This paper investigates the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). In this scheduling problem, there exist alternative ways to execute subsets of activities that belong to work packages. One alternative execution mode must be selected for each work package and, subsequently, the selected activities in the project structure should be scheduled. Therefore, the RCPSP-AS consists of two subproblems: a selection and a scheduling subproblem. A key feature of this research is the categorisation of different types of alternative subgraphs in a comprehensive classification matrix based on the dependencies that exist between the alternatives in the project structure. As the existing problem-specific datasets do not support this framework, we propose a new dataset of problem instances using a well-known project network generator. Furthermore, we develop a tabu search that uses information from the proposed classification matrix to guide the search process towards high-quality solutions. We verify the overall performance of the metaheuristic and different improvement strategies using the developed dataset. Moreover, we show the impact of different problem parameters on the solution quality and we analyse the impact of distinct resource characteristics of alternatives on the selection process.

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In the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS), we model alternative execution modes for work packages in the project. In contrast to the traditional RCPSP, the project network consists of different alternative work packages. To that purpose, the scheduling problem selects the best possible alternatives for the construction of the baseline schedule. On top of that, several back-up schedules are created in order to cope with unexpected changes along the project progress. In the presence of uncertainty, we can then switch between these alternative schedules at different decision moments in order to bring the project back on track. The alternative schedules are combined in a set of schedules that should be constructed by the project manager prior to project execution. We present a computational experiment to investigate the ability of using such a set of schedules in the presence of uncertainty during project execution. The experiments indicate that using a set of schedules outperforms the use of a single schedule, even when the uncertainty level is relatively low. The results also show that the composition of this schedule set is important. Therefore, a degree of schedule similarity is proposed to analyse this composition, and results show that a mix of similar and dissimilar schedules performs best. Finally, we show that the solution quality of each schedule in the set has an impact on the performance of the schedule switches given the project disruptions.

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