Multi-mode resource-constrained project scheduling problems with non-preemptive activity splitting

In this paper, we explore the difference between preemption and activity splitting in the resource-constrained project scheduling problem (RCPSP) literature and identify a new set of RCPSPs that only allows non-preemptive activity splitting. Each activity can be processed in multiple modes and both renewable and non-renewable resources are considered. Renewable resources have time-varying resource constraints and vacations. Multi-mode RCPSP (MRCPSP) with non-preemptive activity splitting is shown to be a generalization of the RCPSP with calendarization. Activity ready times and due dates are considered to study the impact on project makespan. Computational experiments are conducted to compare optimal makespans under three different problem settings: RCPSPs without activity splitting (P1), RCPSPs with non-preemptive activity splitting (P2), and preemptive RCPSPs (P3). A precedence tree-based branch-and-bound algorithm is modified as an exact method to find optimal solutions. Resource constraints are included into the general time window rule and priority rule-based simple heuristics are proposed to search for good initial solutions to tighten bounding rules. Results indicate that there are significant makespan reductions possible when non-preemptive activity splitting or preemptions are allowed. The higher the range of time-varying renewable resource limits and the tighter the renewable resource limits are, the bigger the resulting makespan reduction can be.