Stochastic Programming with Aspiration or Fractile Criteria

The general linear programming problem is considered in which the coefficients of the objective function to be maximized are assumed to be random variables with a known multinormal distribution. Three deterministic reformulations involve, respectively, maximizing the expected value, the \alpha -fractile (\alpha fixed, 0 < \alpha < ½), and the probability of exceeding a predetermined level k of payoff. In this paper the author's previous work on "bi-criterion programs" is specialized to give an algorithm for routinely and efficiently solving the second and third reformulations. A by-product of the calculations in each case is the tradeoff-curve between the criterion being maximized and expected value. The intimate relationships between all three reformulations are illuminated, with the cumulative effect of considerably lessening the burden on the decision-maker to preselect with finality a particular value of \alpha or k.