Multistage Stochastic Programming with Recourse: The Equivalent Deterministic Problem

Multistage stochastic programming with recourse is defined recursively as a natural extension of two-stage stochastic programming with recourse. Some existing results for two-stage problems are extended to problems with $K + 1$ stages, where 1 K < + ∞, in the special case of a fixed technology matrix. These results generally involve characterization of the “equivalent deterministic problem”—showing, for example, that it has a convex objective function, a lower-semicontinuous convex objective function, a Lipschitzian objective function, or linear induced constraints.