How Much Demand Should Be Fulfilled

TLDR: In this article, the inventory replenishment of a product whose demand can be manipulated by restricting the supply is studied and the optimal policy is characterized as a state-dependent, monotone, base-stock policy.

Abstract: We study the inventory replenishment of a product whose demand can be manipulated by restricting the supply. This research is motivated by a novel marketing tactic employed by manufacturers of fashion and luxury items. Such a tactic combines innovative marketing with deliberate understocking in an attempt to create shortages (i.e., waitlists) that add to the allure and sense of exclusivity of a product and stimulate its demand. We model the problem as a finite-horizon, periodic-review system where demand in each period is a decreasing function of the net ending inventory in the previous period. Although the optimal structure can be complex in general, under certain conditions we are able to characterize the optimal policy as a state-dependent, monotone, base-stock policy. We compare this policy with the optimal policy for the case in which demand is independent of the net inventory. We also show that understocking is optimal in various scenarios. We then propose a novel strategy, called the inventory-withholding strategy, to further explore the wait-list effect by making customers wait even when there is inventory on hand to satisfy them. Our numerical experiments study the impact of various model parameters in combination with the wait-list effect on the optimal policy and the corresponding expected profits.