Joint Decision of Optimal Procurement Policy and Optimal Order Size for a Product Recovery System

We consider a product recovery system that a single product is stocked in order to meet a demand from customers who may return products after usage. This paper addresses a problem of when to release a procurement process to replenish serviceable inventory and how many new products to procure. The structure of the optimal procurement policy is examined and numerically identified as a monotonic threshold curve. A numerical procedure is presented to jointly find the optimal procurement order size, optimal procurement policy, and optimal discounted profit. Sensitivity analysis also indicates that these optimal performance measurements have monotonic properties with respect to system parameters.