Optimization Modelling A Practical Approach

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