Chance Constrained Programming of the Machine Loading Problem with Stochastic Processing Times

M. Resh
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M. Resh: Bell Telephone Laboratories, Incorporated, Holmdel, New Jersey

Management Science, 1970, vol. 17, issue 1, 48-65

Abstract: The statistical model of a chance constrained variable which is the sum of stochastically independent random variables is considered, using the machine loading problem as an expository case. The resulting chance constrained statement, Pr {\sum n i =1 \sum x i k =0 a ik > H} n i =1 a' i x i \beta, where x i denotes the variable of the program and a ik and a' i denote the random variables. A formal mathematical analysis is carried out on the deterministic equivalent nonlinear problem with solutions over a set that may be nonconvex. The mathematical results are then used in stating and evaluating a linear approximation, thus enabling one to state the problem using a generalized transportation problem formulation.

Date: 1970
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