Linear Optimization in Applications

This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems. The topics include linear programming, integer programming and goal programming. The book can be used by teachers, taught-course students and research students of engineering and business/management disciplines. It is, however, not suitable for students of pure mathematics as its emphasis is on applications rather than theories. Title Page ......Page 4 verso ......Page 5 Table of Contents ......Page 6 Preface ......Page 8 1.1. Formulation of a linear programming problem ......Page 10 1.2. Solving a linear programming problem ......Page 11 1.2.1. Graphical method ......Page 12 1.2.2. Simplex method ......Page 13 1.2.3. Revised simplex method ......Page 15 2.2. The dual model ......Page 18 2.3. Comparing primal and dual ......Page 20 2.4. Algebraic way to find shadow prices ......Page 22 2.5. A worked example ......Page 24 3.1. Transportation problem ......Page 28 3.2. Transportation problem with distributors ......Page 31 3.3. Trans-shipment problem ......Page 33 3.4. Earth moving optimization ......Page 36 3.5. Production schedule optimization ......Page 39 3.6. Aggregate blending problem ......Page 41 3.7. Liquid blending problem ......Page 43 3.8. Wastewater treatment optimization ......Page 46 3.9. Critical path of a precedence network ......Page 49 3.10. Time-cost optimization of a project network ......Page 51 4.1. The general form of a transportation problem ......Page 60 4.2. The algorithm ......Page 62 4.3. A further example ......Page 68 4.4.1. Trans-shipment problem ......Page 74 4.4.2. Earth moving problem ......Page 77 4.4.3. Product schedule problem ......Page 78 4.5. An interesting example using transportation algorithm ......Page 80 5.1. An integer programming example ......Page 84 5.2. Use of zero-one variables ......Page 86 5.3. Transportation problem with warehouse renting ......Page 88 5.4. Transportation problem with additional distributor ......Page 90 5.5. Assignment problem ......Page 93 5.6. Knapsack problem ......Page 96 5.7. Set-covering problem ......Page 98 5.8. Set-packing problem ......Page 99 5.9. Either-or constraint (resource scheduling problem) ......Page 101 5.10. Project scheduling problem ......Page 104 5.11. Travelling salesman problem ......Page 107 6.1. An example of integer linear programming solutioning ......Page 114 6.2. Solutioning for models with zero-one variables ......Page 121 7.1. Linear programming versus goal programming ......Page 126 7.2. Multiple goal problems ......Page 129 7.3. Additivity of deviation variables ......Page 131 7.4. Integer goal programming ......Page 136 8.1. The revised simplex method as a tool for solving goal programming models ......Page 140 8.2. A further example ......Page 146 8.3. Solving goal programming models using linear programming software packages ......Page 149 Appendix A. Examples on Simplex Method ......Page 154 Appendix B. Examples on Revised Simplex Method ......Page 162 Appendix C. Use of Slack Variables, Artificial Variables and Big-M ......Page 170 Appendix D. Examples of Special Cases ......Page 171 Table of Contents; Preface; Chapter 1 : Introduction; Chapter 2 : Primal and Dual Models; Chapter 3 : Formulating Linear Optimization Problems; Chapter 4 : Transportation Problem and Algorithm; Chapter 5 : Integer Programming Formulation; Chapter 6 : Integer Programming Solution; Chapter 7 : Goal Programming Formulation; Chapter 8 : Goal Programming Solution; Appendix A. Examples on Simplex Method; Appendix B. Examples on Revised Simplex Method; Appendix C. Use of Slack Variables, Artificial Variables and Big-M; Appendix D. Examples of Special Cases.