Dynamic Inventory Control with Stockout Substitution and Demand Learning

We consider an inventory control problem with multiple products and stockout substitution. The firm knows neither the primary demand distribution for each product nor the customers' substitution probabilities between products a priori, and needs to learn such information from sales data on the fly. A main challenge in this problem is that the firm cannot distinguish between primary demand and substitution (overflow) demand from the sales data of any product, and due to data censoring, lost customers from either demand sources cannot be observed. To circumvent these difficulties, we construct learning stages with each stage including a cyclic testing scheme and a benchmark exploration interval. The benchmark interval allows us to isolate the primary demand information from the sales data, that is used against the sales data from a cyclic exploration interval to estimate substitution probabilities. Since raising inventory level helps obtain primary demand information but hinders substitution demand information, inventory decisions have to be carefully balanced to learn both of them. We design learning algorithms for both stationary and dynamically changing environments, and show that their regret rates (almost) match the theoretical lower bounds. Numerical experiments reveal that the proposed algorithms perform very well