Optimal Ordering Policy for Perishable Products by Incorporating Demand Forecasts

Abstract

Inventory management of perishable products has seen extensive study over the years; the perishable nature capturing the real-world phenomena of expiration after a limited shelf life. Such problems are challenging as they involve balancing demand fulfillment with minimal wastage. An added dimension to such problems, given the rise of machine learning, is that demand predictions are often available. In this paper, we study the structural properties of the optimal ordering policy for a perishable product with a fixed shelf life in a periodic-review single-item inventory system over a finite horizon, where demand predictions are available. We consider both lost-sales and backlogging cases. The objective is to find the optimal ordering policy that minimizes the total expected cost over a finite horizon. The total expected cost consists of linear ordering cost, inventory holding cost, wastage cost, and shortage cost. By using the concept of L-convexity, we show that under particular assumptions on the demand forecasts, the optimal policy is a state-dependent base-stock policy in which the base-stock values are a function of the system’s state, the inventory level, a vector of current and previous demand forecasts, and previous demand values. Moreover, we explore the monotonicity properties of the optimal policy. The monotonicity properties motivate us to propose a heuristic in which the order quantity is an affine function of the inventory level and forecast-dependent target inventory levels. Numerical results show that the proposed heuristic is effective in minimizing the total cost while maintaining low on-hand inventory levels.

Keywords: Inventory, Forecasting, Dynamic programming, L-convexity, Submodularity