Verfügbarkeit: Optimization modelling

Optimization modelling: a practical approach

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Hauptverfasser:	Sarker, Ruhul Amin (VerfasserIn), Newton, Charles S. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton, Fla. [u.a.] CRC Press, Taylor & Francis 2008
Schlagworte:	Modèles mathématiques Optimisation mathématique Mathematisches Modell Mathematical models Mathematical optimization Optimierung
Online-Zugang:	Table of contents only Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XXXII, 469 S. graph. Darst.
ISBN:	9781420043105

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adam_text	OPTIMIZATION MODELLING / SARKER, RUHUL A. : C2008 TABLE OF CONTENTS / INHALTSVERZEICHNIS INTRODUCTION THE PROCESS OF OPTIMIZATION INTRODUCTION TO MODELLING SIMPLE MODELLING TECHNIQUES I SIMPLE MODELLING TECHNIQUES II MODELLING LARGE-SCALE AND WELL-KNOWN PROBLEMS I MODELLING WELL-KNOWN PROBLEMS II ALTERNATIVE MODELLING SOLUTION APPROACHES : AN OVERVIEW INPUT PREPARATION AND MODEL SOLVING OUTPUT ANALYSIS AND PRACTICAL ISSUES BASIC OPTIMIZATION TECHNIQUES MODELS FOR PRACTICAL PROBLEMS I MODELS FOR PRACTICAL PROBLEMS II SOLVING PRACTICAL PROBLEMS. DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. Table of Contents List of Figures..................................................... xv List of Tables................................................... xxi List of Mathematical Notations....................................xxiv Preface............................................................xxv Acknowledgments...................................................xxix Authors......................................................... xxxi Section I Introduction to Optimization and Modelling 1 Introduction.....................................................3 1.1 General Introduction........................................3 1.2 History of Optimization................................... 4 1.3 Optimization Problems.......................................5 1.4 Mathematical Model...................................... 6 1.4.1 Characteristics and Assumptions.......................6 1.5 Concept of Optimization.....................................8 1.6 Classification of Optimization Problems.................. 11 1.7 Organization of the Book................................. 13 Exercises...................................................... 14 References.......................................................15 2 The Process of Optimization......................................17 2.1 Introduction........................................... 17 2.2 Decision Process....................................... 17 2.3 Problem Identification and Clarification...................19 2.4 Problem Definition....................................... 20 2.5 Development of a Mathematical Model........................21 2.5.1 Measure of Effectiveness.............................23 2.6 Deriving a Solution.................................... 25 2.7 Sensitivity Analysis.......................................26 2.8 Testing the Solution.......................................26 2.9 Implementation.............................................27 vi 2.10 Summary.................................................28 Exercises........... ..........................................29 3 Introduction to Modelling.....................................31 3.1 Introduction........................................ 31 3.2 Components of a Mathematical Model......................31 3.2.1 Decision Variables.............................. 32 3.2.2 Objective Function................................32 3.2.3 Constraints.......................................32 3.3 Simple Examples....................................... 32 3.4 Analyzing a Problem.....................................34 3.4.1 A Nonmathematical Programming Problem.............35 3.5 Modelling a Simple Problem..............................36 3.5.1 Defining the Variables............................37 3.5.2 Objective Function.............................. 37 3.5.3 Constraints.......................................37 3.6 Linear Programming Model................................39 3.7 More Mathematical Models................................39 3.8 Integer Programming................................... 42 3.9 Multi-Objective Problem.................................45 3.9.1 Objective versus Goal........................... 47 3.10 Goal Programming...................................... 47 3.11 Nonlinear Programming...................................49 3.12 Summary.................................................52 Exercises.....................................................52 Section II Modelling Techniques 4 Simple Modelling Techniques I.................................59 4.1 Introduction............................................59 4.2 Use of Subscripts in Variables..........................59 4.3 Simple Modelling Techniques........................... 