Dynamic pricing for deteriorating products with menu cost

Retail operation practice has empirically demonstrated that menu costs (i.e., the costs of adjusting a price) play a critical role in retailer pricing decisions. In this paper, we propose four dynamic pricing models for deteriorating products based on different pricing adjustment frequencies with and without menu costs. Under Poisson demand, we provide (1) the rank of these models in terms of expected profits and note that (2) the optimal prices of deteriorating products consistently decrease over time when menu costs are negligible. To investigate the impact of menu costs on dynamic pricing decisions, we conduct several numerical experiments based on different menu costs, decay rates, holding costs and initial inventories. The results demonstrate that (1) the one-time price adjustments typically employed in practice provide the most benefit from dynamic pricing when menu costs are moderate and that (2) it is typically preferable to adjust the price in the middle of the products shelf life rather than to make early or late adjustments. The same conclusions follow under compound Poisson demand and general customer utility functions.