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I am very pleased to have this book available. Algorithms for equitable resource allocation are extremely useful in a variety of practical application areas, but are not as widely known as they should be among engineering and operations research professionals. Much of the research has taken place in the last 20 years or so, and had been scattered among various journals. It has now been brought together into one coherent and convenient volume. Dr. Luss does an excellent job of motivating the various models and of describing the algorithms in a logical step-by-step fashion. The set of problems that can be solved using these lexicographic min-max algorithms is quite broad. Initially, they were developed to solve resource allocation problems in the manufacturing area. Specifically, they addressed the question of how to allocate electronic components to various product lines, when there was a shortage of components. This can be naturally extended to allocating other sorts of scarce resources (e.g. manpower, computing resources, funding). But what I find exciting is that these very same mathematical programming techniques can be directly applied to problems that seem totally unrelated. For example, they can be used to impute a traffic matrix for a packet communications network (such as the network operated by an Internet Service Provider). I wholeheartedly recommend this book to professionals – both in academia and in industry – in Operations Research, Management Science, Industrial Engineering, Telecommunications and Computer Science. -John G. Klincewicz
Mathematical models and methods for optimization enable resources of various kinds to be used ‘as best as possible’ under given constraints, and have been responsible for major advances in various fields, including control systems, operations research, and telecommunication networks. When there are multiple and competing objectives to be considered for optimization, the trade-off among the competing objectives introduces the new dimension of ‘fairness’ into the optimization. In such cases, the use of a single criterion for optimization is often inadequate and artificial. A particular form of posing multiple optimization criteria that captures a notion of fairness among competing objectives gives rise to the class of problems known as ‘lexicographic’ optimization, which goes beyond the usual minimax or maximin criterion to define the concept of ‘equitable’ optimization. Such equitable optimization is the subject of the book “Equitable Resource Allocation: Models, Algorithms, and Applications” by Dr. Hanan Luss.
The book is a clear and systematic exposition of lexicographic optimization. After introductory chapters on single-criterion optimization, the book discusses algorithms for the usual minimax (or maximin) criterion for dealing with multi-objective problems, and shows how algorithms for lexicographic optimization can be built up from those for the minimax (or maximin) criterion. The later chapters consider various extensions of the basic model to take account of substitutable resources and multi-period optimization. The book considers theory and algorithms for both continuous and discrete decision variables.
The book contains a variety of illustrative applications of the optimization models, drawn from the author’s long and distinguished research career at AT&T Labs and Bellcore/Telcordia. The material is organized in a clear and helpful manner among the chapters and within each chapter, and the writing is crisp and precise. A notable feature of the book is the neat classification of the various algorithms that are presented, making it a valuable compendium of optimization models and algorithms. The book will be a valuable text-book for an advanced course in optimization and a comprehensive reference for scientists and practitioners in operations research, engineering, telecommunications, and economics.
-K.R. Krishnan (Bellcore/Telcordia - Retired)