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 (censored demand) on the fly. One 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 lost-sales are not observable. To circumvent these difficulties, we construct learning stages with each stage consisting of a cyclic exploration 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 the cyclic exploration intervals 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 them together. We show that our learning algorithm admits a worst-case regret rate that (almost) matches the theoretical lower bound, and numerical experiments demonstrate that the algorithm performs very well. This is a joint work with Beryl Chen.
Brief Bio: Xiuli Chao is a professor of Industrial and Operations Engineering at the University of Michigan, Ann Arbor. Prior to joining Michigan, he was on the faculty of Industrial and Systems Engineering at NC State University. His recently research interests include queueing, inventory control, game theory, supply chain management, and data-driven optimization. He is the co-author of two books, “Operations Scheduling with Applications in Manufacturing and Services” (Irwin/McGraw-Hill, 1998), and “Queueing Networks: Customers, Signals, and Product Form Solutions” (John Wiley & Sons, 1999). Chao received the Erlang Prize from the Applied Probability Society of INFORMS in 1998, and the David F. Baker Distinguished Research Award from Institute of Industrial Engineers (IIE) in 2005. Chao holds doctoral degree in Operations Research from Columbia University