Dynamic inventory and pricing control of a perishable product with multiple shelf life phases

Abstract

This paper investigates a dynamic inventory-pricing system with perishable products of multiple freshness levels. The firm may set different prices for items of different freshness levels, and customers either balk or choose to buy the freshness level that maximizes their utility. We model this inventory-pricing problem as a Markov decision process, where the assortment dynamically changes based on the freshness levels of the available items. Using the concept of anti-multimodularity, we characterize the structure of the optimal policy. Specifically, we show that the optimal production policy has a state-dependent threshold-based structure. The production decisions are more sensitive to the inventory of fresher items than less fresh ones. Moreover, the optimal price of a freshness level is nonincreasing in the inventory of items of any freshness level, and it is more sensitive to those of a closer freshness level. The structural properties enable us to devise three novel heuristic policies with good performance. We further extend the model by considering donations and a system with multiple freshness phases. Our research suggests that freshness-dependent pricing and dynamic pricing are two substitutable strategies, while freshness-dependent pricing and donation are strategic complements. The results further imply that the firm can benefit from high variability in freshness among items under dynamic pricing, but such variability may lead to a significant loss when single, static pricing is used. The results of our heuristic policies show that considering inventory and pricing decisions as a parametrized function of the inventory state leads to nearly optimal solutions.