EOQ Models for Imperfect Items under Time Varying Demand Rate

Abstract

In the classical Economic Order Quantity (EOQ) model, the common unrealistic assumptions are that all the purchased items are of perfect quality and the demand is constant. However, in a real-world environment, a portion of the purchased items might be damaged due to mishandling or an accident during the shipment process, and the demand rate may increase or decrease over time. Many companies are torn between repairing or replacing the imperfect items with new ones. The right decision on that options is crucial in order to guarantee that there is no shortage of stocks while at the same time not jeopardising the items’ quality and maximising the company’s profit. This paper investigates two EOQ models for imperfect quality items by assuming the demand rate varies with time. Under Policy 1, imperfect items are sent for repairs at an additional cost to the makeup margin; under Policy 2, imperfect items are replaced with equivalent quality items from a local supplier at a higher price. Two mathematical models are developed, and numerical examples along with sensitivity analyses are provided to illustrate these models. Our results reveal that Policy 1 is preferable to Policy 2 most of the time. However, Policy 2 outperforms Policy 1 if there is no minimum threshold on the purchased stock quantity. This research allows a company to discover solutions to previously identified inventory problems and make the inventory-patching process more controlled.