Stochastic Programming

This book is devoted to the problems of shastic (or probabilistic) programming. The author took as his basis the specialized lectures which he delivered to the graduates from the economic cybernetics department of Leningrad University beginning in 1967. Since 1971 the author has delivered a specialized course on Shastic Programming to the gradu­ ates from the faculty of applied mathematics/management processes at Leningrad University. The present monograph consists of seven chapters. In Chapter I, which is of an introductory character, consideration is given to the problems of uncertainty and probability, used for modelling complicated systems. Fundamental indications for the classification of shastic pro­ gramming problems are given. Chapter II is devoted to the analysis of various models of chance-constrained shastic programming problems. Examples of technological and applied economic problems of management with chance-constraints are given. In Chapter III two-stage shastic programming problems are investigated, various models are given, and these models are qualitatively analyzed. In the conclusion of the chapter consideration is given to: the transport problem with random data, the problem of the determination of production volume, and the problem of planning the flights of aircraft as two-stage shastic programming problems. Multi-stage shastic programming problems are investigated in Chapter IV. The dependencies between prior and posterior decision rules and decision distributions are given. Dual problems are investigated.