An enumeration algorithm for the Max-NPV problem with linear time-dependent cash flows

We study the unconstrained project scheduling problem with discounted cash flows where the net cash flows are assumed to be linear dependent on the completion times of the corresponding activities. The objective is to schedule the activities in order to maximize the net present value (npv) subject to the precedence constraints and a fixed deadline. We present an efficient enumeration algorithm which solves the problem in a reasonable time. In order to illustrate the efficiency of the algorithm, we validate it on a randomly generated problem set.