Integrated production planning and preventive maintenance in deteriorating production system
The traditional production planning model based upon the famous linear programming formulation has been well documented. However, the integration of preventive maintenance planning in the same model is a recent problem. This paper proposes an extended linear programming model as a hybrid approach for computing the optimum production plan with minimum total cost. The dual objective problem of production planning and maintenance is treated into a mixed integer linear program. This program is not only considering cases of multi-lines, multi-periods and multi-items but also taking into account the deterioration of the lines. This deterioration is represented in the model as a reduction of production lines capacities in function of the time evolution. Maintenance operations are supposed to provide lines in an operational state as good as new, i.e. with a maximum capacity. Through the study of the models limits, it is shown that the proposed approach can deal with a broader range of problems than that of Aghezzaf and Najid (2008) . An optimal relaxation technique based on the polyhedral theory is developed to improve the computational time and expand the limits of the proposed model. Also, a ‘‘Fix and Relax heuristic’’ is developed for complex problems. Their computation time and their difference are computed referring to the same lower bound and the same considerations as those presented by Aghezzaf and Najid. It is proved through more than 880 several simulations for each model with different capacities and different setup costs, that this approach can solve large size problems with moderate computational time and gap.