Solving a Preemptive Project Scheduling Problem with Coloring Techniques

In this paper we describe an exact algorithm to solve a preemptive project scheduling problem with scarce resources. As most of the scheduling problems also the studied one is NP-hard. Many different approaches, such as mathematical programming, heuristics, simulating annealing, etc., have been presented to solve this class of intractable problems. In our approach we consider a graph-theoretical method based on new coloring techniques. In particular, given a disjunctive graph we examine the correspondences between an assignment of time windows (i.e. activities starting time and finishing time) and an assignment of colors to the activities of a project, defining when an exact weighted coloring is an optimal preemptive schedule. We present computational results on randomly generated test problems of the branch and bound algorithm proposed. From the results obtained emerges that the possibility to manage hard problems using new coloring techniques seems to be more efficient than others, referring in particular to the performances of the algorithm proposed.

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