A closed-form solution approach for optimal reorder point in economic order quantity models with uncertain demands

Abstract

The reorder point formula in the Economic Order Quantity (EOQ) model traditionally assumes that demand during the lead-time follows a normal distribution. However, this assumption presents several challenges. First, alternative probability distributions may better capture demand patterns for specific products and markets. Second, historical data may not always be available to predict these distributions; in such cases, fuzzy set theory can be used to estimate demand based on expert opinions and judgments. Third, the conventional reorder point formula overlooks important factors, such as unit wholesale price and unit shortage costs. For instance, when unit shortage or goodwill costs are high, increasing the reorder point can help minimize the risk of stockouts. To address these issues, we reformulate the inventory problem during the lead-time as a newsvendor problem and derive closed-form solutions for the optimal reorder point. In this model, demand during the lead-time is represented using both fuzzy numbers (to capture possibility) and probability distributions, allowing us to incorporate factors like unit wholesale price and shortage or goodwill costs. Additionally, we provide managerial insights through numerical analysis, helping to guide decisions on reorder point adjustments.