Operation Research Notes
Subject Overview
Operation Research is the final-semester quantitative decision-making paper — using mathematical models to solve real business optimisation problems. You'll cover linear programming (graphical and simplex methods), transportation and assignment problems, decision-making under uncertainty and game theory, then queuing theory and network models (PERT/
Subject at a glance
4
Units
27
Topics
6
Credits
4
Infographics
Unit-wise Syllabus
4 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- Basic definitions
- scope
- objectives
- phases and limitations of operations research
- formulation and graphical solution of linear programming problems
- the Simplex method
- artificial variables
- Big-M method
- transportation problem
- assignment model
- Hungarian method
- travelling salesman problem
- 1Formulate the problem
- 2Build a model
Objective and constraints
- 3Solve
Find the optimal solution
- 4Test
Check the model against reality
- 5Implement
Apply and monitor
Study guide
Operations research uses mathematical models to make better decisions. You study its definition, scope, objectives, phases and limitations, formulating and solving linear programming problems graphically and with the Simplex method (including artificial variables and Big-M), the transportation problem, the assignment model and Hungarian method and the travelling salesman problem. Practise at least one LPP problem a day; it takes careful steps.
- Decision-making under uncertainty (maximin/minimax)
- decision trees
- game theory — solution of two-person zero-sum games
- introduction to deterministic and probabilistic dynamic programming
Maximax
Optimistic: best of the best
Maximin
Pessimistic: best of the worst
Minimax regret
Minimise the largest regret
Laplace
Treat all outcomes as equally likely
Study guide
This unit covers decision making under uncertainty (maximin and minimax), decision trees, game theory with the solution of two-person zero-sum games and an introduction to deterministic and probabilistic dynamic programming. Learn to find the saddle point of a game.
- Types of queuing situations
- queuing models with Poisson input and exponential service
- PERT and CPM
- construction of networks
- critical path identification
- slack and float
- crashing a network for cost reduction
Activity times
Three estimates (optimistic, likely, pessimistic)
One fixed estimate
Nature
Probabilistic
Deterministic
Focus
Time
Time and cost (crashing)
Used for
Research, new projects
Construction, repeat projects
Study guide
You study types of queuing situations, models with Poisson arrivals and exponential service times, PERT and CPM, network construction, critical path identification, slack and float and crashing a network to reduce cost. Practise finding the critical path and float on a network diagram.
- Replacement of items that deteriorate with time
- individual and group replacement policy for items that fail suddenly
- inventory costs
- deterministic demand models with uniform and non-uniform demand and finite/infinite production rates
EOQ
√(2DS / H)
D = demand, S = order cost, H = holding cost
Number of orders
D / EOQ
Total inventory cost
(D/Q)S + (Q/2)H
Replace when
Average annual cost is at its minimum
Study guide
The last unit covers replacement of items that deteriorate with time, group and individual replacement of items that fail suddenly, inventory costs and deterministic inventory models with uniform and non-uniform demand and finite and infinite production rates. Know the EOQ formula and its assumptions.
Why Operation Research Matters
Operations research drives decisions in logistics, production, scheduling and supply chains, and its techniques appear in management entrance exams and in analytics and operations roles.
How to Prepare for Operation Research
- Practise LPP, transportation and assignment problems with full step-by-step workings.
- Draw PERT/CPM networks neatly and mark the critical path.
- Memorise the EOQ formula and the steps of the Hungarian method.
Operation Research: Frequently Asked Questions
What is linear programming?
Linear programming is a method for finding the best outcome, such as maximum profit or minimum cost, in a mathematical model with linear constraints.
What is the difference between PERT and CPM?
CPM uses fixed, known activity times, while PERT uses probabilistic time estimates, and both identify the critical path of a project.