Infinitesimal perturbation analysis for optimal production control in a reverse logistic system with different demands

This paper deals with the production control of a manufacturing/remanufacturing system within a closed loop reverse logistics system with machines subject to random failures and repairs. Three types of inventories are involved in this system. The manufactured and remanufactured products are stored respectively in the manufacturing and remanufacturing inventories. The returned products are collected in the recovery inventory and then remanufactured. The customer demands are constant and known. To describe the system, a stochastic fluid model is adopted and which take into account returned products and remanufacturing products. The objective of this paper is to evaluate the optimal inventory levels of the manufacturing and remanufacturing products that allow minimizing the total cost which is the sum of inventory and lost sales costs. Infinitesimal perturbation analysis is used for optimization of the considered system. The trajectories of the inventories levels are studied and the infinitesimal perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then they are implemented in an optimization algorithm which determines the optimal inventories levels.