A Model to Analyze Airbase Oil Inventory System with Endogenous Lead Time

Abstract

In this paper, we analyze airplane oil inventory problem of a base in the Republic of Korea Air Force (ROKAF) which should keep maintaining an appropriate inventory level of oil for the efficient operation of flights. In ROKAF, airplane oil supply is ordered (or delivered) at a constant time period, which means reorder point is not stochastic but deterministic. Since the airplane oil inspection time occupies large proportion of time between a reorder point and the time the oil is available for usage, it is imperative to analyze the inspection time which causes delay in fulfilling an order. In addition, if demands increase dramatically because of a war or an unexpected training, the reorder point could be shortened than in normal situations. In such abnormal circumstances, the shortened reorder point may require more delay for order fulfillment. In this setting, the inspection time endogenously determines the replenishment lead time (or supply lead time) and the pattern of the inventory. Meanwhile, since the procedure of airplane oil inspection is composed of several steps, it may be better that the distributions of inspection times are treated as phase-type distributions. In this context, we use D/PH/1/m queue and counting process of D-BMAP (Discrete-time Batch Markovian Arrival Process) with 2-class to analyze the delay (lead time) for order fulfillment. Using this model, we find a way to derive decision variables such as the number of inventory replenishments and average fill rate.

Key Words:

• Airbase oil inventory
• D/PH/1/m
• D-BMAP
• endogenous lead time
• phase-type distribution
• queueing theory.

Additional information

Notes on contributors

Kyung-Hwan Choi

Kyung Hwan Choi is in charge of international contracts at DAPA (Defense Acquisition Program Administration) and has received Ph.D. degree from KNDu (Korea National Defense University) in 2013. His main research areas are inventory management, stochastic modeling, performance evaluation and analysis.

Mohan L. Chaudhry

Mohan L. Chaudhry moved to Canada as a senior postdoctoral fellow at the University of Toronto before moving to the Royal Military College of Canada in 1967, where he is currently a senior professor. He has held an invited professor’s position at George Mason University, USA in 1988, a distinguished professor’s position at Korea Advanced Institute of Science and Technology in 2001, Ghent University, Belgium in 2004, and Indian Institute of Technology, Kharagpur, in 2008. He has held associate editorship for several Operational Research Journals. In 2003, Operational Research Society of Canada gave him an Award of Merit and in 2005 a Service Award. Besides many scientific publications, he has co-authored a few books among which “A First Course in Bulk Queues”, has gained high reputation and is well quoted by many researchers. His current interests are in stochastic processes, applied probability and queueing theory.

Bong-Kyoo Yoon

Bong-Kyoo Yoon Associate Professor in the Dept. of Operations Research at Korea National Defense University (KNDU), has received Ph.D. degree in Industrial Engineering from Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea. He provided consultancy on financial management and cost innovation to various global companies at IBM BCS. He has been working for KNDU since 2006. His major interest focuses on applying stochastic models to Logistics Optimization and Performance Innovation in public sector including defense industry.