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An inventory model for deteriorating items with exponential declining demand and partial backlogging

This study proposes an EOQ inventory mathematical model for deteriorating items with exponentially decreasing demand. In the model, the shortages are allowed and partially backordered. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, we show that the minimized objective cost function is jointly convex and derive the optimal solution. A numerical example is presented to illustrate the model and the sensitivity analysis is also studied. | Yugoslav Journal of Operations Research 15 (2005), Number 2, 277-288 AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH EXPONENTIAL DECLINING DEMAND AND PARTIAL BACKLOGGING Liang-Yuh OUYANG Department of Management Sciences and Decision Making, Tamkang University, Tamsui, Taipei 251, Taiwan liangyuh@mail.tku.edu.tw Kun-Shan WU Department of Business Administration, Tamkang University, Tamsui, Taipei 251, Taiwan Mei-Chuan CHENG Graduate Institute of Management Sciences, Tamkang University, Tamsui, Taipei 251, Taiwan. Received: March 2003 / Accepted: August 2004 Abstract: This study proposes an EOQ inventory mathematical model for deteriorating items with exponentially decreasing demand. In the model, the shortages are allowed and partially backordered. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, we show that the minimized objective cost function is jointly convex and derive the optimal solution. A numerical example is presented to illustrate the model and the sensitivity analysis is also studied. Keywords: Inventory, deteriorating items, exponential declining demand, partial backlogging. 1. INTRODUCTION In daily life, the deteriorating of goods is a common phenomenon. Pharmaceuticals, foods, vegetables and fruit are a few examples of such items. Therefore, the loss due to deterioration cannot be neglected. Deteriorating inventory models have been widely studied in recent years. Ghare and Schrader [7] were the two earliest researchers to consider continuously decaying inventory for a constant demand. Later, 278 L.-Y. Ouyang, K.-S. Wu, M.-C. Cheng / An Inventory Model for Deteriorating Items Shah and Jaiswal [13] presented an order-level inventory model for deteriorating items with a constant rate of deterioration. Aggarwal [1] developed an order-level inventory model by correcting and modifying the error in Shah and Jaiswal’s analysis [13] in calculating the average inventory holding cost. Covert and .