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Useful for CSIR NET · ASRB NET · ISS

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  1. Welcome
  2. Course Outcomes
  3. Units in this Course
  4. Recommended Textbooks

Welcome

This is the complete study package for Operations Research — the science of optimal decision-making using mathematical models. The course covers Linear Programming Problems (LPP) from formulation through graphical, simplex, Big-M, two-phase and dual-simplex methods, and concludes with the powerful theory of duality. Each topic has two worked examples.

Pre-requisite: Courses 1–11. Strong comfort with linear algebra (matrix operations, systems of linear equations) and basic calculus is essential.

Course Outcomes

  1. Know the scope and applications of Operations Research.
  2. Link OR techniques with business, industry and life sciences.
  3. Convert real-life problems into mathematical models.
  4. Find optimal solutions to LPPs in different scenarios.
  5. Develop logical thinking to solve optimisation problems.

Units in this Course

UNIT 1

Introduction & LPP Formulation

Origin and development of OR, scientific method, modelling, advantages & limitations; introduction to LPP and mathematical formulation with illustrative problems.

UNIT 2

Graphical Method

Graphical solution for max & min objectives up to 3 variables; convex / non-convex hull; alternative, unbounded and infeasible solutions.

UNIT 3

Simplex Method

General LPP, matrix form, slack & surplus variables, standard & canonical forms; basic feasible solution; simplex algorithm for max and min problems.

UNIT 4

Big-M & Two-Phase Methods

Artificial variable techniques — Big-M penalty method, Two-Phase simplex; degeneracy & how to resolve it; special cases via simplex; solving simultaneous equations.

UNIT 5

Duality & Dual Simplex

Concept of duality, primal-dual conversion rules, relation between primal and dual solutions; solving primal via dual; the dual simplex method.

PRACTICAL

Practical Course (7 Experiments)

Worked LPP labs: graphical method, simplex, Big-M, Two-Phase, special cases, primal-dual, dual simplex.

REFERENCE

Official Syllabus

Course outline, textbooks, references and exam blueprint.

Next course in learning order: Optimization Techniques Applied statistics