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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