Keywords: resource-constrained project scheduling, stochastic project scheduling, robust scheduling.

This paper presents a new scheduling model for resource-constrained projects with uncertain activity durations. The model produces "robust" resource-feasible schedules which are totally immune against uncertainties in the activity durations. In the presented approach, it is assumed that each activity duration is a random variable with a beta distribution. Theoretically the robust schedule searching process is formulated as a mixed integer linear programming problem. The proposed model is based on the so-called "forbidden set" concept. The output of the model is the set of the optimal conflict repairing relations. We will demonstrate by simulation that, according to the "robust nature" of the central limit theorem, the distribution of the makespan will be nearly normal in the optimal schedule. The presented probabilistic (density function oriented) approach can be replaced by a possibilistic (membership function oriented) one, because the model invariant to the "real meaning" of the duration estimations. In order to illustrate the essence of the proposed approach detailed computational results for two problems are presented. The first problem is a small motivating example, the second problem is a larger project instance presented firstly by Golenko-Ginzburg and Gonic [1] and discussed by several authors in the literature. To generate the optimal solutions a state-of-the-art mixed integer linear programming solver (CPLEX) was used.

1

D. Golenko-Ginzburg, A. Gonik, "Stochastic network project scheduling with non-consumable limited resources", International Journal of Production Economics, 48, 29-37, 1997. doi:10.1016/S0925-5273(96)00019-9

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