This book consists of five parts with 26 chapters. Included at the end of each part is a chapter on Discussion, Extensions, and Exercises. In Part I, a framework for decision making is discussed and several models involving transportation, urban planning, and inventory control are presented. In Part 11, linear programming application models such as the diet problem, the caterer problem, the trim problem, assignment problem, activityanalysis problem and set covering problem are presented, as well as algorithms for the assignment problem and the set covering problem. In Part 111, the simplex algorithm, duality theory, sensitivity analysis and efficiency of the simplex algorithm are discussed. In Part IV, network problems such as maximal flow, minimal cost flow, traveling salesman, shortest route, PERT/CPM, Hamiltonian circuit, Chinese postman, and minimal spanning tree are presented, as well as algorithms for transportation, assignment, maximal flow, shortest route, traveling salesman and integer programming problems. In Part V, twoperson zero-sum and nonzero-sum games, decision trees, and Saaty's analytic hierarchy process are discussed. This is quite an interesting and unique textbook written for undergraduate students. The author states in the preface that he believes "undergraduate training in mathematics should move away from the current required calculus-based program to a more varied one that stresses the importance and modern applied areas contained in the mathematical decision sciences, as practiced by o p ons researchers and management scientists." The book is to "strengthen students' ab s to analyze decision situations," it "emphasizes the decision nature of problems" and moreover "challenges the instructors to motivate students to study variations of a problem under changing assumptions, and encourage students to use their knowledge and intuition in developing solution techniques."
It is not easy to write a good introductory text in mathematical decision sciences. However, it seems that the author has been quite successful in meeting his objectives in preparing this book. I find this to be an excellent first course book that introduces readers to an exciting area: mathematical decision sciences. The author's narrative style describes decision problems clearly and interestingly, which is a tribute to his long teaching experience. Readers can naturally participate in the decision making process with the author and are able to develop analytical skills while reading the book. The book discusses a number of interesting problems and algorithms taken from various books and thus readers are easily guided t o further studies. I find Part IV is a very good collection of network and related combinatorial problems and their algorithms.
Even though the heavy emphasis on linear programming models is a logical consequence of the cited purpose of the book, it would be better to also include dynamic programming models and stochastic decisions models such as queueing models, in order to be comprehensive. These are very important in many practical decision problems in industry and government.
Some chapters on Discussions, Extensions, and Exercises are somewhat lengthy. Chapter 21 in Part IV has actually more pages than the other three chapters put together in Part IV. It would be better if some subjects in Chapter 21 are included in these chapters