60 4.3.1 Additional Work Requirement in the Formulation....61 4.3.2 Variables as Fractions of Other Variables.........64 4.3.3 Maintaining Certain Ratios among Different Variables.... 68 4.3.4 One Constraint Is a Fraction of Another Constraint.70 4.3.5 Maxi-Min or Mini-Max Objective Function...........75 4.3.6 Multi-Period Modelling........................ 77 4.3.7 Transforming Infeasible Solutions to Satisfactory Solutions.........................................79 4.3.8 Single to Multiple Objectives.....................81 4.4 Special Types of Linear Programming.....................82 4.4.1 Transportation Problem............................83 4.4.2 Assignment Problem................................86 4.4.3 Transshipment Problem.............................88 4.4.4 Project Management Problem...................... 91 vii 4.5 Summary...................................................98 Exercises............. ........................................98 Bibliography.......... ........................................102 5 Simple Modelling Techniques II................................103 5.1 Introduction.............................................103 5.2 Precedence Constraints................................. 103 5.3 Either-or Constraints.................................. 104 5.4 K out of N Constraints Must Hold.........................105 5.5 Yes-or-No Decisions......................................106 5.6 Functions with N Possible Values.........................108 5.7 Mutually Exclusive Alternatives and Contingent Decisions.109 5.8 Linking Constraints with the Objective Function..........Ill 5.9 Piecewise Linear Functions...............................113 5.10 Nonlinear to Approximate Functions.......................116 5.11 Deterministic Models with Probability Terms..............118 5.12 Alternate Objective Functions............................121 5.13 Constrained to Unconstrained Problem.....................122 5.14 Simplifying Cross Product of Binary Variables.......... 124 5.15 Fractional Programming...................................126 5.16 Unrestricted Variables...................................128 5.17 Changing Constraint and Objective Type...................129 5.17.1 From to = Constraints...........................129 5.17.2 From to = Constraints...........................130 5.17.3 From to Constraints...........................130 5.17.4 From to Constraints...........................130 5.17.5 From = Constraint to and Constraints..........130 5.17.6 Changing Objective Type......................... 131 5.18 Conditional Constraints..................................132 5.19 Dual Formulation..................................... 133 5.20 Regression Model.........................................136 5.21 Stochastic Programming...................................137 5.22 Constraint Programming...................................137 5.23 Summary..................................................138 Exercises........................... ..........................138 Bibliography.......... ........................................142 References.....................................................143 6 Modelling Large-Scale and Well-Known Problems I................145 6.1 Introduction........................................... 145 6.2 Use of the Summation (2) Sign............................145 6.3 Use of the Subset (e) Sign...............................147 6.4 Network Flow Problems....................................149 6.4.1 Shortest Path Problem.............................149 6.4.2 Maximum Flow Problem..............................150 6.4.3 Multi-Commodity Flow Problem......................152 viii 6.5 Knapsack Problem...........................................154 6.5.1 Capital Budgeting Problem............................154 6.5.2 Bin Packing Problem..................................155 6.5.3 Cutting Stock Problem................................157 6.6 Facility Location and Layout...............................159 6.6.1 Facility Location Problem............................159 6.6.2 Facility Layout Problem..............................161 6.7 Production Planning dnd Scheduling.........................164 6.7.1 Relevant Literature..................................165 6.8 Logistics and Transportation...............................167 6.8.1 Airlift Problem......................................167 6.8.2 Relevant Literature..................................168 6.9 Summary.................................................. 