An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem

In this paper a branch-and-bound procedure is described for scheduling project activities subject to precedence and resource constraints, where activities can be preempted at any discrete time instant and where the objective is to minimize the project duration. The procedure is based on a depth-first solution strategy in which nodes in the solution tree represent resource and precedence feasible partial schedules. Branches emanating from a parent node correspond to exhaustive and minimal combinations of activities, the delay of which resolves resource conflicts at each parent node. A precedence based lower bound and several dominance rules are introduced in order to restrict the growth of the solutions tree. The solution procedure has been programmed in the C language and extensive computational experience is reported.