This book is devoted to the problems of stochastic (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 Stochastic 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
stochastic pro- gramming problems are given. Chapter II is devoted to
the analysis of various models of chance-constrained stochastic
programming problems. Examples of technological and applied economic
problems of management with chance-constraints are given. In Chapter III
two-stage stochastic 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
stochastic programming problems. Multi-stage stochastic programming
problems are investigated in Chapter IV. The dependencies between prior
and posterior decision rules and decision distributions are given. Dual
problems are investigated.
