Optimal pricing on an age-specific inventory system for perishable items

With aging over time, perishable items with fixed shelf lives, can be differentiated by their ages. The age which reflects the quality level of the item can directly affect consumers' willingness to pay, and then affect the consumer demand. Therefore, we consider that consumers' sensitivity to item's age is heterogeneous, which can induce price differentiation to balance consumers' purchasing preferences. Taking the age heterogeneity into account, we model an age-specific inventory system to explore the optimal pricing problem for perishable items, which in fact, is an optimal control problem for distributed parameter system. We describe the evolution of the stock by a first-order partial differential equation of both time and age. Through applying the distributed parameter optimal control theory, we explicitly derive the optimal pricing strategy which prices items differentially based on their different ages. Numerical examples show that, for the different aged items at the same time, it is beneficial for the firm to discount the items with their ages, while for the same aged items, taking the penetration pricing policy over time is a better choice.