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Resource constrained project scheduling problem with multiple routes for flexible project activities (RCPSP-MR) is a generalization of the RCPSP, in which for the implementation of each flexible activity in main structure of the project, several exclusive sub-networks are considered. Each sub-network is regarded as a route for the flexible activity. The routes are considered for each flexible activity that are varied in terms of: 1) Number of activities required to execute; 2) Precedence relationship between activates; 3) Allocation of different renewable and nonrenewable resources to each activity; and 4) Effectiveness on the duration and cost of project completion. In this paper, a new mathematical formulation of RCPSP-MR is firstly presented. Then, two solving approaches based on particle swarm optimization (PSO) and genetic algorithm (GA) are proposed to minimize costs of project completion. To evaluate the effectiveness of these proposed approaches, 50 problems (in very small, small, medium, and large-sized test problems) are designed and then are solved; Finally, comparisons are provided. Computational results show that the proposed GA generates high-quality solutions in a timely fashion.

Designing a resource-constrained project scheduling model considering multiple routes for flexible project activities: meta-heuristic algorithms