Joint Dynamic Pricing with Acquisition and Selling Opportunities

Abstract We analyze a novel dynamic pricing problem, where not only the demand depends on the dynamic selling price, but also the supply can be influenced through the dynamic acquisition price. This paper is motivated by firms that acquire and resell pre-owned items, such as cell phones. A firm with fixed inventory is always under pressure to sell the remaining inventory, yet when acquisition opportunities arise, the firm may become under pressure to acquire inventory in anticipation of a surge in demand. We establish conditions under which the firm will find itself under pressure to acquire versus pressure to sell. We study how the optimal acquisition and selling prices, and the difference between them (the optimal margin) behaves with respect to time and inventory. In addition, we devise heuristics with fixed prices based on a deterministic approximation, and we evaluate how much the firm gains by using a dynamic acquisition or selling price as opposed to fixing them at the beginning of the horizon.