Dynamic Inventory and Price Controls Involving Unknown Demand on Discrete Nonperishable Items

AbstractData-Driven Ordering and PricingWhen a new product has just been introduced or the economy has just entered a new phase, a firm is often at a loss as to what the underlying demand pattern has become, let alone how best to respond to it. A natural idea is to manage ordering and pricing activities while simultaneously learning about the demand pattern. In “Dynamic Inventory and Price Controls Involving Unknown Demand on Discrete Nonperishable Items,” Katehakis, Yang, and Zhou formalize this idea. They design control policies that adapt with demand observations made over time. A policy’s regret is the lag of its performance behind that of an all-knowing one tailor-made for a specific demand pattern. For the proposed policies, the worst regrets over large ambiguity sets of unknown demand patterns are found to grow reasonably slowly over time.We study adaptive policies that handle dynamic inventory and price controls when the random demand for discrete nonperishable items is unknown. Pure inventory control is achieved by targeting newsvendor ordering quantities that correspond to empirical demand distributions learned over time. On this basis we conduct the more complex joint inventory-price control, where demand-affecting prices await to be evaluated as well. We identify policies that strive to balance between exploration and exploitation, and measure their performances via regrets, that is, the prices to pay for not knowing demand distributions a priori over a given horizon. Multiple bounds are derived on regrets’ growth rates; they vary with how thoroughly unknown the demand distributions are and whether nonperishability has indeed been accounted for. Our simulation study illustrates order-of-magnitude differences between pure inventory and joint inventory-price controls.