Minimizing Costs of Resource Requirements in Project Networks Subject to a Fixed Completion Time

We consider the problem of minimizing the resource costs in a project network N_o subject to a time limit for the completion of N_o, when resource requirements per activity and costs for obtaining resources are independent of time. Our results show that the optimum is determined for all possible resource requirements and costs by certain sets of “feasible structures,” which are networks that extend the precedence relation of N_o and respect the given time limit. We characterize the least such sets, and give methods for determining them as well as for determining the optimum. Furthermore, we establish duality relations with the problem of scarce resources (minimizing project duration subject to limited resources) and characterize all “essentially different” problems.