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- Title
STOCHASTIC PROGRAMMING WITH ASPIRATION OR FRACTILE CRITERIA.
- Authors
Geoffrion, Arthur M.
- 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 κ of payoff. In this paper the author's previous work on "hi-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 ease 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 κ.
- Subjects
STOCHASTIC programming; LINEAR programming; RANDOM variables; ALGORITHMS; PROBABILITY theory; MATHEMATICAL programming; MATHEMATICAL reformulation; MATHEMATICAL models of decision making; DECISION theory; MANAGEMENT science; QUADRATIC programming; MULTIPLE criteria decision making
- Publication
Management Science, 1967, Vol 13, Issue 9, p672
- ISSN
0025-1909
- Publication type
Article
- DOI
10.1287/mnsc.13.9.672