Optimization Modelling: A Practical Approach

ISBN-13: 9781420043105 / Angielski / Twarda / 2007 / 502 str.

Ruhul Amin Sarker; Charles S. Newton

Opis

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.

Spis treści

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

O autorze

Ruhul Amin Sarker, Charles S. Newton