Data-driven inventory control involving fixed setup costs and discrete censored demand

We investigate a data-driven dynamic inventory control problem involving fixed setup costs and lost sales. Random demand arrivals stem from a demand distribution that is only known to come out of a vast ambiguity set. Lost sales and demand ambiguity would together complicate the problem through censoring, namely, the inability of the firm to observe the lost portion of the demand data. Our main policy idea advocates periodically ordering up to high levels for learning purposes and, in intervening periods, cleverly exploiting the information gained in learning periods. By regret, we mean the price paid for ambiguity in long-run average performances. When demand has a finite support, we can accomplish a regret bound in the order of O(T-2/3 center dot (ln T)(1/2)) which almost matches a known lower bound as long as inventory costs are genuinely convex. Major policy adjustments are warranted for the more complex case involving an unbounded demand support. The resulting regret could range between O(T-0.779) and O(T-0.889) depending on the nature of moment-related bounds that help characterize the degree of ambiguity. These are improvable to O(T-2/3 center dot (ln T)(2)) when distributions are light-tailed. Our simulation demonstrates the merits of various policy ideas.