Stochastic Programming with Aspiration or Fractile Criteria

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Abstract
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 α-fractile (α fixed, 0 < α < 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 α or k.

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