Capacity expansion—analysis of simple models with applications, by John Freidenfels, North Holland, 1981, 291 pp. Price: $39.50

North Holland, 198 1, 29 1 pp. Price: $39.50. This excellent book on capacity expansion planning has been written by one of the researchers working on these problems at Bell Telephone Laboratories. Not surprisingly, several of his examples come from the field of communications, and they reveal quite clearly why Bell Labs has taken such an interest in this area. The cost involved in these decisions is tremendous. Equally important is the outcome in the form of a smoothly functioning, high quality communication network of sufficient capacity. Seen against this background, the book by John Freidenfels provides impressive evidence of the very real contributions that operations research techniques have made towards the solutions of these problems. After an introductory chapter, Chapter 2 contains an extensive discussion of the net worth criterion, comparing it with the internal rate of return approach. The influence of uncertainty and inflation is also examined. Chapters 3 and 4 deal with the linear deterministic demand case for a variety of capacity cost functions, and with dynamic programming. The nonlinear demand case, discussed in Chapter 5 , is, of course, more complicated; apart from dynamic programming, special attention is paid to the case of quasilinear exponential demand. In Chapters 6 and 7, the model is extended to allow for different types of capacity and for uncertain demand, respectively; the case in which demand is generated by a simple stochastic process receives special attention. Chapter 8 deals with congestion cost, and Chapter 9 with blockage cost; both these topics are of immediate relevance to the telephone network design problem treated in detail in Chapter 10. The final chapter contains a brief discussion of other capacity expansion models, many of which are of more combinatorial nature. As mentioned above, this is an excellent book. The exposition is very clear with many examples, and the book is suitable for independent self-study. It is particularly appealing to find how a few basic ideas and techniques are stretched further and further, until they can cope with (reasonable approximations of) very complicated real-life problems. As Donald Erlenkotter, whose strong influence on the field is reflected through the many references to his work, points out in his foreword, this is particularly true for a technique such as dynamic programming. Its full power is demonstrated here in a very convincing manner. The only criticism that one might have of the book is that the author obviously feels more at ease with probabilistic models than with mathematical programming formulations. Thus, it is only in the last chapter that we are cautiously informed about the pros and cons of integer programming as opposed to linear programming. This is in strange contrast with the fairly advanced ideas from probability theory such as the use of the Laplace transform that readers are supposed to have mastered before they start reading the book. In that sense, the presentation is unbalanced, and this is particularly evident in the last chapter where several important ideas from capacity expansion models with a more combinatorial flavor are presented in a rather haphazard manner. A second edition would benefit from further development of this latter area. If that expansion is planned carefully, the ultimate result should be the definitive book on this topic for some time to come.