In this paper, we present an extension of the classical Resource Constrained Project Scheduling Problem (RCPSP). We present a new type of resource constraints in which staff members are involved. We present a new model where staff members can have several skills with different proficiency, i.e., a staff member is able to perform more than one kind of activity as well as the time need is complete the task assign depends on the staff individual skill. We call this model the Weighted-Multi-Skill Project Scheduling Problem (WMSPSP). In our model, an activity has specific skill requirements that must be satisfied. To solve this problem, we propose a lower bound that uses a linear programming scheme for the RCPSP.
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