Optimization Modelling A Practical Approach

Although a useful and important tool, the potential of mathematical modelling for decision making is often neglected. Considered an art by many and weird science by some, modelling is not as widely appreciated in problem solving and decision making as perhaps it should be. And although many operations research, management science, and optimization books touch on modelling techniques, the short shrift they usually get in coverage is reflected in their minimal application to problems in the real world. Illustrating the important influence of modelling on the decision making process, Optimization Modelling: A Practical Approach helps you come to grips with a wide range of modelling techniques. Highlighting the modelling aspects of optimization problems, the authors present the techniques in a clear and straightforward manner, illustrated by examples. They provide and analyze the formulation and modelling of a number of well-known theoretical and practical problems and touch on solution approaches. The book demonstrates the use of optimization packages through the solution of various mathematical models and provides an interpretation of some of those solutions. It presents the practical aspects and difficulties of problem solving and solution implementation and studies a number of practical problems. The book also discusses the use of available software packages in solving optimization models without going into difficult mathematical details and complex solution methodologies. The emphasis on modelling techniques rather than solution algorithms sets this book apart. It is a single source for a wide range of methods, classic theoretical and practical problems, data collection and input preparation, the use of different optimization software, and practical issues of modelling, model solving, and implementation. The authors draw directly from their experience to provide lessons learned when applying modelling techniques to practical problem solving and implementation difficulties.

INTRODUCTION Introduction General Introduction History of Optimization Optimization Problems Mathematical Model Concept of Optimization Classification of Optimization Problems Organization of the Book References Exercises The Process of Optimization Introduction Decision Process Problem Identification and Clarification Problem Definition Development of a Mathematical Model Deriving a Solution Sensitivity Analysis Testing the Solution Implementation Chapter Summary Exercises Introduction to Modelling Introduction Components of a Mathematical Model Simple Examples Analysing a Problem Modelling a Simple Problem Linear Programming Model More Mathematical Models Integer Programming Multi-Objective Problem Goal Programming Nonlinear Programming Chapter Summary Exercises MODELLING TECHNIQUES Simple Modelling Techniques I Introduction The Use of Subscripts in Variables Simple Modelling Techniques Special Types of LP Chapter Summary References Exercises Simple Modelling Techniques II Introduction Precedence Constraints Either-or Constraints K out of N Constraints must Hold Yes-or-No Decisions Functions with N Possible Values Mutually Exclusive Alternatives and Contingent Decisions Linking Constraints with the Objective Function Piecewise Linear Functions Nonlinear to Approximate Functions Deterministic Models with Probability Terms Alternate Objective Functions Constrained to Unconstrained Problem Simplifying Cross Product of Binary Variables Fractional Programming Unrestricted Variables Changing Constraint and Objective Type Conditional Constraints Dual Formulation Regression Model Stochastic Programming Constraint Programming Chapter Summary References Bibliography Exercises Modelling Large-Scale and Well-Known Problems I Introduction Use of the Summation Sign Use of the Subset Sign Network Flow Problems The Knapsack Problem Facility Location and Layout Production Planning and Scheduling Logistics and Transportation Chapter Summary References Exercises Modelling Well-Known Problems II Introduction Job and Machine Scheduling Assignment and Routing Staff Rostering and Scheduling Scheduling and Timetabling Problem Chapter Summary References Exercises Alternative Modelling Introduction Modelling under Different Assumptions Hierarchical Modelling: An Introduction Chapter Summary References MODEL SOLVING Solution Approaches: An Overview Introduction Complexity and Complexity Classes Classical Optimization Techniques Heuristic Techniques Optimization Software Chapter Summary References Appendix-9A: LINDO /LINGO Appendix -9B: MPL Appendix -9C: GAMS Appendix -9D: Solver Appendix -9E: Win QSB Input Preparation and Model Solving Introduction Data and Data Collection Data Type Data Preparation Data Preprocessing Model Driven Data vs. Data Driven Model Model Solving Chapter Summary References Exercises Appendix-10A: Additional Problem Solving using LINGO Output Analysis and Practical Issues Introduction Solutions and Reports Sensitivity Analysis Practical Issues and Tips Risk Analysis Chapter Summary Exercises Basic Optimization Techniques Introduction Graphical Method Simplex Method Branch and Bound Method Chapter Summary References Exercises PRACTICAL PROBLEMS Models For Practical Problems I Introduction A Crop Planning Problem Power Generation Planning A Water Supply Problem A Supply Chain Problem Coal Production and Marketing Plan General Blending Problem Chapter Summary References Models for Practical Problems II Introduction A Combat Logistics Problem A Lot Sizing Problem A Joint Lot-Sizing and Transportation Decision Problem Coal Bank Scheduling A Scaffolding System A Gas-Lift Optimization Problem Multiple Shifts Planning Chapter Summary References Solving Practical Problems Introduction A Product-Mix Problem A Two-Stage Transportation Problem A Crop Planning Problem Power Generation Planning Problem Gas Lift Optimization Chapter Summary References Appendix-A: Crop Planning LP Model