Inventory management of vertically differentiated perishable products with stock-out based substitution

The need for optimal inventory control strategies for perishable items is of the utmost importance to reduce the large share of food products that expire before consumption and to achieve responsible food stocking policies. Our study allows for a multi-item setting with substitution between similar goods, deterministic deterioration, delivery lead times and seasonality. Namely, we model demand by a linear discrete choice model to represent a vertical differentiation between products. The verticality assumption is further applied in a novel way within product categories. Specifically, the same product typology is vertically decomposed according to the age of the single stock-keeping unit in a quality-based manner. We compare two different policies to select the daily size of the orders for each product. On the one hand, we apply one of the most classical approaches in inventory management, relying on the Order-Up-To policy, modified to deal with the seasonality. On the other hand, we operate a state-of-the-art actor-critic technique: Soft Actor-Critic (SAC). Although similar in terms of performance, the two policies show diverse replenishment patterns, handling products differently.