A Comparison of Simple Closed-Form Solutions for the EOQ Problem for Exponentially Deteriorating Items

Abstract

Some inventory items deteriorate and lose their useful life while in storage due to evaporation, spoilage, pilferage, and chemical or mechanical breakdown. Some examples of this phenomenon are the inventories of fresh food, batteries, electronic items, and petroleum products (such as gasoline and turpentine). Economic and environmental sustainability requires minimizing deterioration losses in inventories throughout the supply chain while optimizing the ordering decisions. This is especially important for food items because, globally, about one third of the food that is produced for human consumption is wasted, causing economic, environmental, political, and societal problems. Food production consumes large amounts of resources such as land, freshwater, fossil fuels, and labor. The same is true for items such as petroleum and chemical products. Exponential deterioration is a commonly used approach to model this phenomenon, which results in an exponentially decreasing inventory level function. An important extension of the basic economic order quantity (EOQ) model is its application to exponentially deteriorating items. In the exponentially deteriorating items model, the rate of deterioration per unit time for the stocked items is proportional to the amount of available physical inventory at any given time. This results in an exponentially declining inventory level over time. This problem normally does not lend itself to a closed-form optimal solution due to the coexistence of polynomial and exponential terms; hence, approximations are used, but the existing approximations yield closed-form solutions that are far from intuitive. In this research, we develop new approximate closed-form solutions for the basic problem and its backordering extensions that are intuitive and very easy to interpret, as well as more accurate; therefore, they are very attractive to practitioners. We provide extensive experimental results to demonstrate superiority of our approximate closed-form solutions.