Abhivyakti Paper 01 Operation Research

                              M.Sc. Mathematics Final Year Battle

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1.Introduction

• The origin and the development of O.R.; 

• The Nature and Definition of OR;

• Objective of OR: 

• Phases of OR Method: 

• Areas of Applications of OR; 

• Scientific Method in OR; 

• Characteristics of Operations Research; 

• Modeling in OR; 

• Types of Models; 

• General Methods of Solution for OR Models;

2- Mathematical Preliminaries

• Elementary Probability Theory: 

• Matrices and Determinants; 

• Vectors and Vector Spaces; 

• Simultaneous Linear Equations;

• Finite Difference; 

• Differentiation of Integrals,

• Generating Functions

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3- Inventory Theory

• Inventory; 

• Variables in an Inventory Problems;

• Need of Inventory: 

• Classification or Categories of Inventory Models; 

• Deterministic Models; 

• Deterministic Models with Shortage, 

• Multi Item, 

• Deterministic Models with one Constant; 

• Probabilistic Models: 

• Purchase Inventory Models with Price Breaks:

4- Replacement Problems

• Replacement and Replacement Situations; Replacement of Major of Capital Item that Deteriorates with time; 

• To determine the Best Replacement Age of Items whose Maintenance Costs Increase with time and the value of money also change with time; 

• Replacement of Items in Anticipation of Complete Failure the Probability of Which Increase with time; 

• To Determine the interval of Optimum Replacement; 

• Problems in Mortality; 

• Staffing Problem; Mortality Tables;

5- Allocation (General Linear Programming Problems)

• General Linear Programming Problems; 

• Mathematical Formulation of a L.P.P; 

• Basic Solution;

• Solution of a Linear Programming Problem; 

• Geometrical Method for the solution of a Linear Programming Problem;

• Analytic Method; 

• Slack and Surplus Variables; 

• Application of Linear Programming Techniques;

• Limitations of Linear Programming;

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6- Convex Sets and Their Properties

• Some Important Definitions; 

• Some Important Theorems;

7- Simplex Method

• Simplex Method;

•  Fundamental Theorem of Linear Programming; 

• To obtain B.F.S. from a F.S.; 

• To Determine Improved B.F.S.;

• Unbounded Solutions; 

• Optimality Conditions; 

• Alternative Optimal Solutions; Inconsistency and Redundancy in Constraint Equations;

• Artificial Variables Technique;

• Degeneracy in Simplex Method; 

• Solution of System of Simultaneous Linear Equations by Simplex Method;

• Inverse of a Matrix by Simplex Method;

……….

8- Transportation Problem

• Transportation Problem;

• Mathematical Formulation of a Transportation Problem; 

• Solution of a Transportation Problem; 

• Optimality Test; 

• Degeneracy in Transportation Problems; 

• Unbalanced Transportation Problems; 

• Profit Maximization Problems;

9- Network Analysis (PERT-CPM)

• The Theory of Graphs; 

• Network; CPM/PERT Techniques;