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Introduction to Operations Research

Introduction to Operations Research. Instructor: Prof. G. Srinivasan, Department of Management Studies, IIT Madras. Operations research is a field of study about optimizing performance under given constraints. Operations research also helps us develop models for decision making. The course covers topics on linear programming, graphical and algebraic solutions, simplex algorithm, duality, understanding the dual, solving LPs using solver, transportation problem and assignment problem. (from nptel.ac.in)

Lecture 32 - Solving the Assignment Problem


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Linear Programming: Introduction and Formulations
Lecture 01 - Product Mix Problem and Notations
Lecture 02 - Manpower and Production Planning Formulations
Lecture 03 - Media Selection Problem and Bicycle Problem
Lecture 04 - Caterer Problem
Lecture 05 - Maximum Flow and Bin Packing Problems
Graphical and Algebraic Methods
Lecture 06 - Graphical Method (Maximization)
Lecture 07 - Graphical Method (Minimization)
Lecture 08 - Algebraic Method (Maximization)
Lecture 09 - Algebraic Method (Minimization)
Lecture 10 - Comparing Graphical and Algebraic Methods
Simplex Algorithm
Lecture 11 - Algebraic Form of Simplex Algorithm
Lecture 12 - Tabular Form of Simplex (Maximization)
Lecture 13 - Tabular Form of Simplex (Minimization)
Lecture 14 - Unboundedness
Lecture 15 - Infeasibility
Dual of a Linear Programming Problem
Lecture 16 - Motivation to the Dual
Lecture 17 - Writing the Dual for a General LP
Lecture 18 - Writing the Dual for a General LP (cont.)
Lecture 19 - Duality Theorems
Lecture 20 - Complementary Slackness Theorem
Primal Dual Relationships
Lecture 21 - Dual Solution using Complementary Slackness
Lecture 22 - Dual Solution from Simplex Table; Economic Interpretation of Dual
Lecture 23 - Economic Interpretation of the Dual; Dual Simplex Algorithm
Lecture 24 - Solving LPs with Mixed Type of Constraints
Lecture 25 - Matrix Method for LP Problems
Transportation Problem
Lecture 26 - Introducing the Transportation Problem
Lecture 27 - North West Corner Rule and Minimum Cost Method
Lecture 28 - Penalty Cost Method
Lecture 29 - Stepping Stone Method and Modified Distribution Method
Lecture 30 - MODI Method; Dual of the Transportation Problem and the Optimality of the MODI Method
Assignment Problem
Lecture 31 - Introducing the Assignment Problem
Lecture 32 - Solving the Assignment Problem
Lecture 33 - Hungarian Algorithm; Alternate Optimum
Lecture 34 - Unequal Number of Rows and Columns; Dual of the Assignment Problem
Lecture 35 - Optimality of the Hungarian Algorithm
Solving LPs using a Solver
Lecture 36 - Setting up the Problem and Solving Simple LP Problems
Lecture 37 - Unboundedness and Infeasibility
Lecture 38 - Solving Other Formulations
Lecture 39 - Solving a Transportation Problem
Lecture 40 - Solving an Assignment Problem