Abstract
ABSTRACTIn 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.
Highlights
Inventory rationing among different customer classes arises in several contexts
We focus on a two-demand-class stocking problem, in which pooled inventory is managed with a continuous review order-up-to policy, together with a static rationing policy, under which low-priority customers are not served as long as the on-hand inventory is at or below a fixed threshold level
We present a solution to this challenge and integrate the results with Table 3 to present an algorithm for solving the Continuous-Time Markov Chain (CTMC) balance equations
Summary
Inventory rationing among different customer classes arises in several contexts. Our primary motivation is the situation of managing service parts inventory in a parts distribution center serving multiple customer classes, each of which has contracted for a specific level of customer service, typically measured as fill rate. We further show that if the independence assumption of the embedded Markov chain approach is true, these same service-level expressions are true for generally distributed lead times These expressions are computed using recursive procedures that are several orders of magnitude less computationally complex than the embedded Markov chain approach. This article presents an extensible and computationally efficient way of computing optimal stocking and threshold levels for a two-demand-class model and provides service level estimates comparable to the best existing heuristic. We note that the model can be extended to three-demand-class models but leave the development and discussion to a supplemental technical report (Vicil and Jackson, 2015)
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