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ABSTRACT
In this article we develop a procedure for estimating service levels (fill rates) and for optimizing stock and threshold levels in a two-demand-class model managed based on a lot-for-lot replenishment policy and a static threshold allocation policy. We assume that the priority demand classes exhibit mutually independent, stationary, Poisson demand processes and non-zero order lead times that are independent and identically distributed. A key feature of the optimization routine is that it requires computation of the stationary distribution only once. There are two approaches extant in the literature for estimating the stationary distribution of the stock level process: a so-called single-cycle approach and an embedded Markov chain approach. Both approaches rely on constant lead times. We propose a third approach based on a Continuous-Time Markov Chain (CTMC) approach, solving it exactly for the case of exponentially distributed lead times. We prove that if the independence assumption of the embedded Markov chain approach is true, then the CTMC approach is exact for general lead time distributions as well. We evaluate all three approaches for a spectrum of lead time distributions and conclude that, although the independence assumption does not hold, both the CTMC and embedded Markov chain approaches perform well, dominating the single-cycle approach. The advantages of the CTMC approach are that it is several orders of magnitude less computationally complex than the embedded Markov chain approach and it can be extended in a straightforward fashion to three demand classes.
Additional information
Notes on contributors
Oguzhan Vicil
Oguzhan Vicil is an Adjunct Faculty Member in the Industrial Engineering Department at Bilkent University, Turkey, and an operations research and technology management consultant in the private sector. He received his Ph.D. in Operations Research and Information Engineering from Cornell University in 2006. Since then, he has been managing projects in both the public and private sectors, especially within the scope of applied operations research, information systems, and technological innovation management. His major research interests are in stochastic modeling and optimization in supply chain management, scheduling, inventory theory, and control. He is also active in contributing to the dissemination of scientific literacy among public and bridging the gap between scientific community and policy makers.
Peter Jackson
Peter Jackson is a Professor in the School of Operations Research and Industrial Engineering (ORIE), Cornell University. He received his Ph.D. in Operations Research from Stanford University in 1980. He has served at Cornell since 1980. He is the Director of Graduate Studies for, and a former Director of, the Systems Engineering Program within the College of Engineering. He also serves as the Director of Undergraduate Studies for ORIE. His research interests include planning and scheduling for integrated production, transportation and inventory management systems, supply chain management, and business modeling and data analysis. He has consulted with several companies in these areas, including Agco, PTC-Servigistics, General Motors, Cleveland Clinic, Xelus, Clopay Building Products, General Electric, Aeroquip, and Quaker Oats. He was the recipient of a General Motors Research and Development Innovation award in 2011 for a business process to optimize retail inventories. He is also active in educational curriculum development for operations research and systems engineering. He is the recipient of several awards for curriculum innovation in addition to numerous student-voted awards for teaching excellence. He is the author of an introductory textbook to systems engineering, Getting Design Right: A Systems Approach (CRC Press, 2009).