On maximizing the net present value of a project under renewable resource constraints

In this paper we study the resource-constrained project-scheduling problem with discounted cash flows. Each activity of this resource-constrained project-scheduling problem has certain resource requirements and a known deterministic cash flow that can be either positive or negative. Deterministic cash flows are assumed to occur over the duration of the activities. Progress payments and cash outflows occur at the completion of activities. The objective is to schedule the activities subject to a fixed deadline to maximize the net present value subject to the precedence and resource constraints. With these features the financial aspects of project management are taken into account. We introduce a depth-first branch-and-bound algorithm that makes use of extra precedence relations to resolve a number of resource conflicts and a fast recursive search algorithm for the max-npv problem to compute upper bounds. The recursive search algorithm exploits the idea that positive cash flows should be scheduled as early as possible while negative cash flows should be scheduled as late as possible within the precedence constraints. The procedure has been coded in Visual C++, Version 4.0 under Windows NT, and has been validated on two problem sets.