Stochastic Linear Programming with Recourse under Partial Information

Stochastic programming models with random variables with only incompletely-known distributions were up to now comparatively seldom analysed, although an attempt to declare probability distribution not always gives a satisfactory description of factors of influence in a decision model: “In any specific problem the selection of a definite probability distribution is made on the basis of a number of factors, such as the sequence of past demands, judgements about trends, etc. For various reasons, however, these factors may be insufficient to estimate the future distribution. As an example, the sample size of the past demands may be quite small, or we have reason to suspect that the future demand will come from a distribution which differs from that governing past history in an unpredictable way” (Scarf, 1958).