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A recurring problem in project management involves the allocation of scarce resources to the individual jobs comprising the project. In many situations such as audit scheduling, the resources correspond to individuals (skilled labour). This naturally leads to an assignment type project scheduling problem, i.e. a project has to be processed by assigning one of several individuals (resources) to each job. In this paper we consider the nonpreemptive variant of a resource-constrained project job-assignment problem, where job durations as well as costs depend upon the assigned resource. Regarding precedence relations as well as release dates and deadlines, the question arises, to which jobs resources should be assigned in order to minimize overall costs. For solving this time-resource-cost-tradeoff problem we present a hybrid brand and bound/dynamic programming algorithm with a (rather efficient Monte Carlo type) heuristic upper bounding technique as well as various relaxation procedures for determining lower bounds. Computational results are presented as well.
Andreas Drexl (Sun,) studied this question.