A steepest ascent approach to maximizing the net present value of projects

We study the scheduling of projects subject to general temporal constraints between activities such that the project net present value is maximized. The proposed algorithm is based on a first-order steepest ascent approach, where the steepest ascent directions are normalized by the supremum norm. In each iteration, the procedure ascends from a vertex of the feasible region to some non-adjacent vertex, which leads to a considerable speed-up compared to standard line-search. In an experimental performance analysis, we compare previous solution methods from literature to the algorithm presented in this paper. On the basis of two randomly generated test sets, the efficiency of the steepest ascent approach is demonstrated. Problem instances with up to 1000 activities can be solved in less than one second on a personal computer.