170 Exercises.......................................................170 References......................................................172 7 Modelling Well-Known Problems II................................177 7.1 Introduction...............................................177 7.2 Job and Machine Scheduling.................................177 7.2.1 Relevant Literature..................................179 7.3 Assignment and Routing.....................................180 7.3.1 Generalized Assignment Problem.......................180 7.3.2 Traveling Salesperson Problem........................181 7.3.3 Relevant Literature on Traveling Salesperson Problem..............................................184 7.3.4 Vehicle Routing Problem..............................185 7.3.5 Relevant Literature on Vehicle Routing Problem.......188 7.4 Staff Rostering and Scheduling.............................189 7.4.1 Staff Scheduling: A Weekly Problem...................189 7.4.2 Daily Rostering Problem..............................191 7.4.3 Relevant Literature on General Staff Scheduling......192 7.4.4 Crew Planning/Scheduling Problem.....................193 7.5 Scheduling and Timetabling Problem.........................194 7.5.1 School Timetabling Problem...........................194 7.5.2 University Timetabling...............................196 7.5.3 Relevant Literature..................................197 7.6 Summary....................................................199 Exercises.......................................................199 References......................................................201 8 Alternative Modelling..........................................205 8.1 Introduction...............................................205 8.2 Modelling under Different Assumptions......................205 8.2.1 A Coal Blending Problem..............................205 8.2.2 First Alternative Blending Model................... 207 8.2.3 Second Alternative Blending Model....................209 IX 8.2.4 Comparing the Two Simple Alternative Models......210 8.2.5 A Crop Planning Problem..........................211 8.2.6 Crop Planning Model 1........................... 212 8.2.7 Crop Planning Model 2 ............................213 8.3 Hierarchical Modelling: An Introduction.................214 8.3.1 Hierarchical Modelling in a Manufacturing Context.... 215 8.3.2 Aggregate Model...................................216 8.3.3 Family Scheduling Model...........................217 8.3.4 Individual Item Scheduling Model..................218 8.4 Summary.................................................219 References...................................................220 Section III Model Solving 9 Solution Approaches: An Overview..........................223 9.1 Introduction..........................................223 9.2 Complexity and Complexity Classes.....................223 9.2.1 Complexity of Algorithms........................223 9.2.2 Complexity Classes..............................224 9.3 Classical Optimization Techniques.....................225 9.3.1 Linear Programming............................ 225 9.3.2 Integer Programming: The Curse of Dimensionality...............................227 9.3.3 Integer Linear Program: Solution Approaches.....228 9.3.4 Special Linear Programming Models...............230 9.3.5 Goal Programming................................230 9.3.6 Nonlinear Programming......................... 231 9.3.7 Multi-Objective Models..........................232 9.4 Heuristic Techniques..................................233 9.4.1 Hill Climbing...................................233 9.4.2 Simulated Annealing........................... 233 9.4.3 Tabu Search................................... 234 9.4.4 Genetic Algorithms..............................234 9.4.5 Ant Colony Optimization.........................235 9.4.6 Memetic Algorithms..............................236 9.4.7 Other Heuristics.............................. 236 9.5 Optimization Software.................................236 9.5.1 LINGO/LINDO.....................................237 9.5.2 MPL with OptiMax 2000, CPLEX, and XPRESS......................................237 9.5.3 GAMS............................................237 9.5.4 Solver and Premium Solver.......................238 9.5.5 Win QSB.........................................238 9.5.6 MINOS...........................................238 9.6 Summary............................................. 239 X References.................................................... 239 Appendix-9 A LINGO: An Introduction.............................241 9A.1 Introduction.............................................241 9A.2 Inputting Model in LINGO.................................241 9A.3 Solving the Model........................................243 9A.3.1 Solver Status Window.............................243 9A.3.2 LINGO Special Features...........................244 9A.4 Another Example...........................................246 9A.4.1 Objective Function...............................246 9A.4.2 Constraints......................................247 9A.4.3 Complete LINGO Model.............................248 9A.4.4 Defining the Sets................................249 9A.4.5 Inputting the Data...............................250 9A.5 LINGO Syntax.............................................252 Appendix-9B MPL: An Introduction................................253 9B.1 Introduction........................................... 