The resource renting problem subject to temporal constraints

We introduce a project scheduling problem subject to temporal constraints where the resource availability costs have to be minimized. As an extension of known project scheduling problems which consider only time-independent costs, this problem includes both time-independent procurement costs and time-dependent renting costs for the resources. Consequently, in addition to projects where all resources are bought, we can deal with projects where resources are rented. Based on the enumeration of a finite set of schedules which is proved to contain an optimal schedule, we develop a depth-first branch-and-bound procedure. Computational experience with a randomly generated test set containing 10,800 problem instances is reported.