Strategic Capacity Management When Customers Have Boundedly Rational Expectations

In retailing industries, such as apparel, sporting goods, customer electronics, and appliances, many firms deploy sophisticated modeling and optimization software to conduct dynamic pricing in response to uncertain and fluctuating market conditions. However, the possibility of markdown pricing creates an incentive for customers to strategize over the timing of their purchases. How should a retailing firm optimally account for customer behavior when making its pricing and stocking/capacity decisions? For example, is it optimal for a firm to create rationing risk by deliberately under stocking products? In this study, we develop a stylized modeling framework to answer these questions. In our model, customers strategize over the timing of their purchases. However, customers have boundedly rational expectations in the sense of anecdotal reasoning about the firm's fill rate, i. e., they have to rely on anecdotes, past experiences, or word-of-mouth to infer the firm's fill rate. In our modeling framework, we distinguish two settings: (i) capacity commitment, where the firm commits to its capacity level in the long run, or (ii) the firm dynamically changes it in each season. For both settings, within the simplest form of anecdotal reasoning, we prove that strategic capacity rationing is not optimal independent of customer risk preferences. Then, using a general form of anecdotal reasoning, we provide sufficient conditions for capacity rationing to be optimal for both settings, respectively. We show that the result of strategic capacity rationing being suboptimal is fairly robust to different valuation distributions and utility functions, heterogeneous sample size, and price optimization.