253 9B.2 Use of MPL...............................................253 9B.3 Using Vectors and Indexes in MPL.........................255 9B.4 A Product-Mix Model with Three Variables.................256 Appendix-9C GAMS: An Introduction...............................260 9C. 1 Introduction..............................................260 9C.2 An Example...............................................260 Appendix-9D Excel Solver: An Introduction..................... 264 9D.1 Introduction.............................................264 9D.2 Solving Linear Programs with Solver......................264 9D.2.1 Defining the Target Cell (Objective Function)....266 9D.2.2 Identifying the Changing Cells (Decision Variables).............................266 9D.2.3 Adding Constraints...............................267 9D.2.4 Some Important Options...........................269 9D.2.5 The Solution....................................270 Appendix-9E Win QSB: An Introduction............................273 9E. 1 Introduction.............................................273 9E.2 Problem Solving with Win QSB........................... 273 9E.3 Reference............................................ 275 10 Input Preparation and Model Solving.............................277 10.1 Introduction.............................................277 10.2 Data and Data Collection............................... 277 10.3 Data Type................................................279 10.4 Data Preparation.........................................280 10.4.1 Data Requirements.............................. 282 10.4.2 Data Aggregation.................................283 10.5 Data Preprocessing.......................................287 10.6 Model-Driven Data versus Data-Driven Model...............292 XI 10.7 Model Solving............................................292 10.7.1 Excel Solver.....................................293 10.7.2 LINGO and MPL....................................295 10.8 Summary.............................................. 304 Exercises.......................................................304 References......................................................308 Appendix-10A Additional Problem-Solving Using LINGO..........309 10A.1 Example 4.6 (Model 4.7)................................ 309 10A.1.1 LINGO Code.....................................309 10A.1.2 LINGO Solution.................................310 10A.2 A Transportation Model.................................. 310 10A.2.1 LINGO in Algebraic Form...................... 311 10A.2.2 LINGO Solution Report..........................311 10A.2.3 LINGO Codes (Alternative)......................312 10A.2.4 LINGO Solution Report (Using Alternative Codes)..............................312 10A.2.5 A Modified Transportation Model..................313 10A.2.6 LINGO Solution Report (with Restricted Path)...........................................314 10A.3 Example 4.14 (Model 4.15)................................315 10A.3.1 LINGO in Algebraic Form........................315 10A.3.2 LINGO Solution Report..........................316 10A.3.3 LINGO Codes (Alternative Form).................316 10A.3.4 LINGO Solution Report (for Alternative Codes).........................317 10A.4 Example 3.6 (Model 4.1)..................................318 10A.4.1 LINGO in Algebraic Form........................318 10A.4.2 LINGO Model Statistics.........................318 10A.4.3 LINGO Solution.................................318 10A.4.4 LINGO Codes (Alternative Form).................319 10A.4.5 LINGO Solution for Alternative Codes...........319 10A.5 Example 5.3 (Model 5.2)..................................320 10A.5.1 LINGO Codes....................................320 10A.5.2 LINGO Solution Report..........................321 10A.5.3 LINGO Alternative Codes........................321 10A.5.4 LINGO Solution Report (for Alternative Codes)..........................................321 10A.6 Example 5.16.............................................322 10A.6.1 LINGO Codes....................................322 10A.6.2 LINGO Solution Report..........................322 10A.7 Example 4.11 (Model 4.12)................................323 10A.7.1 LINGO Codes....................................323 10A.7.2 LINGO Solution Report..........................324 10A.8 Example 5.10 (Model 5.7).................................324 10A.8.1 LINGO Codes....................................324 10A.8.2 LINGO Solution Report..........................325 ,327 .327 .327 329 330 .331 331 332 332 333 333 .336 336 336 336 337 338 338 339 339 339 340 340 340 340 341 342 342 342 343 .344 .344 ,347 347 .347 355 365 ,374 375 .377 Output Analysis and Practical Issues....................... 11.1 Introduction......................................... 