Optimal control for a remanufacturing reverse logistics system under buy-back policy

In remanufacturing reverse logistics system, the used products inventory is difficult to control because the supply of used products is uncertain. In this paper, Buy-back policy will be taken, i.e., used products will be bought back from end users. Moreover, in order to decrease the impact of the uncertainty on the whole reverse logistics system, an optimal control problem was considered based on a multi-echelon stochastic Inventory system. The object of optimal control is to determine the optimal buy-back price and the optimal remanufacturing quantity so that the cost of the whole system is minimum. The problem was formulated into a Markov Decision Process model with two state variables and two decision variables. By decomposing the model, the optimal policy of whole system can be obtained from the optimal policy of sub-problems. Finally, the dynamic programming algorithms for the optimal policies were proposed.