130 Book Reviews

domestic factors in particular cases, this area is not given the weight one suspects it deserves. In fairness, this weakness is in no way peculiar to Brams' work.

The illustrative analysis offered in the book is all post hoc, perhaps reflecting the political scien- tist's quest for general understanding as opposed to OR's concern for helpful immediate recom- mendations. On the face of it indeed, Brams' examples may appear somewhat tired: the deter- rence episodes analyzed are the Good Old Cuban Missile Crisis and the 1973 U.S. alert during the Yom Kippur War. However, such an impression would be unfair. The book does not simply offer up the same old models applied to the same old examples. For example, though the discussion of the Cuban crisis starts with the well-known Chicken model, Brams is anxious to explore other possibilities, including that of an 'honourable' at- tack on Cuba actually being the most highly-pre- ferred outcome for the U.S. The construction and testing of alternative models for events is an al- together valuable hallmark of Brams' approach. His extensions of the simple 2 X 2 modelsmpar- ticularly the sequential move-by-move analy- s e s - a r e well explained and instructive. Brams also pays attention to the possibility of the 'games' being perceived differently by those involved, though only in a fairly limited way. Several cases provoke discussion of what happens if preferences are misperceived: however, there is no attempt to embrace the not ion that those involved might construe the issues at stake in quite different terms.

Altogether, those interested in Game Theory, and in the analysis of international policy gener- ally, will find this book well worth reading. Com- paring the Brams of 1985 with the Schelling of 1960, it is hardly Brains' fault that one is left with a slight feeling of disappointment. Have we really accomplished so little new in the last twenty-five years?

Peter BENNET University of Sussex

Brighton, United Kingdom

Reference

Schelling, T.C. (1960), The Strategy of Conflict Harvard Uni- versity Press, Cambridge, MA.

Saul I. GASS

Decision Making, Models and Algorithms: A First Course

Wiley, New York, 1985, xvi + 412 pages, £34.25

The problem with this delightful book is defi- ning its audience. It is Saul Gass' belief that "undergraduate training in mathematics must move away from the current required calculus- based program to a more varied one that stresses the important and modern applied areas con- tained in the mathematical decision sciences, as practised by operations researchers and manage- ment scientists". So he has written a marvellous book to further this aim .. . but who for? Accord- ing to his preface, there is a simple answer to this: he has written for undergraduates, junior and senior levels, the text being a basis for a one semester course. That being so, the price--which I accept as fair for such a beautifully produced book--effectively rules out its intended audience, at least in so far as this side of the Atlantic is concerned.

Moreover, I am not so sure that I would recom- mend its use as a text-book. The demands made of the student vary too much from chapter to chapter. There is no increasing progression from 'easy to hard' as one reads the book: rather there are wild oscillations of difficulty, both in content and pre- Sentation. Chapter 1 begins easily enough, but Chapter 2 moves rapidly into a fairly abstract discussion of modelling, long before the reader has met enough examples of modelling to give body to the arguments. Examples come in the next few chapters in the form of various transportation and LP models. These are developed beautifully clearly, using doubly subscripted x ' s in the alge- bra. If the reader is expected to follow these examples--and I can think of few with basic mathematics who could no t - -why is it necessary in Chapter 10 to develop an LP model of a furniture production problem with pictorial sub- scripts of bull's heads, glue pots, etc. to denote leather, glue and various other resource con- straints? Similarly I cannot imagine any reader of this book needing the pictorial use of 'stop signs' to explain single variable constraints in Chapter 12. True, Saul Gass wrote Chapter 12 for the ' true beginner', but the true beginner would not get that far. By Chapter 16, we are back in an entirely

Book Reviews 131

algebraic presentation, albeit a brilliantly clear one, of the Simplex method. I could go on, but I won't. I think I have conveyed my point.

Despite these comments I do think that this is a marvellous book: it is just not a text-book, What it is, I think, is an outstanding teaching resource. I, like most academic OR teachers, have to teach courses at very different levels: third year mathematicians, second year social scientists, nat- ural scientists opting for a ' fun' subsidiary, and so on. I need thought-provoking, teasing examples at all these levels, and this book is full of them. Furthermore, I am heavily involved in an initiative in the UK to introduce decision mathematics into the sixth-form curriculum. At last I have a book to recommend to teachers that both conveys the excitement of the subject and gives them ways to teach it.

As a reviewer I have been remiss in not describ- ing the topics that are covered. Basically, they are LP as far as the simplex method, transportation and assignment; network flows and simple combi- natorial problems, including an introduction to the TSP; and very brief coverage of game theory, decision trees and Saaty's AHP method. However, each section ends with a chapter of discussion and extensions which relate these topics to many other areas of OR.

Finally, may I pay tribute to Saul Gass' style. It conveys so much good humour and love of OR that, for that reason alone, I would recommend the book. For teachers everywhere here is a superb book.

Shnon FRENCH Department of Decision Theory

University of Manchester Manchester M13 9PL, United Kingdom

Paul N. FINLAY

Mathematical Modelling in Business Decision- Making

Croom Helm, London, 1985, i x + 3 0 2 pages, £19.95

This book is an introduction into mathematical modelling worth reading for both managers and business students. Operational Researchers can use it as a birthday-present for those managers who see no point in a mathematical approach to business problems.

The author, lecturer in the depar tment of management studies at the University of Lough- borough, states that in schools mathematics is almost taught as a philosophy, in which dry manipulations of abstractions are carried out de- void of almost any apparent practical purpose. This is a great pity since mathematics can also be used to cover a more practical area of concern, in which symbols are used as identifiers of everyday objects and concepts; the book is a demonstration of this way of handling mathematics.

The first part of the book is an introduction to the methodology of mathematical modelling. The different ways of thought of managers and model builders, their operating in two different cultures, with their own goals and methods, is clearly described in Chapter 7: "The manager-modeller interaction". The chapter on validation, t h e pro- cess of ensuring a model's appropriateness to the real world problem is essential in model building.

The second part starts with "Guidelines for mathematical modelling". The author gives twenty-two propositions concerning the modelling as such, as well a the acceptability of the model. The second kind of propositions is very important for the OR-specialist in " the field". Other subjects in this part of the book are financial planning models, investment problem, queuing, simulation, stock control, linear programming and forecast- ing. According to the aim of the book the subjects are treated on a managerial level, not on a special- ist's level.

The third part deals with the next steps for both the manager and the modeller on what might be the personal developments necessary to ad- vance the use of modelling.

Finally we remark that each chapter ends with a summary and a proposal for further reading.

B. van der VEEN Ehzdhoven University of Technology

Eindhoven, Netherlands

A.J. Hughes HALLETT

Applied Decision Analysis and Economic Be- haviour

Volume 3in" Advanced Studies in Theoretical and Applied Econometrics, Martinus Nijhoff, Dor- drecht, 1984, ix + 360 pages, Dfl.130.00