Inventory optimization of manufacturing/remanufacturing hybrid system with stochastic leadtime

This paper deals with the inventory control problem for the hybrid production system. The manufacturing and remanufacturing operations simultaneously satisfy the customer demand. The product returns can enter the global serviceable inventory after being remanufactured. The global serviceable inventory takes the (s, S) continuous review replenishment policy. When the global serviceable inventory level drops to s, the manufacturing activity begins to produce in a batch and to replenish the global serviceable inventory up to S after a stochastic lead time. The changes of inventory state under the stochastic demand and product returns are illustrated with the Markov quasi-birth-death (QBD) processes. The hybrid inventory system is formulated as a Markov decision model. The matrix-geometric approach is used to derive the steady stationary transition probabilities. The optimal inventory parameters can be obtained by minimizing the long-run average cost. One numerical example is taken to illustrate the proposed methodology.