Perturbation analysis for discrete flow model: optimization of a manufacturing-remanufacturing system

In this paper, a discrete flow model is used to study a manufacturing-remanufacturing system composed by two parallel machines, a serviceable inventory, a recovery inventory and customers who demand a constant quantity of product. The goal of this paper is to evaluate the optimal serviceable inventory level which allows minimizing the sum of inventory and lost sales costs. Perturbation analysis is applied to the discrete flow model to optimize the considered system. The trajectories of the serviceable inventory level are studied and the perturbation analysis estimates are evaluated. The unbiasedness of these estimates is proved and then they are implemented in an optimization algorithm which determines the optimal serviceable inventory in the presence of returned products.