11.2 Solutions and Reports................................ 11.2.1 Shadow Price................................. 11.2.2 Reduced Cost................................. 11.3 Sensitivity Analysis................................. 11.3.1 Changes in the Objective Coefficients........ 11.3.2 Changes in the RHS Values..................... 11.3.3 Changes in the Constraint Coefficients......... 11.3.4 Addition of New Product or Variable.......... 11.3.5 Sensitivity Analysis for Integer and Nonlinear Models....................................... 11.4 Practical Issues and Tips............................ 11.4.1 Solutions to Goal Programming Problems....... 11.4.2 Multi-Objective Optimization................. 11.4.3 Reduction of Variables and Constraints....... 11.4.4 Solutions and Number of Basic Variables...... 11.4.5 Variables with No Restriction in Sign........ 11.4.6 Negative RHS................................. 11.4.7 Scaling Factors in Modelling................. 11.4.8 Linear vs. Nonlinear Relationships........... 11.4.9 Non-Smooth Relationships..................... 11.4.10 Linear vs. Integer and Nonlinear Models...... 11.4.11 Rounding for Integer Solutions............... 11.4.12 Improved Initial Solutions................... 11.4.13 Variable Bounds.............................. 11.4.14 Management Issues in Solution Implementation 11.4.15 Gap between Solutions and Outcomes........... 11.4.16 Nontechnical Report.......................... 11.4.17 Special Cases in LP Models................... 11.5 Risk Analysis........................................ 11.6 Summary.............................................. Exercises.................................................. Basic Optimization Techniques.............................. 12.1 Introduction......................................... 12.2 Graphical Method..................................... 12.3 Simplex Method....................................... 12.4 Branch-and-Bound Method.............................. 12.5 Summary.............................................. Exercises.................................................. Bibliography............................................... X1U Section IV Practical Problems 13 Models for Practical Problems I.......................... 381 13.1 Introduction............................................381 13.2 A Crop Planning Problem.................................381 13.2.1 Linear Programming Model........................382 13.2.2 Goal Programming (GP) Model................... 385 13.3 Power Generation Planning...............................387 13.3.1 Linear Programming Model........................387 13.3.2 Multi-Objective Optimization Model..............391 13.4 A Water Supply Problem..................................392 13.4.1 Linear Programming Model........................393 13.4.2 Goal Programming Model..........................394 13.5 A Supply Chain Problem................................ 395 13.6 Coal Production and Marketing Plan......................398 13.6.1 Multi-Objective Problem.........................403 13.6.2 Multi-Period Problems...........................403 13.7 General Blending Problem................................404 13.8 Summary.................................................409 References...................................................409 14 Models for Practical Problems II.............................411 14.1 Introduction............................................411 14.2 A Combat Logistics Problem..............................411 14.3 A Lot-Sizing Problem....................................415 14.3.1 Finished Product Inventory......................417 14.3.2 Raw Material Inventory..........................418 14.3.3 Total Cost Function per Year....................419 14.4 A Joint Lot-Sizing and Transportation Decision Problem..420 14.5 Coal Bank Scheduling....................................423 14.5.1 Static Model....................................424 14.5.2 Dynamic Model...................................426 14.6 A Scaffolding System....................................427 14.7 A Gas-Lift Optimization Problem.........................429 14.8 Multiple Shifts Planning................................432 14.9 Summary.................................................434 References...................................................435 15 Solving Practical Problems...................................437 15.1 Introduction............................................437 15.2 A Product Mix Problem...................................437 15.3 A Two-Stage Transportation Problem......................443 15.4 A Crop Planning Problem.................................445 15.4.1 Constraint and Variable Reduction...............448 15.4.2 Scaling the Model...............................450 15.4.3 Working with Solutions........................ 450 15.4.4 Multi-Objective Crop Planning Problem...........451 XIV 15.5 Power Generation Planning Problem......................452 15.5.1 Nlodel Vialidation..............................452 15.6 Gas-Lift Optimization 455 l5»7 SlllllUldry Appendix-15A Crop Planning Linear Programming Model.........459
