Multi-mode resource-constrained project scheduling with uncertain activity cost

The multi-mode resource-constrained project scheduling problem under uncertain activity cost (MRCPSP-UAC) has a wide range of applications in production planning and project management. We first build a new mixed-integer nonlinear programming (MINLP) model with the objective of minimizing the risk of project cost overrun, which provides a vehicle to obtain optimal solutions. To overcome the computational challenge of exact method for solving large instances, we devise a construction heuristic (CH) with a multi-pass greedy improvement procedure to obtain a feasible solution efficiently. To further improve solution quality, a hybrid CH and genetic algorithm (CH-GA) is developed with a custom fitness function to properly calibrate the quality of an individual. A comprehensive computational study is performed to examine the impact of various problem parameters on the optimal solutions, and the performance of our algorithms. Our hybrid CH-GA performs well for large instances with significantly less computational time than the exact method.