A Monte-Carlo ant colony system for scheduling multi-mode projects with uncertainties to optimize cash flows

Project scheduling under uncertainty is a challenging field of research that has attracted an increasing attention in recent years. While most existing studies only considered the classical single-mode project scheduling problem with makespan criterion under uncertainty, this paper aims to deal with a more realistic and complicated model called the stochastic multi-mode resource constrained project scheduling problem with discounted cash flows (S-MRCPSPDCF). In the model, uncertainty is sourced from activity durations and costs, which are given by random variables. The objective is to find an optimal baseline schedule so that the project's expected net present value (NPV) of cash flows is maximized. In order to solve this intractable problem, an ant colony system (ACS) algorithm is designed. The algorithm dispatches a group of ants to build baseline schedules iteratively based on pheromones and an expected discounted cost (EDC) heuristic. In addition, because it is impossible to evaluate the expected NPVs of baseline schedules directly due to the presence of random variables, the algorithm adopts Monte Carlo (MC) simulations to evaluate the performance of baseline schedules. Experimental results on 33 instances demonstrate the effectiveness of the proposed scheduling model and the ACS approach.