Periodic review inventory systems with fixed order cost and uniform random yield

We consider periodic review stochastic inventory control problems with both fixed order cost and uniform random yield. Our objective is to characterize some structural properties of the optimal policies so that efficient approaches can then be established towards finding an optimal policy. In particular, we provide a lower-and-upper bound structure for the optimal policy at the beginning of any period, such that it is optimal not to order anything if the initial stock level is above the upper bound, and it is optimal to order a positive quantity if the initial stock level is below the lower bound, where the optimal quantity can be found efficiently. For any initial stock level in-between the upper and lower bounds in each period, a partial characterization of the optimal policy is provided. Furthermore, we show that the optimal order quantity is monotonically decreasing in the initial stock level in any period and this will help the search for the optimal order quantity at any initial stock level. In addition, we illustrate a few interesting phenomena about the behavior of an optimal policy. These phenomena show that the structure of the optimal policy for this problem is in general significantly different from that for the traditional periodic review inventory control problems with certain yield and fixed order cost.