Brief overview Preface Table of contents
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 Preface Table of contents
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A Published Review
David Pannell has
been a major player, in mathematical programming in Australia,
for a number of years, as one of the team, in Western Australia,
who developed the MIDAS family of whole farm models. This effort
involved working with a variety of people from different
disciplines. The outcome was a modelling system that is widely
accepted as a good representation of reality in the West
Australian wheat belt, both agronomically and economically. The
need to explain linear programming to a variety of people from
different disciplines must have influenced him in writing a book
on linear programming that makes the technique accessible to
non-specialists.
He particularly notes that this is the first book on Linear
programming to include "no coverage at all of the simplex
algorithm". Traditionalists may argue that this approach is
like Hamlet without the Prince of Denmark. They will ask how such
a complex technique can be approached and mastered except through
the established mathematical route? Pannell reminds readers of
Hirshfield's (1990) remark that "desktop computers have
brought a whole new class of analysts to the LP community.
...These people are familiar with LP but do not want to become
experts." This book is for them. Even an experienced user
will find that there is plenty to learn from it and indeed that
they do not much miss 'Hamlet'. The story goes with a swing
without the gloomy Dane soliloquising everywhere.
The plan of the book is straightforward. It begins with five
chapters that lead the reader through the basics of linear
programming then passes on to more advanced techniques. There is
a useful summary of key points at the end of each chapter. The
first chapter describes the typical structure of a linear
programming problem and its application. In the second chapter,
there is a careful exposition of the graphical solution approach.
This chapter is thorough and clear and anyone working through it
carefully will have a good intuitive grasp of linear programming.
This basis should enable them to understand what is happening
when a model is solved. The third chapter progresses to the
specifics of matrix construction in a helpful way that stresses
the importance of thinking clearly about the units used, a
frequent cause of grief. The description of a strategy for matrix
building should save the beginner from a lot of confusion. The
fourth chapter consists of a careful explanation of the output
from linear programming and its interpretation. Finally chapter
five concludes the introductory part of the book with a set of
examples. The hundred pages of the first five chapters are a
clear and concise introduction to linear programming that
certainly does not suffer from the lack of mathematical
complexity.
The remaining two hundred pages of the book take the reader
deeper into linear programming. Chapters deal with negative
coefficients and transfer rows, non-linear relationships, integer
variables and expositions of multiperiod and multiregional
models. A chapter of examples reinforces this material. The final
six chapters cover the interpretation of range and sensitivity
analysis, the representation of risk and uncertainty and chapters
on "Some complications", including unboundedness, and
"Debugging your model". Both of these are very helpful
expositions for the struggling modeller.
The book therefore deals with some sophisticated issues without
leaving linear programming. The author assumes that the target
audience of this book need to go no further into mathematical
programming. These readers will benefit by learning that a
non-linear relationship can be represented in linear programming.
They will also see that it is possible to handle, at least the
simpler integer problems, by manually seeking the best integer
solution near the continuous optimal. Similarly, the treatment of
risk and uncertainty shows the use of linear relationships to
cast light in these areas.
The final chapter of the book discusses some practical issues
with a good summary of the strengths and weaknesses of linear
programming. Three particular weaknesses cited are the high
information requirement, the dangers of misuse and the resources
needed to maintain a model. Pannell quotes the maintenance needs
of a large model as being half a person each year for a 400
column by 300 row model. This is a daunting amount of time and
effort and reinforces the need to get all the benefits possible
from the modelling system as a store of data and focus of
research.
The maintenance problem indicates that the non-mathematical
approach of this book does have some disadvantages. Explicitly
mathematical systems such as GAMS (referred to in chapter 11),
allow much more efficient data storage and management than are
possible in a matrix format. In GAMS the user begins by writing
the mathematical equations and never explicitly draws up a matrix
at all. Such systems also provide a choice of solvers for
non-linear and integer problems. Desktop programs have brought
basic linear programming to a new audience. Similarly, more
sophisticated approaches allow experienced practitioners to
advance to what were once unmanageable areas of analysis. It is
only fair to say they may also allow the novice to flounder in a
bottomless swamp of possibilities and over-sophisticated analysis
This book is intended for novices and they should exhaust its
possibilities before trying to go further. What is in this book
will take them a long way and cover a large part of all the
analysis that they will do with linear programming. Besides the
text, the book also contains a helpful disk of linear programming
software to work through the examples. The book is an excellent
introduction to linear programming, that most practitioners of
the art could read with profit. I shall certainly keep it close
at hand in future.
Nigel Hall, Australian Bureau of Agricultural and Resource
Economics, Canberra, Australia, 15 Feb 1997
From the Australian Journal of Agricultural and Resource Economics, 1997, Issue 3.