Optimal Inventory Policies for Perishable Products Under Demand and Lead Time Uncertainty

Abstract

This paper presents an advanced inventory model for perishable products, moving beyond the deterministic assumptions of traditional Economic Order Quantity (EOQ) models. The research explicitly incorporates uncertainty in demand and lead time, which are critical factors that impact inventory costs and operational efficiency. By formulating the problem as a system of non-linear equations, we derive a robust analytical and numerical framework to determine the optimal order quantity (Q∗) and reorder point (R∗) that minimize the total expected annual cost, including a crucial component for the expected cost of shortages.
Through a comprehensive sensitivity analysis, we demonstrate the model’s response to variations in key parameters, such as holding cost, shortage cost, and the standard deviation of lead time demand. The results highlight how the optimal policy dynamically adjusts to market volatility. A comparison with the traditional EOQ model reveals that while our stochastic approach yields a higher total cost, this is a more accurate representation of the true operational expenses as it quantifies the financial impact of uncertainty. This research provides managers with a powerful and practical tool for making more informed inventory decisions for perishable goods in a volatile environment.