Analysing the impact of alternative network structures on resource-constrained schedules: Artificial and empirical experiments

Abstract

In this research, we investigate an extension of the resource-constrained project scheduling problem (RCPSP) with alternatives in the project structure, the so-called RCPSP with alternative subgraphs (RCPSP-AS). The RCPSP-AS consists of a selection subproblem to decide amongst the alternatives in the project structure and a scheduling subproblem to schedule the selected activities in the resulting project structure. In case of a high number of alternatives, however, the selection subproblem might become very complex. In this research, we therefore present a two-step procedure to reduce the complexity of the selection subproblem of the RCPSP-AS. First, we construct a set of high-quality schedules and, subsequently, we analyse the selected alternatives in this set of schedules. Based on two thresholds, defined as the schedule diversity and choice frequency thresholds, we aim at reducing the number of alternatives in the problem. In doing so, the selection subproblem becomes easier to solve thanks to the lower number of alternatives to choose from, and consequently, the solution procedure to solve the RCPSP-AS should now focus on the scheduling subproblem. However, the computational experiments show that both thresholds should be set with care since the low complexity of the selection subproblem might result in some side effects. More precisely, we investigate the impact of both thresholds on the quality of the final schedule as they impact the stop criterion and the size of the neighbourhood in a solution procedure. We have developed our approach based on empirical case studies and validated the results on a large set of artificial projects.