We examine the case of items with a limited shelf-life where storing an item (before consumption) may carry a cost to a buyer (or distributor). For example, eggs, milk, or Groupon coupons have a fixed expiry date, and seasonal goods can suffer a decrease in value. We show how this setting contrasts with recent results by (arXiv:1509.07330(v5)) for items with infinite shelf-life. We prove tight bounds on the seller's profits showing how they relate to the items' shelf-life. We show, counterintuitively, that in our limited shelf-life setting, increasing storage costs can sometimes lead to less profit for the seller which cannot happen when items have unlimited shelf-life. We also provide an algorithm that calculates optimal prices. Finally, we examine empirically the relationship between profits and buyer utility as the storage cost and shelf-life duration change, and observe properties, some of which are unique to the limited shelf-life setting.
We study the optimal pricing of a finite quantity of a fashion-like seasonal good in the presence of forward-looking (strategic) customers. We distinguish between two classes of pricing strategies: contingent and announced fixed-discount. In both cases, the seller acts as a Stackelberg leader announcing his pricing strategy, while consumers act as followers taking the seller's strategy as given and determining their purchasing behavior. In each case, we identify a subgame-perfect Nash equilibrium and show that given the seller's strategy, the equilibrium in the consumer subgame is unique and consists of symmetric threshold purchasing policies. For both cases, we develop a benchmark model in which customers are nonstrategic (myopic). We conduct a comprehensive numerical study to explore the impact of strategic consumer behavior on pricing policies and expected revenue performance. We show that strategic customer behavior suppresses the benefits of price segmentation, particularly under medium-to-high values of heterogeneity and modest rates of decline in valuations. However, when the level of consumer heterogeneity is small, the rate of decline is medium-to-high, and the seller can optimally choose the time of discount in advance, segmentation can be used quite effectively even with strategic consumers. We find that the seller cannot avoid the adverse impact of strategic consumer behavior even under low levels of initial inventory. We argue that while the seller expects customers to be more concerned about product availability at discount time, he cannot use high-price “betting” strategies as he would in the case of low inventory and myopic customers. Under certain qualifications, announced fixed-discount strategies perform essentially the same as contingent pricing policies in the case of myopic consumers. However, under strategic consumer behavior, announced pricing policies can be advantageous to the seller, compared to contingent pricing schemes. Interestingly, those cases that announced discount strategies offer a significant advantage compared to contingent pricing policies. They appear to offer only a minimal advantage in comparison to fixed-pricing policies. Finally, when the seller incorrectly assumes that strategic customers are myopic in their purchasing decisions, it can be quite costly, reaching potential revenue losses of about 20 .