Constrained Project Scheduling with Activity Overlapping

The overlapping of activities is a common practice to accelerate the execution of engineering projects. This technique consists in executing in parallel two activities, normally executed in a sequential way, by allowing the downstream activity to start before the end of the upstream activity based on preliminary information. In this paper, we propose a constructive heuristic for the Resource-Constrained Project Scheduling Problem with Overlapping Modes (RCPSP-OM). Given a set of activities to execute, the RCPSP-OM consists in determining the order of execution in time of a set of activities so as to minimize the total project duration, while respecting precedence relations, resource constraints and overlapping possibilities. The heuristic implies that rework tasks related to overlapping are added to downstream activities and that the consumption of the resources is constant throughout the execution of the project (including rework). The method also considers that the possible overlapping modes for every couple of activities and the duration of rework tasks associated with every mode are known in advance. Results show that, when the objective consists in minimizing the project duration, the consideration of the costs associated to activity overlapping allows to significantly reducing the cost of reworks. On the other hand, when the objective consists in maximizing the gains related to the project execution, the search for the best trade-off between acceleration and increase of project costs enables to avoid losses.