Inventory renewal for a perishable product: Economies of scale and age‐dependent demand

We consider a finite‐horizon, periodic‐review system for a perishable product at a retailer that faces stochastic, age‐dependent demand and loses excess demand, if any. For this system, we build three models that capture two sources of unfilled demand, insufficient inventory and inappropriate age, and penalize them at different rates. The models are characterized by increasing replenishment flexibility, and the goal of each model is to identify when to place an order and the quantity whenever an order is placed. In the first model, reorder intervals are equal. In the second model, reorder intervals can vary across orders. In the third model, reorder intervals continue to remain flexible but the retailer can also partially salvage her inventory whenever she has excess inventory. Using the models, we explore the effect of lost‐sales penalties on the structure of the optimal value function. We find that the inventory‐related cost in a period may lack convexity if the ratio of penalties for stockout and high age is below a threshold, which percolates to the value function as well. We also identify properties of the optimal replenishment policy for the three models. Finally, we conduct numerical experiments to identify the marginal value added by the flexibility in reorder intervals and the option to partially salvage inventory as a function of model parameters.