adam_txt	OPTIMIZATION MODELLING / SARKER, RUHUL A. : C2008 TABLE OF CONTENTS / INHALTSVERZEICHNIS INTRODUCTION THE PROCESS OF OPTIMIZATION INTRODUCTION TO MODELLING SIMPLE MODELLING TECHNIQUES I SIMPLE MODELLING TECHNIQUES II MODELLING LARGE-SCALE AND WELL-KNOWN PROBLEMS I MODELLING WELL-KNOWN PROBLEMS II ALTERNATIVE MODELLING SOLUTION APPROACHES : AN OVERVIEW INPUT PREPARATION AND MODEL SOLVING OUTPUT ANALYSIS AND PRACTICAL ISSUES BASIC OPTIMIZATION TECHNIQUES MODELS FOR PRACTICAL PROBLEMS I MODELS FOR PRACTICAL PROBLEMS II SOLVING PRACTICAL PROBLEMS. DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. Table of Contents List of Figures. xv List of Tables. xxi List of Mathematical Notations.xxiv Preface.xxv Acknowledgments.xxix Authors. xxxi Section I Introduction to Optimization and Modelling 1 Introduction.3 1.1 General Introduction.3 1.2 History of Optimization. 4 1.3 Optimization Problems.5 1.4 Mathematical Model. 6 1.4.1 Characteristics and Assumptions.6 1.5 Concept of Optimization.8 1.6 Classification of Optimization Problems. 11 1.7 Organization of the Book. 13 Exercises. 14 References.15 2 The Process of Optimization.17 2.1 Introduction. 17 2.2 Decision Process. 17 2.3 Problem Identification and Clarification.19 2.4 Problem Definition. 20 2.5 Development of a Mathematical Model.21 2.5.1 Measure of Effectiveness.23 2.6 Deriving a Solution. 25 2.7 Sensitivity Analysis.26 2.8 Testing the Solution.26 2.9 Implementation.27 vi 2.10 Summary.28 Exercises. .29 3 Introduction to Modelling.31 3.1 Introduction. 31 3.2 Components of a Mathematical Model.31 3.2.1 Decision Variables. 32 3.2.2 Objective Function.32 3.2.3 Constraints.32 3.3 Simple Examples. 32 3.4 Analyzing a Problem.34 3.4.1 A Nonmathematical Programming Problem.35 3.5 Modelling a Simple Problem.36 3.5.1 Defining the Variables.37 3.5.2 Objective Function. 37 3.5.3 Constraints.37 3.6 Linear Programming Model.39 3.7 More Mathematical Models.39 3.8 Integer Programming. 42 3.9 Multi-Objective Problem.45 3.9.1 Objective versus Goal. 47 3.10 Goal Programming. 47 3.11 Nonlinear Programming.49 3.12 Summary.52 Exercises.52 Section II Modelling Techniques 4 Simple Modelling Techniques I.59 4.1 Introduction.59 4.2 Use of Subscripts in Variables.59 4.3 Simple Modelling Techniques. 60 4.3.1 Additional Work Requirement in the Formulation.61 4.3.2 Variables as Fractions of Other Variables.64 4.3.3 Maintaining Certain Ratios among Different Variables. 68 4.3.4 One Constraint Is a Fraction of Another Constraint.70 4.3.5 Maxi-Min or Mini-Max Objective Function.75 4.3.6 Multi-Period Modelling. 77 4.3.7 Transforming Infeasible Solutions to Satisfactory Solutions.79 4.3.8 Single to Multiple Objectives.81 4.4 Special Types of Linear Programming.82 4.4.1 Transportation Problem.83 4.4.2 Assignment Problem.86 4.4.3 Transshipment Problem.88 4.4.4 Project Management Problem. 91 vii 4.5 Summary.98 Exercises. .98 Bibliography. .102 5 Simple Modelling Techniques II.103 5.1 Introduction.103 5.2 Precedence Constraints. 103 5.3 Either-or Constraints. 104 5.4 K out of N Constraints Must Hold.105 5.5 Yes-or-No Decisions.106 5.6 Functions with N Possible Values.108 5.7 Mutually Exclusive Alternatives and Contingent Decisions.109 5.8 Linking Constraints with the Objective Function.Ill 5.9 Piecewise Linear Functions.113 5.10 Nonlinear to Approximate Functions.116 5.11 Deterministic Models with Probability Terms.118 5.12 Alternate Objective Functions.121 5.13 Constrained to Unconstrained Problem.122 5.14 Simplifying Cross Product of Binary Variables. 124 5.15 Fractional Programming.126 5.16 Unrestricted Variables.128 5.17 Changing Constraint and Objective Type.129 5.17.1 From to = Constraints.129 5.17.2 From to = Constraints.130 5.17.3 From to Constraints.130 5.17.4 From to Constraints.130 5.17.5 From = Constraint to and Constraints.130 5.17.6 Changing Objective Type. 131 5.18 Conditional Constraints.132 5.19 Dual Formulation. 133 5.20 Regression Model.136 5.21 Stochastic Programming.137 5.22 Constraint Programming.137 5.23 Summary.138 Exercises. .138 Bibliography. .142 References.143 6 Modelling Large-Scale and Well-Known Problems I.145 6.1 Introduction. 145 6.2 Use of the Summation (2) Sign.145 6.3 Use of the Subset (e) Sign.147 6.4 Network Flow Problems.149 6.4.1 Shortest Path Problem.149 6.4.2 Maximum Flow Problem.150 6.4.3 Multi-Commodity Flow Problem.152 viii 6.5 Knapsack Problem.154 6.5.1 Capital Budgeting Problem.154 6.5.2 Bin Packing Problem.155 6.5.3 Cutting Stock Problem.157 6.6 Facility Location and Layout.159 6.6.1 Facility Location Problem.159 6.6.2 Facility Layout Problem.161 6.7 Production Planning dnd Scheduling.164 6.7.1 Relevant Literature.165 6.8 Logistics and Transportation.167 6.8.1 Airlift Problem.167 6.8.2 Relevant Literature.168 6.9 Summary. 