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OPERATIONS RESEARCH MAKAUT MBA SECOND SEM

AUTHOR: Dr. Amrita Bhattacharya
ISBN : 978-93-5755-527-2
Tax excluded
Contents
MODULE-1 |
||
Chapter 1: Linear Programming |
||
1.1. |
Linear Programming Problems(LPP) |
13 |
1.1.1. |
Meaning and Definition |
13 |
1.1.2. |
General Mathematical Model of LPP |
13 |
1.1.3. |
Assumptions of Linear Programming Model |
14 |
1.1.4. |
Components of Linear Programming Problem |
14 |
1.1.5. |
Applications of Linear Programming(LP) |
15 |
1.1.6. |
Formulation of Linear Programming Model |
15 |
1.1.7. |
Methods of Solving LP Problems |
18 |
1.2. |
Graphical Solution |
18 |
1.2.1. |
Introduction |
18 |
1.2.2. |
Graphical Solution Method of LPP/Steps of Graphical Methods of LPP |
19 |
1.2.3. |
Maximisation Problems |
19 |
1.2.4. |
Minimisation Problems |
21 |
1.2.5. |
Mixed Constraints Problems |
24 |
1.2.6. |
Special Types of LPP in Graphical Method |
25 |
1.2.6.1. |
Infeasibility |
25 |
1.2.6.2. |
Unboundedness |
26 |
1.2.6.3. |
Multiple Optimal Solutions |
26 |
1.3. |
Simplex Method |
27 |
1.3.1. |
Introduction |
27 |
1.3.2. |
Steps of Simplex Algorithm |
27 |
1.3.3. |
Slack, Surplus Variables and Artificial Variables |
28 |
1.3.4. |
Maximisation Problems |
28 |
1.3.5. |
Minimisation Problems |
31 |
1.3.6. |
Big-M Method/Primal-Penalty Method |
33 |
1.3.7. |
Special Types of LPP in Simplex Method |
35 |
1.3.7.1. |
Infeasibility |
35 |
1.3.7.2. |
Unboundedness |
37 |
1.3.7.3. |
Multiple Optimal Solutions |
38 |
1.3.7.4. |
Degeneracy |
38 |
1.4. |
Duality |
40 |
1.4.1. |
Introduction |
40 |
1.4.2. |
Primal and Dual Problem |
40 |
1.4.3. |
Relationship between Primal and Dual |
40 |
1.4.4. |
Principles of Duality |
41 |
1.4.5. |
Economic Interpretation of Duality |
43 |
1.4.5.1. |
Economic Interpretation of Dual Variables |
43 |
1.4.5.2. |
Economic Interpretation of Dual Constraints |
43 |
1.5. |
Post Optimality /Sensitivity Analysis |
44 |
1.5.1. |
Introduction |
44 |
1.5.2. |
Effects on an LP Model by Sensitivity Analysis |
44 |
1.5.3. |
Graphical Approach to Sensitivity Analysis |
44 |
1.5.3.1. |
Changes in Objective Function Coefficients |
45 |
1.5.3.2. |
Changes in Right-Hand-Side(RHS) Values (Constraints) |
45 |
1.5.3.3. |
Shadow Prices |
46 |
1.5.4. |
Simplex Method Approach to Sensitivity Analysis |
46 |
1.5.4.1. |
Addition of Variables |
47 |
1.5.4.2. |
Deletion of Variables |
47 |
1.5.4.3. |
Addition of Constraints |
49 |
1.5.4.4. |
Deletion of Constraints |
49 |
1.6. |
Exercise |
50 |
|
|
|
Chapter 2: Transportation Problems |
||
2.1. |
Transportation Problems (TP) |
53 |
2.1.1. |
Introduction |
53 |
2.1.2. |
Mathematical Formulation of Transportation Problem |
53 |
2.1.3. |
Assumptions in Transportation Problem |
54 |
2.1.4. |
Terminologies Used in Transportation Problem |
54 |
2.1.5. |
Transportation Algorithm |
55 |
2.1.6. |
Applications of Transportation Model |
55 |
2.1.7. |
Transportation Methods for Finding Initial Solutions |
55 |
2.1.7.1. |
North-West Corner Method (NWCM) |
55 |
2.1.7.2. |
Least Cost / Matrix Minima Method |
58 |
2.1.7.3. |
Vogel’s Approximation Method (VAM) |
60 |
2.1.8. |
Test for Optimality Using Modified Distribution Method (MODI) Method |
62 |
2.1.8.1. |
Steps of MODI Method |
63 |
2.1.8.2. |
Loops in Transportation Table |
64 |
2.1.9. |
Special Cases in Transportation Problems |
71 |
2.1.9.1. |
Balanced Transportation Problems |
72 |
2.1.9.2. |
Unbalanced Transportation Problems |
73 |
2.1.9.3. |
Minimisation Transportation Problems |
76 |
2.1.9.4. |
Maximisation Transportation Problem |
77 |
2.1.9.5. |
Degeneracy in Transportation Problems |
82 |
2.2. |
Exercise |
84 |
|
|
|
Chapter 3: Assignment Problems |
||
3.1. |
Assignment Problems |
85 |
3.1.1. |
Introduction |
85 |
3.1.2. |
Mathematical Statement of the Problem |
85 |
3.1.3. |
Applications of Assignment Model |
85 |
3.1.4. |
Hungarian Method of Solution |
86 |
3.1.5. |
Special Cases in Assignment Problems |
87 |
3.1.5.1. |
Balanced Assignment Problems |
88 |
3.1.5.2. |
Unbalanced (Non Square Matrix) Assignment Problems |
89 |
3.1.5.3. |
Minimisation Assignment Problems |
91 |
3.1.5.4. |
Maximisation Assignment Problems |
93 |
3.1.5.5. |
Multiple Optimal Solutions |
95 |
3.1.5.6. |
Restrictions on Assignment Problems/ Restricted Assignment Problems |
98 |
3.1.5.7. |
Traveling Salesman’s Model (Or Routing Problem) |
100 |
3.1.6. |
Difference between Transportation and Assignment Problem |
101 |
3.2. |
Exercise |
102 |
|
|
|
Chapter 4: Theory of Games |
||
4.1. |
Theory of Games/Game Theory |
104 |
4.1.1. |
Introduction |
104 |
4.1.2. |
Concept of Game |
104 |
4.1.3. |
Competitive Situations |
104 |
4.1.4. |
Terminology of Game |
105 |
4.1.5. |
Assumptions of Game |
105 |
4.1.6. |
Saddle Point |
105 |
4.1.7. |
Value of Game |
106 |
4.1.8. |
Strategies of Game |
106 |
4.1.8.1. |
Pure Strategy |
107 |
4.1.8.2. |
Mixed Strategy |
107 |
4.1.9. |
Solutions of Game |
107 |
4.1.10. |
Advantages of Game Theory |
107 |
4.1.11. |
Disadvantages of Game Theory |
108 |
4.1.12. |
Application of Game Theory |
108 |
4.1.13. |
Types of Game |
108 |
4.2. |
Two Person Zero-Sum Game |
109 |
4.2.1. |
Introduction |
109 |
4.2.2. |
Payoff Matrix |
109 |
4.2.3. |
Assumptions of Two Person Zero Sum Game |
110 |
4.2.4. |
Pure Strategies - Games with Saddle Points: Minimax & Maximin Criteria |
110 |
MAKAUT2024/MBA/2/01
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