An optimal procedure for the resource-constrained project scheduling problem with discounted cash flows and generalized precedence relations

In this paper, we consider the resource-constrained project scheduling problem (RCPSP) with discounted cash flows and generalized precedence relations (RCPSPDC-GPR). The RCPSPDC-GPR extends the RCPSP to (a) arbitrary minimal and maximal time lags between the starting and completion times of activities and (b) the non-regular objective function of maximizing the net present value of the project with positive and/or negative cash flows associated with the activities. To the best of our knowledge, the literature on the RCPSPDC-GPR is completely void. We present a depth-first branch-and-bound algorithm in which the nodes in the search tree represent the original project network extended with extra precedence relations which resolve a number of resource conflicts. These conflicts are resolved using the concept of minimal delaying modes, which is an extension of the notion of minimal delaying alternatives originally developed for the RCPSP. An upper bound on the project net present value as well as several dominance rules are used to fathom large portions of the search tree. Extensive computational experience on a randomly generated benchmark problem set is reported.