Solving a new mixed integer non-linear programming model of the multi-skilled project scheduling problem considering learning and forgetting effect on the employee efficiency

In this paper, we propose a new mathematical programming model to tackle the multi-skilled project scheduling problem. Considering the effect of learning and forgetting on the human skills, an exponential learning function has been developed by assuming the efficiency of employees performing activities to be dynamic. Taking the nonlinearity of the function into account, we use separable programming to acquire an appropriate linear approximation for it. Moreover, the proposed model allows us to relax some of the binary variables linearly without any modifications. At the end, the final model is tested with some instances and is solved by CPLEX in order to confirm the implemented simplifications and linear approximation. After examination of the results and checking the constraints, the validity of the model and its modifications have been approved. Regarding NP-hardness of the MSPSP, this process can be a prominent step for developing meta-heuristic algorithms to solve real world problems.