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Operations Research Full pdf Ebook download
Neeraj Yadav

Operations Research Full pdf Ebook download

Neeraj Yadav | 13-Feb-2016 |
Introduction , Theory of Linear Programming , Applications of Linear Programming , Non-Linear Programming ,

Hi friends, here Neeraj Yadav uploaded notes for OPERATION RESEARCH with title Operations Research Full pdf Ebook download. You can download this lecture notes, ebook by clicking on the below file name or icon.

I Introduction 5
1 On Operations Research 6
1.1 What is Operations Research . . . . . . . . . . . . . . . . . . . 6
1.2 History of Operations Research* . . . . . . . . . . . . . . . . . 8
1.3 Phases of Operations Research Study . . . . . . . . . . . . . . . 10
2 On Linear Programming 13
2.1 Example towards Linear Programming . . . . . . . . . . . . . . 13
2.2 Solving Linear Programs Graphically . . . . . . . . . . . . . . . 15
3 Linear Programming with GNU Linear Programming Kit 21
3.1 Overview of GNU Linear Programming Kit . . . . . . . . . . . 21
3.2 Getting and Installing GNU Linear Programming Kit . . . . . . 23
3.3 Using glpsol with GNU MathProg . . . . . . . . . . . . . . . . 24
3.4 Advanced MathProg and glpsol* . . . . . . . . . . . . . . . . . 32
II Theory of Linear Programming 39
4 Linear Algebra and Linear Systems 40
4.1 Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Solving Linear Systems . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Matrices as Linear Functions* . . . . . . . . . . . . . . . . . . . 50
5 Linear Programs and Their Optima 55
5.1 Form of Linear Program . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Location of Linear Programs’ Optima . . . . . . . . . . . . . . 61
5.3 Karush–Kuhn–Tucker Conditions* . . . . . . . . . . . . . . . . 64
5.4 Proofs* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
CONTENTS 2
6 Simplex Method 68
6.1 Towards Simplex Algorithm . . . . . . . . . . . . . . . . . . . . 68
6.2 Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 75
7 More on Simplex Method 87
7.1 Big M Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2 Simplex Algorithm with Non-Unique Optima . . . . . . . . . . 94
7.3 Simplex/Big M Checklist . . . . . . . . . . . . . . . . . . . . . 102
8 Sensitivity and Duality 103
8.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Dual Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.3 Primal and Dual Sensitivity . . . . . . . . . . . . . . . . . . . . 136
III Applications of Linear Programming 137
9 Data Envelopment Analysis 138
9.1 Graphical Introduction to Data Envelopment Analysis . . . . . 138
9.2 Charnes–Cooper–Rhodes Model . . . . . . . . . . . . . . . . . . 152
9.3 Charnes–Cooper–Rhodes Model’s Dual . . . . . . . . . . . . . . 160
9.4 Strengths and Weaknesses of Data Envelopment Analysis . . . 167
10 Transportation Problems 168
10.1 Transportation Algorithm . . . . . . . . . . . . . . . . . . . . . 168
10.2 Assignment Problem . . . . . . . . . . . . . . . . . . . . . . . . 179
10.3 Transshipment Problem . . . . . . . . . . . . . . . . . . . . . . 184
IV Non-Linear Programming 190
11 Integer Programming 191
11.1 Integer Programming Terminology . . . . . . . . . . . . . . . . 191
11.2 Branch-And-Bound Method . . . . . . . . . . . . . . . . . . . . 192
11.3 Solving Integer Programs with GNU Linear Programming Kit . 199

 

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