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CRITICAL PATH ANALYSES VIA CHANCE CONSTRAINED AND STOCHASTIC PROGRAMMING
NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST
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A question which combines statistics and linear programming considerations was first raised by G. Tintner Econometrica 282, 490-5, April 60. It concerns the distribution of optimum functional values when a linear programming problem has probabilistic constraints. It is proposed to accord a chance constrained programming formulation to this kind of problem and to deal with it in a way that bears on project scheduling of the kind that is usually associated with critical path analysis, for instance, in PERT. The main focus of this paper is on the statistical distributions of the project completion and subcompletion times. The question of total time distributions that we deal with can therefore be given a managerial policy flavor by assuming that, ab initio, a management is considering a contract for a certain project. The task sequences are known but the times are not known except in probability. Before contracting for a target completion date--with resulting delay penalties--this management would like to know the likely distribution of total times in order to decide whether to accept an offered contract or else bargain further on the completion dates, penalty rates and progress payments and prices.
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