Statistical Decision Analysis of a Linear Programming Problem with a Stochastic Objective Function

摘要

A linear programming problem is considered where the constraints are deterministic and the criterion function is a random variable. This stochastic linear programming problem is formulated as a statistical decision problem. When action is to be taken on the basis of a prior distribution of the criterion variable, or on the basis of its distribution posterior to a sample, the decision problem reduces to a standard linear programming problem. Solutions for expected value of perfect information and expected value of sample information are obtained by several procedures. Extreme point solutions of the linear inequality constraints, regarded as the set of alternative solutions available to the decision maker, are used as input to a Monte Carlo integration procedure and as input to a numerical integration procedure. Solutions found by standard algorithms are also used as input to a numerical integration procedure. (Author)