Benders decomposition method for an integrated problem of production Lot-sizing and Scheduling

The main objective of the current work is to present mathematical model and a decision method for production planning issues of a manufacturing organization. It is therefore meant to integrate the medium term and the short term as two levels of decision. These consist in periodical planning with determining the intended produced quantity and scheduling the functioning of machines. It is worth noting that in the literature there exist only few works on the issue of integration because of the shortage of numerical results. Thus, the integrated model presented here allows us to take into consideration the scheduling constraints in the Lot-sizing model. A recent algorithm, based on a heuristic approach to find a production planning with a feasible schedule for each period, has recently been published in which the two levels of decision were applied. In this paper, some of these ideas are developed in order to get an optimal solution. For this, an exact algorithm of Benders' decomposition method is adopted to the integration problem. This has been proved efficient with reliance primarily on modeling view and the link between the two levels of decision and secondly on the numerical view.