18MCA352 Optimization Techniques syllabus for MCA

Introduction

Operations Research-A quantitative approaches to Decision Making, Features of OR, OR Approaches to Problem Solving, Methodology of Operations Research.

Linear programming: Introduction, Structure of Linear Programming Model, Advantages, General Mathematical model of LPP, Examples of LP Model Formulation, Graphical solution methods of LP problem.

Linear Programming:

The Simplex Method, Two-Phase method, Big M method

Duality in Linear Programming, Formulation of Dual Linear Programming Problem and Examples.

Assignment Problem:

Mathematical model of Assignment Problem, Hungarian method for solving Assignment problem.

Transportation Problem:

Transportation Problem, Mathematical model of Transportation Problem, Methods of finding Initial solution (North west corner rule, Least cost method, Vogel's Approximation method), Test for Optimality in TP using MODI method (uv -method).

Theory of Games:

Introduction, Two-person zero-sum game, pure strategies (Minmax and Maxmin principles),Mixed strategies, The rules principles of Dominance, Algebraic method to solve games without saddle point, Graphical method to solve the games.

Sequencing Problems:

Processing n jobs through two machines (Johnson's Procedure)

Course Outcomes (CO):

At the end of this course, the students will be able to

CO1: Understand the importance of operations research & acquire skills to develop linear programming mathematical models to real world problems

CO2: Understand the essence and foundations of the simplex algorithm and write the dual of the given primal problems.

CO3: Recognize, formulate and giving optimal solution to a Transportation problem and Assignment problems.

CO4: Analyse & Solve Simple Game Theory Problems.

CO5: Solve problems of job sequencing of production runs

Question Paper Pattern:

• The question paper will have ten questions.
• Each full question consists of 16 marks.
• There will be 2 full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer 5 full questions, selecting one full question from each module.

Text Books:

1. Operations Research Theory and Applications By JK Sharma, 5th Edition, MACMILLAN publishers India,(Chapter1,2,3,4,5,9,10,11,12,20)

Reference Books:

1. Operation Research, S. D. Sharma - Kedarnath Ramnath and Co ,2002

2.Operations Research – An Introduction, Taha H.A. –Low price Edition, 7th Edn,2006

3. Introduction to Operation Research, Hiller and Liberman, Mc Graw Hill. 5th edition 2001

4. Operation Research, Prem Kumar Gupta, D S Hira,S Chand pub, New Delhi, 2007.