zbMATH — the first resource for mathematics

Data envelopment analysis. A comprehensive text with models, applications, references and DEA-solver software. With CD-ROM. 2nd ed. (English) Zbl 1111.90001
New York, NY: Springer (ISBN 978-0-387-45281-4/hbk). xxxviii, 490 p. (2007).
Data Envelopment Analysis (DEA) is a quantitative tool for measuring and evaluating performance. The co-authors of the textbook are renowned researchers and experienced educators in this field: the first co-author, W. W. Cooper, is a founder (together with A. Charnes and E. Rhodes) of DEA, and the two other co-authors are involved in research and applications of DEA from its early beginning. The textbook presents the basic theoretical results and methods aiming at a broad audience of readers. An introductory undergraduate course in mathematics is sufficient to understand the material of the textbook.
The first five chapters of the book (about one third of the volume) constitute an introduction to DEA sufficient for its application to standard practical problems. Here a classical model by Charnes, Cooper and Rhodes (CCR) is introduced, and examples of application of both versions of the model (input oriented and output oriented) are presented. Relations between CCR model and Pareto optimality principle are discussed, as well as algorithmic implementation of CCR model based methods. Finally, the introduced methods are analyzed with respect to returns to scale.
In the subsequent chapters various generalizations and extensions of basic methods are considered. In Chapter 6 DEA methods are combined with subjective and expert evaluations expressed as assurance region and cone-ratio. In Chapter 7 the DEA model is extended to allow non-discretionary and categorical variables. Chapter 8 turns to “allocative efficiency” where inefficiency can emerge because costs and prices are not known precisely; such an analysis is important to avoid misleading efficiency measurement based on assumption on common prices and costs while actually they are different from enterprise to enterprise. Sensitivity of solutions with respect to data variations is considered in Chapter 9. In Chapter 10 the concept of super-efficiency is introduced enabling, e.g., to rank efficient decision making units, and to compare performance of two groups. The contents of the subsequent chapters is well reflected by their titles: 11. Efficiency change over time, 12. Scale elasticity and congestion, 13. Undesirable output models, and 14. Economies of scope and capacity utilization. Chapter 15 (A DEA Game) deals with consensus-making under multiple criteria, e.g., a fair division between teammates of a price won by the team. The case of noisy data is considered in the last chapter “Multi-Stage Use of Parametric and Non-Parametric Models”. Two appendices describe basic results on linear programming and duality, and the use of DEA solver whose CD is enclosed. The textbook includes a good collection of problems for classroom exercises. An advantage of these problems in self-depending study is the suggested responses immediately after the problems.
The first edition was published in 1999; see the review in Zbl 0990.90500.

90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90B50 Management decision making, including multiple objectives