170 Exercises.170 References.172 7 Modelling Well-Known Problems II.177 7.1 Introduction.177 7.2 Job and Machine Scheduling.177 7.2.1 Relevant Literature.179 7.3 Assignment and Routing.180 7.3.1 Generalized Assignment Problem.180 7.3.2 Traveling Salesperson Problem.181 7.3.3 Relevant Literature on Traveling Salesperson Problem.184 7.3.4 Vehicle Routing Problem.185 7.3.5 Relevant Literature on Vehicle Routing Problem.188 7.4 Staff Rostering and Scheduling.189 7.4.1 Staff Scheduling: A Weekly Problem.189 7.4.2 Daily Rostering Problem.191 7.4.3 Relevant Literature on General Staff Scheduling.192 7.4.4 Crew Planning/Scheduling Problem.193 7.5 Scheduling and Timetabling Problem.194 7.5.1 School Timetabling Problem.194 7.5.2 University Timetabling.196 7.5.3 Relevant Literature.197 7.6 Summary.199 Exercises.199 References.201 8 Alternative Modelling.205 8.1 Introduction.205 8.2 Modelling under Different Assumptions.205 8.2.1 A Coal Blending Problem.205 8.2.2 First Alternative Blending Model. 207 8.2.3 Second Alternative Blending Model.209 IX 8.2.4 Comparing the Two Simple Alternative Models.210 8.2.5 A Crop Planning Problem.211 8.2.6 Crop Planning Model 1. 212 8.2.7 Crop Planning Model 2 .213 8.3 Hierarchical Modelling: An Introduction.214 8.3.1 Hierarchical Modelling in a Manufacturing Context. 215 8.3.2 Aggregate Model.216 8.3.3 Family Scheduling Model.217 8.3.4 Individual Item Scheduling Model.218 8.4 Summary.219 References.220 Section III Model Solving 9 Solution Approaches: An Overview.223 9.1 Introduction.223 9.2 Complexity and Complexity Classes.223 9.2.1 Complexity of Algorithms.223 9.2.2 Complexity Classes.224 9.3 Classical Optimization Techniques.225 9.3.1 Linear Programming. 225 9.3.2 Integer Programming: The Curse of Dimensionality.227 9.3.3 Integer Linear Program: Solution Approaches.228 9.3.4 Special Linear Programming Models.230 9.3.5 Goal Programming.230 9.3.6 Nonlinear Programming. 231 9.3.7 Multi-Objective Models.232 9.4 Heuristic Techniques.233 9.4.1 Hill Climbing.233 9.4.2 Simulated Annealing. 233 9.4.3 Tabu Search. 234 9.4.4 Genetic Algorithms.234 9.4.5 Ant Colony Optimization.235 9.4.6 Memetic Algorithms.236 9.4.7 Other Heuristics. 236 9.5 Optimization Software.236 9.5.1 LINGO/LINDO.237 9.5.2 MPL with OptiMax 2000, CPLEX, and XPRESS.237 9.5.3 GAMS.237 9.5.4 Solver and Premium Solver.238 9.5.5 Win QSB.238 9.5.6 MINOS.238 9.6 Summary. 239 X References. 239 Appendix-9 A LINGO: An Introduction.241 9A.1 Introduction.241 9A.2 Inputting Model in LINGO.241 9A.3 Solving the Model.243 9A.3.1 Solver Status Window.243 9A.3.2 LINGO Special Features.244 9A.4 Another Example.246 9A.4.1 Objective Function.246 9A.4.2 Constraints.247 9A.4.3 Complete LINGO Model.248 9A.4.4 Defining the Sets.249 9A.4.5 Inputting the Data.250 9A.5 LINGO Syntax.252 Appendix-9B MPL: An Introduction.253 9B.1 Introduction. 253 9B.2 Use of MPL.253 9B.3 Using Vectors and Indexes in MPL.255 9B.4 A Product-Mix Model with Three Variables.256 Appendix-9C GAMS: An Introduction.260 9C. 1 Introduction.260 9C.2 An Example.260 Appendix-9D Excel Solver: An Introduction. 264 9D.1 Introduction.264 9D.2 Solving Linear Programs with Solver.264 9D.2.1 Defining the Target Cell (Objective Function).266 9D.2.2 Identifying the Changing Cells (Decision Variables).266 9D.2.3 Adding Constraints.267 9D.2.4 Some Important Options.269 9D.2.5 The Solution..270 Appendix-9E Win QSB: An Introduction.273 9E. 1 Introduction.273 9E.2 Problem Solving with Win QSB. 273 9E.3 Reference. 275 10 Input Preparation and Model Solving.277 10.1 Introduction.277 10.2 Data and Data Collection. 277 10.3 Data Type.279 10.4 Data Preparation.280 10.4.1 Data Requirements. 282 10.4.2 Data Aggregation.283 10.5 Data Preprocessing.287 10.6 Model-Driven Data versus Data-Driven Model.292 XI 10.7 Model Solving.292 10.7.1 Excel Solver.293 10.7.2 LINGO and MPL.295 10.8 Summary. 304 Exercises.304 References.308 Appendix-10A Additional Problem-Solving Using LINGO.309 10A.1 Example 4.6 (Model 4.7). 309 10A.1.1 LINGO Code.309 10A.1.2 LINGO Solution.310 10A.2 A Transportation Model. 310 10A.2.1 LINGO in Algebraic Form. 311 10A.2.2 LINGO Solution Report.311 10A.2.3 LINGO Codes (Alternative).312 10A.2.4 LINGO Solution Report (Using Alternative Codes).312 10A.2.5 A Modified Transportation Model.313 10A.2.6 LINGO Solution Report (with Restricted Path).314 10A.3 Example 4.14 (Model 4.15).315 10A.3.1 LINGO in Algebraic Form.315 10A.3.2 LINGO Solution Report.316 10A.3.3 LINGO Codes (Alternative Form).316 10A.3.4 LINGO Solution Report (for Alternative Codes).317 10A.4 Example 3.6 (Model 4.1).318 10A.4.1 LINGO in Algebraic Form.318 10A.4.2 LINGO Model Statistics.318 10A.4.3 LINGO Solution.318 10A.4.4 LINGO Codes (Alternative Form).319 10A.4.5 LINGO Solution for Alternative Codes.319 10A.5 Example 5.3 (Model 5.2).320 10A.5.1 LINGO Codes.320 10A.5.2 LINGO Solution Report.321 10A.5.3 LINGO Alternative Codes.321 10A.5.4 LINGO Solution Report (for Alternative Codes).321 10A.6 Example 5.16.322 10A.6.1 LINGO Codes.322 10A.6.2 LINGO Solution Report.322 10A.7 Example 4.11 (Model 4.12).323 10A.7.1 LINGO Codes.323 10A.7.2 LINGO Solution Report.324 10A.8 Example 5.10 (Model 5.7).324 10A.8.1 LINGO Codes.324 10A.8.2 LINGO Solution Report.325 ,327 .327 .327 329 330 .331 331 332 332 333 333 .336 336 336 336 337 338 338 339 339 339 340 340 340 340 341 342 342 342 343 .344 .344 ,347 347 .347 355 365 ,374 375 .377 Output Analysis and Practical Issues. 