Contents

1. Linear Programming-Simplex Method     

1. Introduction  

2. Two Variable LP Model     

3. Graphical LP Solution     

4. LP Model in Equation Form 

5. Transition from Graphical to Algebraic Solution   

6. The Simplex Method  

7. Artificial Starting Solution    

8. M-Method (Use of Artificial Variables)

9. Special Cases in Simplex Method

2. Dual Simplex Method 

1. Introduction  

2. Dual Simplex Problems     

3. Algorithm For Dual Simplex Method

3. Integer Programming 

1. Introduction  

2. Integer Programming Problem(IPP)

3. Concept of ‘cutting plane’

4. Gomory’s Cutting Plane Technique

5. Mixed IPP     

6. Branch And Bound Method 

4. Transportation and Assignment Problems

1. Introduction  

2. Definition of the Transportation Problems   

3. General Transportation Problem  

4. Initial Basic Feasible Solution 

5. Optimum Solution by ‘Modi’ Method     

6. The Transportation Algorithm    

7. Degeneracy in Transportation Problems 

8. The Assignment Model (Hungarian Method)     

9. Mathematical Model for Assignment Problem   

10.Comparison between TP and AP    

11.Hungarian method of solving an AP     

12.Unbalanced Assignment Problems  

13.Assignment Problems with Restrictions

5. Sequencing    

1. Introduction  

2. Sequencing Problem  

3. Types Of Sequencing Problems    

4. Assumptions In A Sequencing Problem   

5. n JOBS ON 2 MACHINES

6. n JOBS ON 3 MACHINES 285

7. Processing N Jobs On M Machines 

8. Processing Two Jobs On M Machines     

9. Gantt Charts

6. Decision Analysis and Games     

1. Introduction  

2. Optimal Solution of Two-Person, Zero-Sum Games    

3. Solution of Mixed Strategy Games

4. Graphical Method for Solving…

5. Subgames

6. Principle of Dominance and Solving Some Simple Games    

7. Presentation of Game Problem by LPP

7. Replacement Models  

1. Introduction  

2. Types Of Replacement

3. Replacement of item that fail suddenly

8. PERT and CPM  

1. Introduction  

2. Pert / CPM Network Components   

3. Some Errors In Network (Arrow Diagram)

4. Critical Path Method

5. Float (Slack) On Activities And Event 

6. Project Scheduling With Uncertain Activity Times  

7. Cost Considerations In Pert

9. Simulation

1. Introduction  

2. Steps In Simulation Procedure   

3. Monte Carlo Methods Of Simulation     

4. Examples On Simulation    

5. Advantages And Disadvantages Of Simulation

10. Markov Chains

1. Introduction

2. Properties of P (Stochastic Matrix)   

3. Ergodic Matrices

11. Queuing Theory     

1.  Introduction 

2.  Characteristics of Queue 

3.  The Poisson Probability  

4.  Model I: (M/M/1): (FIFO)

5.  Model II: (M/M/1):(FIFO/N)     

6.  Model III: (M/M/S):(FIFO/N) SYSTEM

12. Non-linear Programming   

1. Introduction  

2. General Form Of Non-Linear Programming Problems   

3. Sample Applications 

4. Single Variable Optimization    

5. Quadratic Programming     

6. Separable Convex Programming