Operation Research Applications Notes
Subject Overview
The second Operations Management group elective, covering the historical development and modeling art of OR, linear programming and its applications, transportation/
Subject at a glance
4
Units
24
Topics
4
Credits
4
Infographics
Unit-wise Syllabus
4 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- 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
- 1
Formulate the problem
- 2
Build a mathematical model
- 3
Collect data
- 4
Solve the model
- 5
Validate the solution
- 6
Implement and monitor
Study guide
This unit covers the origins of OR, managerial applications, classical and advanced optimisation, the general approach and model classification. Identify OR problems in daily business.
- Formulation of linear mathematical models
- graphical and simplex techniques
- simplex algorithm and tableau construction
- minimization vs maximization
- Big-M and two-phase methods
- duality theory and sensitivity analysis
Objective
Maximise
Minimise (and vice versa)
Constraints
m constraints
m dual variables
Variables
n variables
n dual constraints
Optimal value
Max Z
Min W: equal at the optimum (Z* = W*)
Study guide
You study LP formulation, graphical and simplex methods, tableau, Big-M and two-phase methods, duality and sensitivity analysis. Solve a full simplex problem.
- Initial basic feasible solution methods
- optimization of transportation and assignment problems
- dynamic programming (deterministic and probabilistic)
- queuing theory — basic structure
- Poisson input and exponential service models
Utilisation
ρ = λ / μ
Average number in system
L = λ / (μ − λ)
Average time in system
W = 1 / (μ − λ)
Average queue length
Lq = λ² / [μ (μ − λ)]
Study guide
You study initial feasible solutions, optimising transportation and assignment, dynamic programming and queuing models. Solve one transportation problem with MODI.
- Shortest route and traveling salesman problems
- PERT and CPM
- network construction
- critical path identification
- slack and float
- crashing for cost reduction
- graphical illustration of non-linear programming problems
- 1Find the critical path
- 2List crash cost per day for critical activities
- 3Crash the cheapest activity by one day
- 4Recheck for new critical paths
- 5Stop when total cost starts rising
Or the deadline is met
Study guide
You study shortest route, travelling salesman, PERT and CPM, slack, float, crashing and non-linear programming. Find the critical path of a project.
Why Operation Research Applications Matters
OR techniques improve decisions on logistics, scheduling and resource allocation and feature in operations and analytics roles.
How to Prepare for Operation Research Applications
- Solve problems by hand and verify with Excel Solver.
- Draw network diagrams carefully.
- Interpret results in business terms.
Operation Research Applications: Frequently Asked Questions
What is sensitivity analysis?
Sensitivity analysis shows how changes in the inputs of an LP model affect the optimal solution.