A note about ‘on replenishment schedule for deteriorating items with time-proportional demand’

Abstract

In the Economic Order Quantity (EOQ) model for exponentially deteriorating items, the inventory deterioration rate is proportional to the inventory level, which leads to an exponentially decreasing inventory level over time. Due to polynomial and exponential terms in the total cost function, an exact closed form solution is not possible. Previously, an approximation for the total cost function and a closed form optimal solution for the order interval have been proposed for this problem. However, the proposed closed form formula is complicated and it is not intuitive. It is also assumed without justification that the average inventory level is equal to half of the order quantity. We justify this assumption and show that the same approximation yields a much more intuitive formula when it is used to determine the optimal order quantity instead of the order interval. Our intuitive optimal order quantity formula is more likely to be adopted in practice.

Keywords:

• Inventory
• EOQ
• exponential decay
• deteriorating items
• optimal order quantity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

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Notes on contributors

Cenk Çalışkan

Dr. Cenk Çalışkan is an Associate Professor in the Department of Strategic Management and Operations, Woodbury School of Business, Utah Valley University. He received his B.S. in Industrial Engineering from Bilkent University and his M.S. and Ph.D. in Industrial and Systems Engineering from the Viterbi School of Engineering, University of Southern California. He was earlier an Assistant Professor in the Alfred Lerner College of Business and Economics, University of Delaware. He has also worked in the banking industry for two years and in the Silicon Valley for five years specializing in production planning software for semiconductor companies. His research interests are transportation, logistics, production planning, inventory, and network optimization. His work has appeared in European Journal of Operational Research, IISE Transactions, Transportation Research, Networks and Computers & Operations Research.