Abstract
We consider a novel variant of the perishable inventory profit management problem faced by a firm that sells a fixed inventory over a finite horizon in the presence of price-adjustment costs. In economics literature, such price-adjustment costs are widely studied and are typically assumed to include a fixed component (e.g., advertising costs), an inventory-dependent component (e.g., inventory relabeling costs), as well as a component that depends on the magnitude of the price adjustment (e.g., cognitive and coordination managerial costs).
We formulate the firm's profit management problem as a finite-horizon dynamic program in which the state of the system is described by the inventory level as well as the current price level. We derive first-order properties of the optimal value function and give a complete characterization of optimal policies for the case of ample inventory. Through a set of examples we demonstrate the complex and counterintuitive nature of optimal price-adjustment policies. Consequently, we focus on developing easily computable and implementable heuristics with demonstrably good performance. To this end, we develop and solve a fluid model based on the original stochastic dynamics and propose three fluid-based heuristic policies. We derive expressions for the expected profit generated by each one of these heuristics when applied to the stochastic problem and derive sufficient conditions for the asymptotic optimality of the policies when the initial inventory levels and planning horizons are proportionally scaled up. We test the performance of the heuristics in a numerical study and demonstrate a robust, near-optimal performance of one of the heuristics (which we call the "Fluid Time" heuristic) for a wide range of problem parameters. Finally, we demonstrate the importance of proper accounting of price-adjustment costs in several alternative business settings.