Critical Path Analyses Via Chance Constrained and Stochastic Programming

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Abstract
Chance-constrained programming methods are applied to examine some statistical properties of PERT networks. Using duality, the PERT method is shown to be equivalent to use of the crudest linear decision rule and the confidence or lack thereof in meeting constraints is explicitly presented. The distribution of completion times = Tintner's stochastic programming follows easily and may often be multimodal, contrasting with erroneous central limit theorem usages in the literature. Possible extensions and developments of PERT using more adequate chance-constrained models and techniques are suggested and will be presented elsewhere.

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