Optimal production planning for a manufacturing system: an approach based on PA

In this paper, a manufacturing system composed by a single-product machine, a buffer and a stochastic demand is considered. A discrete flow model is adopted to describe the system and to take into account the lost demands. The objective of this paper is to determine the optimal production planning taken into account service level. This optimal production planning minimizing the sum of production, inventory, and lost sales costs. Perturbation analysis method is used for optimizing the proposed system. Using the discrete flow model, the trajectories of production rate, buffer level and lost demands are studied and the perturbation analysis estimators are evaluated. These estimators are shown to be unbiased and then they are implanted in an optimization algorithm which determines the optimal production planning in the presence of service level.