Project scheduling under resource and mode identity constraints: Model, complexity, methods, and application

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-staff scheduling, timetabling, and course 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 performed by assigning one or more of several individuals (resources) to each job. In this paper we consider the nonpreemptive variant of a resource-constrained project scheduling problem with mode identity. Mode identity refers to a generalization of the multi-mode case where the set of all jobs is partitioned into disjoint subsets while all jobs forming one subset have to be processed in the same mode. Both time and cost incurred by processing a subset of jobs depend on the resources assigned to it. This problem is a substantial and nontrivial generalization of the well-known multi-mode case. Regarding precedence and temporal 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 tailored parallel randomized solution approach called ramses into which both static and dynamic priority rules can be incorporated. The results of an extensive computational study on a practical application from the field of audit-staff scheduling indicate that ramses is capable of producing ‘good’ solutions in negligible amounts of time.