP, IP, NLP, DP, heuristics).
  • Phases: formulate, model, solve, test, control, implement.
  • Models: iconic, analogue, symbolic; deterministic vs probabilistic; environments: certainty, risk, uncertainty, conflict.

Important exam questions

Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).

Short-answer questions

  1. Q1.Define operations research.
  2. Q2.Who developed the simplex method and when?
  3. Q3.Distinguish classical and advanced optimisation techniques.
  4. Q4.What is a symbolic model?
  5. Q5.Distinguish deterministic and probabilistic models.
  6. Q6.Distinguish decision-making under risk and under uncertainty.

Long-answer questions

  1. Q1.Trace the origin and development of operations research.
  2. Q2.Discuss managerial applications of optimisation.
  3. Q3.Explain the general approach to solving OR problems.
  4. Q4.Explain the classification of OR models and decision-making environments.

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