Information Structures in Stochastic Programming Problems

Problems of multi-stage decision under uncertainty are usually classified into "stochastic" and "adaptive" ones, depending on whether the decision maker does or does not know the relevant probability distribution. If the Bayesian approach is taken, then, in the adaptive case, the decision maker is assumed to know the prior distribution of certain parameters. It is shown in the paper that the adaptive case is then reducible to the stochastic one. The problems can also be classified according to the kind of information (memory) available to the decision maker. In the paper, optimal policies and the expected gains they yield, are determined for some important classes of "information structures." In cases in which added information does not increase the expected gain, a sufficient information structure is specified.