1. Introduction to Operations Research

1.1 Introduction

1.2 Historical Development

1.3 Definitions of Operations Research

1.4 Models in Operations Research

1.5 Elements of Model Construction..

1.6 Scientific Method in OR/ Phases of OR Study

1.7 Operations Research Techniques.

2. Linear Programming : Model Formulation and Applications

2.1 Introduction

2.2 Structure of Linear Programming Model

2.3 General Mathematical model of Linear Programming Model.

2.4 Model Formulation

2.5 Examples of LP Model Formulation (LP Applications)

3. Linear Programming : The Graphical Method

3.1 Introduction

3.2 Graphical Solution Method.

3.3 Extreme Point Enumeration Approach

3.4 Iso- profit (Cost) Function Approach

3.5 Special Cases

3.6 Alternative (or Multiple) Optimal Solutions, Unbounded solution, Infeasible Solution, Redundancy.

4. Linear Programming : The Simplex Method

4.1 Introduction

4.2 Standard Form of the LP Model

4.3 Setting up the Initial Simplex Tableau

4.4 Improving the Solution

4.5 Stopping Criterion

4.6 Solving a Minimization Problem Using the Simplex Method

4.7 Special Cases

4.8 Infeasibility, Unbounded ness, Alternative (Multiple) Optimal Solutions, Degeneracy

5. Transportation Problem

5.1 Introduction

5.2 A Network Model and LP Formulation for a Transportation Problem

5.3 Transportation Tableau

5.4 The Balanced Transportation Problem

5.5 Methods for Finding Initial solution

5.6 North – West Corner Method

5.7 Least Cost Method

5.8 Vogel’s Approximation Method (VAM)

5.9 Determining an Optimal Solution

5.10 The Stepping-Stone Method

5.11 Modified Distribution (MODI) Method

5.12 Variations in Transportation Problem

5.13 Unbalanced Supply and Demand

5.14 Degeneracy

5.15 Alternative / Multiple Optimal Solutions

5.16 Prohibited Routes

5.17 Maximization Transportation Problem

6. Assignment Problem

6.1 Introduction

6.2 LP Formulation of the Assignment Problem

6.3 Difference Between Transportation Problem and Assignment Problem

6.4 The Hungarian Method for Solving an Assignment Problem

6.5 Variations of the Assignment Problem

6.6 Multiple Optimal Solutions

6.7 Maximization Case in Assignment Problem

6.8 Unbalanced Assignment Problem

6.9 Restrictions on Assignments

7. Network Flow Models

7.1 Network Components

7.2 The Shortest Route Problem

7.3 The Shortest Route Solution Approach

7.4 The Minimal Spanning Tree Problem

7.5 The Minimal Spanning Tree Solution Approach

7.6 The Maximal Flow Problem

7.7 The Maximal Flow Solution Approach

8. Project Scheduling : PERT/CPM Network

8.1 Introduction

8.2 Preparation of (Network) Arrow Diagram

8.3 Activity Time Estimates

8.4 Computations for Critical Path

8.5 Determination of the Critical Path

8.6 Probability Considerations in Project Scheduling

8.7 Cost Considerations in Project Scheduling (Time-Cost Trade – Offs)

9. Decision Analysis

9.1 Structuring the Decision Situation : Payoff Tables

9.2 Decision Making without Probabilities

9.3 The Criterion of Optimism (Maximax or Minimin)

9.4 The Criterion of Pessimism (Maximin or Minimax)

9.5 The Minimax Regret Criterion (Savage Criterion)

9.6 The Hurwicz Criterion (The Criterion of Realism.)

9.7 The Equal Likelihood Criterion (Laplace Criterion.)

9.8 Decision Making with Probabilities

9.9 Expected Monetary Value (EMV)

9.10 Expected Opportunity Loss (EOL)

9.11 Expected Value of Perfect Information (EVPI)

9.12 Decision Trees. (Graphical Diagram of the Decision making Process).

10. Dynamic (Multistage) Programming

10.1 Introduction

10.2 Fundamental Concepts of Dynamic Programming

10.3 Applications of Dynamic Programming (Students ate expected to develop the Network models associated with simple problems and find the optimal solutions.)