A hybrid projection method for resource-constrained project scheduling problem under uncertainty

Resource constraint project scheduling problem (RCPSP) is one of the most important problems in the scheduling environment. This paper introduces a new framework to collect the activities' duration and resource requirement by group decision-making, solve the RCPSP with variable durations, and obtain the buffer to protect the schedule. Firstly, the duration and resources of the project's activities are determined by a new expert weighting method. In the group decision-making, hybrid projection measure is introduced to construct the aggregated decision about some RCPSP parameters. The hybrid projection includes the projection, normalized projection, and bi-directional projection. In the second step, a RCPSP model is presented where the duration of activities can change within certain intervals. Thus, the problem is called the RCPSP with variable durations. The intervals for activities' duration and resource requirements are obtained from the group decision-making in the first step. Genetic algorithm and vibration damping optimization are applied to solve the RCPSP with variable durations. In the third step, the project's buffer is determined to protect the schedule. In this step, the intervals for activities' duration are converted into interval-valued fuzzy (IVF) numbers and the buffer sizing method is extended using IVF numbers. Finally, the presented framework is solved for a practical example and the results are reported.