# OPERATIONS RESEARCH by Y. Ilker Topcu LECTURE NOTES and eBook download

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CONTENTS
1. INTRODUCTION TO OR..................................................................................... 1
1.1 TERMINOLOGY ...................................................................................................... 1
1.2 THE METHODOLOGY OF OR ............................................................................. 1
1.3 HISTORY OF OR .................................................................................................... 2
2. BASIC OR CONCEPTS...................................................................................... 6
3. LINEAR PROGRAMMING................................................................................ 11
3.1 FORMULATING LP............................................................................................... 13
3.1.1 Giapetto Example .......................................................................................... 13
3.1.3 Diet Example .................................................................................................. 16
3.1.4 Post Office Example...................................................................................... 17
3.1.5 Sailco Example .............................................................................................. 18
3.1.6 Customer Service Level Example............................................................... 19
3.2 SOLVING LP.......................................................................................................... 20
3.2.1 LP Solutions: Four Cases............................................................................. 20
3.2.2 The Graphical Solution (Minimization) ....................................................... 21
3.2.3 The Graphical Solution (Maximization) ...................................................... 22
3.2.4 The Simplex Algorithm.................................................................................. 23
3.2.5 Example illustrating Simplex (Dakota Furniture) ...................................... 24
3.2.6 Other Solution Cases by Simplex ............................................................... 29
3.2.7 The Big M Method ......................................................................................... 31
3.2.8 Example illustrating Big M (Oranj Juice).................................................... 32
3.3 SENSITIVITY ANALYSIS..................................................................................... 35
3.3.1 Reduced Cost................................................................................................. 35
3.3.3 Simple Example ............................................................................................. 36
3.3.4 Utilizing Lindo Output for Sensitivity........................................................... 37
3.3.5 Additional Example (Utilizing Simplex for Sensitivity).............................. 39
3.4 DUALITY................................................................................................................. 42
3.4.1 The Dual Theorem......................................................................................... 42
3.4.2 Finding the Dual of a Normal Max Problem .............................................. 42
3.4.3 Finding the Dual of a Normal Min Problem ............................................... 43
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3.4.4 Finding the Dual of a Nonnormal Max Problem........................................ 43
3.4.5 Finding the Dual of a Nonnormal Min Problem......................................... 43
3.4.6 An Example for Economic Interpretation (Dakota Furniture).................. 44
4. TRANSPORTATION PROBLEMS.................................................................... 45
4.1 FORMULATING TRANSPORTATION PROBLEMS ....................................... 46
4.1.1 LP Representation......................................................................................... 46
4.1.2 Powerco Example for Balanced Transportation Problem ....................... 46
4.1.3 Balancing an Unbalanced Transportation Problem ................................. 47
4.1.4 Modified Powerco Example for Excess Supply ........................................ 48
4.1.5 Modified Powerco Example for Unmet Demand....................................... 49
4.2 FINDING BFS FOR TRANSPORT’N PROBLEMS.......................................... 50
4.2.1 Northwest Corner Method ............................................................................ 51
4.2.2 Minimum Cost Method.................................................................................. 53
4.2.3 Vogel’s Method .............................................................................................. 55
4.3 THE TRANSPORTATION SIMPLEX METHOD............................................... 57
4.3.1 Steps of the Method ...................................................................................... 57
4.3.2 Solving Powerco Example by Transportation Simplex............................ 58
4.4 TRANSSHIPMENT PROBLEMS ........................................................................ 61
4.4.1 Steps................................................................................................................ 61
4.4.2 Kuruoglu Example ......................................................................................... 62
4.5 ASSIGNMENT PROBLEMS................................................................................ 64
4.5.1 LP Representation......................................................................................... 64
4.5.2 Hungarian Method......................................................................................... 64
4.5.3 Flight Crew Example..................................................................................... 66
5. INTEGER PROGRAMMING ............................................................................. 68
5.1 FORMULATING IP................................................................................................ 69
5.1.1 Budgeting Problems...................................................................................... 69
5.1.2 Knapsack Problems ...................................................................................... 72
5.1.3 Fixed Charge Problems................................................................................ 73
5.1.4 Set Covering Problems................................................................................. 78
5.1.5 Either - Or Constraints .................................................................................. 80
5.1.6 If - Then Constraints...................................................................................... 81
5.1.7 Traveling Salesperson Problems ................................................................ 82