Optimal disposal policies for a single-item inventory system with returns

We consider a single-item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy. It is shown that this problem is equivalent to a problem of controlling a single-server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given. An interesting by-product of our investigation is an approximation for the steady-state behavior of the bulk GI/G/1 queue with a queue limit.