Optimization of stochastic fluid model using perturbation analysis: A manufacturingremanufacturing system with stochastic demand and stochastic returned products

In this paper, a stochastic fluid model is used to study a manufacturing/ remanufacturing system composed by two parallel machines, a serviceable inventory, a remanufacturing inventory and customers who demand a stochastic quantity of product. Stochastic fluid model is adopted to describe the system and to take into account machine failure, stochastic demand, stochastic returned products and remanufacturing products. 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 stochastic fluid 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 stochastic returned products and stochastic demand.