|Title||Stochastic programming with multiple objective functions|
|Publisher||D.Reidel Publishing Company|
|Year of publication||1984|
|Reviewed by||Anatoly Zhigljavsky|
The book concerns various aspects of the multiple criteria decision making theory. It starts with quite a good survey on approaches to the deterministic multiple criteria optimization problem. Unlike this deterministic problem in its stochastic counterpart, the criteria as well as the functions determining the feasible domain are possibly random which means that these functions can be corrupted by a random error. Certainly, stochastic problems are generally more complicated and their statements are more diverse. There are not too many great ideas in this branch of applied mathematics, and in fact, to solve a stochastic multicriteria optimization problem, one normally reduces it to a sequence of either deterministic multicriteria problems or stochastic ones with a single criterion. Both ways as well as applications to some econometric problems are thorougly described in the volume. This basically constitutes the contents of the book. In spite of that the results included into the monograph book are not recent, they still did not lose their value. That is because the whole topic of multiply criteria decision making did not actively progress during the last 30 years.
The book is quite well written and might be helpful for those interesting in multiple criteria decision making. The publication of the book is certainly not a great event in applied mathematics but the book will find its place in a line of the books on the topic of multiply criteria decision making. Among these books it may be worthwhile to mention: Goicoechea A., Hansen D.R., Duckstein L. Multiobjective decision analysis with engineering and business applications, Wiley, 1982; Zeleny M. Linear multiobjective programming, Springer Verlag, 1974; Hansen P. (ed) Essays and surveys on multiply criteria decision making, Springer Verlag, 1982; Moulin H. The strategy of social choice, North Holland 1983; Sen A.K. Social choice theory, North Holland, 1986.
As for the purchase of the volume, I can recommend to do it to the libraries that have decided to have a representative collection of books on either multiple criteria decision making or stochastic programming or both.