Preselective strategies for the optimization of stochastic project networks under resource constraints

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Abstract
This article deals with a stochastic version of the optimization problem for project networks under resource constraints. In this, activity durations are assumed to be realized according to some joint probability distribution and the aim of optimization is to minimize the expected overall project cost (monotonically increasing with project duration). Certain strategies are known that constitute feasible solutions to this problem, the best studied of which are the so‐called ES strategies (“earliest start” with regard to fixed project structures). In this paper, a considerably broader class of strategies is introduced, namely preselective strategies. It is shown that this generalization, for which an algorithmic approach remains possible, preserves almost all the desirable behavior known for ES strategies. In particular, the number of “essential” strategies remains finite and even minimal optimum‐determining sets of such strategies can, in general, be characterized. Also, the analytic behavior is still proper and there is considerable “stability” to weak convergence of the joint distribution of activity durations as well as to a. e. convergence of the cost function. Last but not least, possible generalization to arbitrary regular cost functions is again imminent.