Fuzzy resource-constrained project scheduling with multiple routes: A heuristic solution

The resource-constrained project scheduling problem (RCPSP) with multiple routes by considering flexible activities is one of important subjects in project scheduling problems. The ability to select an appropriate route for implementing the flexible activities is a rational reason for indicating more complexity of the problem relative to common RCPSP that attracted the attention of the researchers in the recent decade. On the other hand, due to lack of access to project crisp information, the needs to consider uncertainty concepts in the RCPSP will be significant. Hence, in this paper, a new fuzzy mixed integer nonlinear programming (MINLP) model is presented under uncertain conditions. A hybrid meta-heuristic approach is also proposed to minimize costs of project completion. In this approach, to generate high quality initial solutions, a heuristic algorithm is designed based on distribution rules. Then, to change and assign an appropriate route from available routes for flexible activities, a meta-heuristic algorithm is presented based on binary particle swarm optimization (PSO). Finally, to generate best solution from routes assigned by the binary PSO, a meta-heuristic based on genetic algorithm (GA) is proposed. To appraise the effectiveness of presented model, different test problems are solved by the proposed approach, and comparisons are provided with results obtained by the GA and PSO.