Parallel machines scheduling problem with skilled operators in a potery handicraft firm

Parallel machines scheduling problems with resource consumption have been extensively studied because of their broad industrial applications. However, these systems, like any other system, are subject to deterioration. In this paper, we treat a parallel machine scheduling problem which is subject to deterioration effect and to resources constraints (manpower). The considered problem is a real problem of a handicraft pottery firm; where the process of a job requires a position in one of the identical parallel machines and manpower which is a craftsman. The craftsmen are skilled to process specific types of jobs, and machines deteriorate after processing a job. The problem is to find the best resources allocation to jobs and jobs assignment to machines, so that makespan is minimized. A mathematical programming model is formulated to solve the dynamic version of the problem. These scheduling problems are known to be NP-hard, especially the dynamic version, so the mathematical programming model is not able to give solutions in affordable computational time. For this reason, an approximate decomposition algorithm is developed to solve the considered problem.