Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows

In this paper, the multi-mode resource constrained project scheduling probl em with discounted cash flows is considered. The objective is the maximizat ion of the net present value of all cash flows. Time value of money is take n into consideration, and cash in- and out-flows are associated with activi ties and/or events. The resources can be of renewable, nonrenewable, and do ubly constrained resource types. Four payment models are considered: lump s um payment at the terminal event, payments at prespecified event nodes, pay ments at prespecified time points and progress payments. For finding soluti ons to problems proposed, a genetic algorithm (GA) approach is employed, wh ich uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an exampl e problem. Sensitivity analyses are performed over the mark up and the disc ount rate. A set of 93 problems from literature are solved under the four d ifferent payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is c ompared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it.