Linear Optimization in Applications

CONTENTS

CONTENTS viÎ 8 12 3 46 I)reface Chapler I : Inlroduclion 1.1 Formulation of a linear programming problem 1.2 Solving a 1încar programming problcm 1.2.1 Graphical method 1.2.2 Simplcx mcthod 1.2.3 Reviscd simplcx mClhod 9 99135 Chapler 2 : Primal and Oual Models 2.1 Shadow price I opportunity C051 2.2 The dual model 2.3 Comparing primal :md dual 2.4 Algebraic way 10 rind shadow prices 2.5 A workcd cxampJc 9 9247024 1 1 22233334 4 Chaptcr 3 : Formulating Linear Optimization Problcms 3.1 Transportation problem 3.2 Transportation problcm with d叫ribut。的 3.3 Trans-shipment problcm 3.4 Earth moving opt間，且llOn 3.5 Produ山 on schcdulc optimi甜Imn 3.6 Aggregatc bJcnding problcm 3.7 Lîquid blcnding problcm 3.8 Wastewatcr trcalmcnt optimization 3.9 Critical path ofa prccedcllcc nctwork 3. 10 Time-cosl optimization ofa project network 1 1 39558 91 5 55566667 Chaptcr 4 : Transporlalion Problern and Algorithrn 4.1 The general fonn of a transportation problem 4.2 The algorithrn 4.3 A further exarnple 4.4 Mo閃 applications oftransportation algorithm 4.4.1 Trans-shipment problem 4.4.2 Earth moving problem 4.4.3 Product schcdulc problem An intercsling cxample using lransportation algorithm 4.5 VI Linear Optimization In Applications Chapter 5 : Integer Programming Formulation 5.1 An integer programming example 5.2 Use of zero-one variables 5.3 Transportation problem with warehouse renting 5.4 Transportation problem with additional distributor 5.5 Assignment problem 5.6 Knapsack problem 5.7 Set-covering problem 5.8 Set-packing problem 5.9 Either-or constraint (resource scheduling problem) 5.10 Project scheduling problem 5.11 Travelling salesman problem 55791 『 I 司 / 呵 / 吋 / O O O O O O O O A Y A V J A Y A V J Chapter 6 : Integer Programming Solution 6.1 An example of integer linear programming solutioning 6.2 Solutioning for models with zero-one variables 105 105 112 Chapter 7 : Goal Programming Formulation 7. 1 Linear programming versus goal programming 7.2 Multiple goal problems 7.3 Additivity of deviation variables 7.4 Integer goal programming 117 117 120 122 127 Chapter 8 : Goal Programming Solution 8.1 The revised simplex method as a tool for solving goal programming models 8.2 A further example 8.3 Solving goal programming models using linear programming software packages 131 131 137 140 AppendixA Appendix B Appendix C Appendix D Examples on Simplex Method Examples on Revised Simplex Method Use of Slack Variables,Artifical Variables and Big-M Examples of Special Cases 145 153 161 162 ...