A Decomposition Method for the Multi-Mode Resource-Constrained Multi-Project Scheduling Problem (MRCMPSP)

Multi-Mode Resource-Constrained Multi-Project Scheduling Problems (MRCMPSP) with large solution search spaces cannot be optimized in an acceptable computation time. In this paper, we have focused on decomposition strategies for such large scale problems. Based on literature review a time-based decomposition approach was adopted for the present problem. With time-based decomposition approaches a schedule is divided into several time periods. All activities in a time period describe an independent problem, termed as a sub-problem. Due to the independent optimization of these sub-problems project information regarding the relationships among activities in different time periods is not considered. This loss of information has a negative impact on the overall solution quality. We developed a decomposition strategy to improve the interactions between the sub-problems for a better target performance while reducing the computation time. Based on an initial solution the sub-problems are created and sequentially optimized in a concept similar to rolling horizon heuristics. We introduce a transition stage with a constant and a variable component at the end of each partial schedule to improve the interactions among sub-problems and thus taking the volatile nature of the examined problems into account. In comparison, our approach proved to provide significant improvements in runtime and target performance.