As an effective way of decreasing production cost, remanufacturing has attracted more and more attention from firms. However, it also brings many difficulties to firms, especial when firms remanufacture products which they produce. A primary problem for the case is how to acquire the used product sold by the firm itself. In this paper, we consider a return compensation policy for acquiring used product from customers. Under this policy, the return quantity of used product is a proportion of demand. We study an inventory replenishment and production planning problem for a two-period inventory system with dependent return and demand. We formulate the problem into a three-stage stochastic programming problem, where the firm needs to make decisions on the replenishment quantity of new raw material inventory in each period and the production quantities of manufacturing and remanufacturing ways. We give the optimal production policy of manufacturing and remanufacturing ways for the realized demand and prove the objective function for each stage to be concave in the inventory replenishment quantity. Moreover, we prove that the basic inventory policy is still optimal for each period and give the analytical conditions of the optimal inventory levels which are unrelated to acquisition price. Finally, we investigate numerical studies to analyze managerial insights.
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