1st Edition

Optimization Modelling A Practical Approach

    502 Pages 96 B/W Illustrations
    by CRC Press

    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

    Biography

    Ruhul Amin Sarker, Charles S. Newton