11.1 Introduction. 11.2 Solutions and Reports. 11.2.1 Shadow Price. 11.2.2 Reduced Cost. 11.3 Sensitivity Analysis. 11.3.1 Changes in the Objective Coefficients. 11.3.2 Changes in the RHS Values. 11.3.3 Changes in the Constraint Coefficients. 11.3.4 Addition of New Product or Variable. 11.3.5 Sensitivity Analysis for Integer and Nonlinear Models. 11.4 Practical Issues and Tips. 11.4.1 Solutions to Goal Programming Problems. 11.4.2 Multi-Objective Optimization. 11.4.3 Reduction of Variables and Constraints. 11.4.4 Solutions and Number of Basic Variables. 11.4.5 Variables with No Restriction in Sign. 11.4.6 Negative RHS. 11.4.7 Scaling Factors in Modelling. 11.4.8 Linear vs. Nonlinear Relationships. 11.4.9 Non-Smooth Relationships. 11.4.10 Linear vs. Integer and Nonlinear Models. 11.4.11 Rounding for Integer Solutions. 11.4.12 Improved Initial Solutions. 11.4.13 Variable Bounds. 11.4.14 Management Issues in Solution Implementation 11.4.15 Gap between Solutions and Outcomes. 11.4.16 Nontechnical Report. 11.4.17 Special Cases in LP Models. 11.5 Risk Analysis. 11.6 Summary. Exercises. Basic Optimization Techniques. 12.1 Introduction. 12.2 Graphical Method. 12.3 Simplex Method. 12.4 Branch-and-Bound Method. 12.5 Summary. Exercises. Bibliography. X1U Section IV Practical Problems 13 Models for Practical Problems I. 381 13.1 Introduction.381 13.2 A Crop Planning Problem.381 13.2.1 Linear Programming Model.382 13.2.2 Goal Programming (GP) Model. 385 13.3 Power Generation Planning.387 13.3.1 Linear Programming Model.387 13.3.2 Multi-Objective Optimization Model.391 13.4 A Water Supply Problem.392 13.4.1 Linear Programming Model.393 13.4.2 Goal Programming Model.394 13.5 A Supply Chain Problem. 395 13.6 Coal Production and Marketing Plan.398 13.6.1 Multi-Objective Problem.403 13.6.2 Multi-Period Problems.403 13.7 General Blending Problem.404 13.8 Summary.409 References.409 14 Models for Practical Problems II.411 14.1 Introduction.411 14.2 A Combat Logistics Problem.411 14.3 A Lot-Sizing Problem.415 14.3.1 Finished Product Inventory.417 14.3.2 Raw Material Inventory.418 14.3.3 Total Cost Function per Year.419 14.4 A Joint Lot-Sizing and Transportation Decision Problem.420 14.5 Coal Bank Scheduling.423 14.5.1 Static Model.424 14.5.2 Dynamic Model.426 14.6 A Scaffolding System.427 14.7 A Gas-Lift Optimization Problem.429 14.8 Multiple Shifts Planning.432 14.9 Summary.434 References.435 15 Solving Practical Problems.437 15.1 Introduction.437 15.2 A Product Mix Problem.437 15.3 A Two-Stage Transportation Problem.443 15.4 A Crop Planning Problem.445 15.4.1 Constraint and Variable Reduction.448 15.4.2 Scaling the Model.450 15.4.3 Working with Solutions. 450 15.4.4 Multi-Objective Crop Planning Problem.451 XIV 15.5 Power Generation Planning Problem.452 15.5.1 Nlodel Vialidation.452 15.6 Gas-Lift Optimization 455 l5»7 SlllllUldry Appendix-15A Crop Planning Linear Programming Model.459
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spellingShingle	Sarker, Ruhul Amin Newton, Charles S. Optimization modelling a practical approach Modèles mathématiques Optimisation mathématique Mathematisches Modell Mathematical models Mathematical optimization Optimierung (DE-588)4043664-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd
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title	Optimization modelling a practical approach
title_auth	Optimization modelling a practical approach
title_exact_search	Optimization modelling a practical approach
title_exact_search_txtP	Optimization modelling a practical approach
title_full	Optimization modelling a practical approach Ruhul A. Sarker ; Charles S. Newton
title_fullStr	Optimization modelling a practical approach Ruhul A. Sarker ; Charles S. Newton
title_full_unstemmed	Optimization modelling a practical approach Ruhul A. Sarker ; Charles S. Newton
title_short	Optimization modelling
title_sort	optimization modelling a practical approach
title_sub	a practical approach
topic	Modèles mathématiques Optimisation mathématique Mathematisches Modell Mathematical models Mathematical optimization Optimierung (DE-588)4043664-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd
topic_facet	Modèles mathématiques Optimisation mathématique Mathematisches Modell Mathematical models Mathematical optimization Optimierung
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