Brief overview Table of contents
A published review
Download latest softwareIntroduction to Practical Linear Programming
David
J. PANNELL
Agricultural
and Resource Economics, University of Western Australia, Nedlands
6907, Australia
Pannell, D.J. (1997). Introduction to Practical Linear Programming, Wiley Interscience, New York, 333 pp. ISBN 0-471-51789-5
Brief overview Table of contents
A published review
Download latest software
Preface
Although there are many books on linear programming (LP), I have long felt the need for a text with a different emphasis. New LP packages for microcomputers are extremely easy to use, making LP much more accessible and increasing its use by non-specialists. Hirshfeld (1990) has observed that desktop computing is bringing a new class of analysts to the LP community. These people are familiar with LP but they do not wish to become experts. New users include business managers, consultants, farmers, social scientists, government planners and applied economists. In order to make use of the computer packages these users do not need to understand the mathematics used to solve an LP model: the simplex algorithm (or one of its relatives). They only need to know how to prepare input, how to interpret output and how to deal with a number of problems which can arise. There has been, until now, no book which provides for all these needs in an easily understandable, non-mathematical way. The aim of this book is to fill the need for a text which stresses practical aspects of applying LP models in the real world without focusing on the underlying mathematical procedures.
This is not the first practically oriented text for LP, but I believe it is the first to include no coverage at all of the simplex algorithm. In its place are several sections which are far more important to LP practitioners but which are normally given scant attention, even in applied texts. These include detailed coverage of interpretation of LP output, the problems which can beset LP models (no feasible solution, unboundedness, degeneracy and multiple optimal solutions), techniques for testing the sensitivity of model solutions to changes and methods for debugging LP models. All these are explained in simple terms, with no reference to the simplex algorithm. The book covers in detail the skill of model construction, with particular attention paid to negative coefficients: an area of some difficulty for many students of the technique. There is also a discussion and some practical advice on how best to have an impact when developing and using an LP model in a real-world setting.
I have three target audiences: (a) students undertaking applied courses in linear programming, (b) individuals who have previously undertaken a mathematically oriented LP course who now wish to make practical use of the technique and (c) individuals who wish to teach themselves about LP. Throughout the book, explanations are kept simple and, where possible, given in several ways: diagrammatically, intuitively, algebraically and by reference to mental devices. There are many examples given as well as exercise problems with solutions at the back of the book. A degree of jargon is unavoidable but is carefully explained on first mention and included in a glossary.
The book proceeds through an introduction to LP concepts (Chapters 1 and 2), a guide to LP model construction and output interpretation (Chapters 3 to 9 and 13) and a range of topics related to real-world LP applications (Chapters 10 to 12 and 14). Here are the chapter contents in a little more detail: Chapter 1 describes the basic structure of an LP problem, gives examples of LP applications and briefly describes the steps in applying LP in the real world. In Chapter 2, graphical representation of simple models is used to instill an understanding of key concepts. Chapter 3 is a step by step presentation of the concepts necessary to build simple LP matrices. Chapter 4 covers the main output produced with every LP solution. Chapter 5 presents a number of examples to reinforce Chapters 3 and 4. Chapter 6 returns to matrix construction and deals with some of the more complex matrix structures involving negative coefficients and transfer rows. Chapter 7 presents specialized matrix structures for representing non-linear relationships, multi-period models and multi-region models. Chapter 8 contains further examples to reinforce Chapters 6 and 7. Chapter 9 explains a useful feature of LP: the ability to obtain range analysis which indicates the stability of the optimal solution. Chapter 10 covers the difficulties and complications which can arise when solving an LP model or interpreting its solution. Chapter 11 deals with the difficult task of ensuring that a model is free of errors. Chapter 12 stresses the importance of testing the sensitivity of a model to changes and suggests several approaches for doing this. In Chapter 13 I outline some methods for explicitly representing risk and uncertainty in an LP model. The book finishes in Chapter 14 with a discussion of practical issues not otherwise mentioned and a review of the strengths and weakness of LP.
It is intended that the book be self-contained and suitable for self- instruction, working progressively through starting with Chapter 1. For a briefer coverage of the material, a course could be based on Chapters 1 to 7 and 10 to 12. The essential chapters for a newcomer to LP are chapters 1 to 7. These contain the information most likely to be covered directly in formal courses on LP. Chapters 9 provides a deeper coverage of output interpretation, which may be skipped or covered only briefly in a short course. Chapters 10 to 12 are essential for any course with a practical orientation. Chapters 13 is somewhat specialized and perhaps more difficult than earlier chapters. Chapter 14 is relatively short and could reasonably be omitted from the formal presentations of a short course.
Even experienced LP users involved in implementing an LP model for a real- world problem will benefit from the information in the later chapters of the book; much of it is hard learned from practical experience. They will also find some ideas of value on matrix construction and output interpretation.
A number of people have contributed in one way or another during the writing of this book. I am especially grateful to Vanessa Stewart, Ian Moncrieff and Andrew Bathgate for their detailed criticisms and corrections to various drafts, to Amir Abadi, David Falconer, Nicole Free, Peter James, Ross Kingwell, Beryl Luke, Barbara Luyben, Lisa Mahoney, Carmel McGinley, David Morrison, Eddy Pol and Doug Sawkins for their various contributions, to the Department of Agricultural Economics at the University of Saskatchewan for hosting me during the study leave which I used to complete the book, to Elvis Costello and Andy Partridge for providing the music which fueled me through many late nights and to my wife Pauline and daughters Hannah and Rosie for their patience and for bearing a share of the sacrifices this effort required.
David J. Pannell
October 1995