A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

Abstract

Motivated by a study of the logistics systems used to manage consumable service parts for the U.S. military, we consider a static threshold-based rationing policy that is useful when pooling inventory across two demand classes characterized by different arrival rates and shortage (stockout and delay) costs. The scheme operates as a (Q, r) policy with the following feature. Demands from both classes are filled on a first-comefirst-serve basis as long as on-hand inventory lies above a threshold level K. Once on-hand inventory falls below this level, low priority (i.e., low shortage cost) demand is backordered while high priority demand continues to be filled. We analyze this static policy first under the assumption that backorders are filled according to a special threshold clearing mechanism. Structural results for the key performance measures are established to enable an efficient solution algorithm for computing stock control and rationing parameters (i.e., Q, r, and K). Numerical results confirm that the solution under this special threshold clearing mechanism closely approximates that of the priority clearing policy. We next highlight conditions where our policy offers significant savings over traditional 'round-up' and 'separate stock' policies encountered in the military and elsewhere. Finally, we develop a lower bound on the cost of the optimal rationing policy. Numerical results show that the performance gap between our static threshold policy and the optimal policy is small in environments typical of the military and high technology industries.

No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems

“…Finally, there is a large body of literature on single-item inventory systems with multiple demand classes; see, for example, Deshpande et al (2003) and references therein. These systems can be viewed as special cases of an ATO system containing only a single common component but no product-specific components.…”

A Single-Product Inventory Model for Multiple Demand Classes

“…Moon and Kang (1998) later extend this model to account for compound Poisson demand processes. Deshpande et al (2003) analyze the same ( , ) Q R inventory rationing model with two demand classes as in Nahmias and Demmy (1981), but without the restriction on the number of outstanding orders. They introduce the threshold clearing mechanism to fill backorders, which permits them to derive expressions for the expected number of backorders for both classes without restrictions on the number of orders outstanding.…”

“…Melchiors et al (2000) also analyze a ( , ) Q R inventory model with two demand classes. Unlike Nahmias and Demmy (1981) and Deshpande et al (2003), they consider a lost sales environment so that demands from the low priority class are rejected whenever inventory level drops to the critical level. Melchiors (2001) extend the model in Melchiors et al (2000) to multiple Poisson demand classes with stochastic replenishment lead-times.…”

“…Melchiors (2001) extend the model in Melchiors et al (2000) to multiple Poisson demand classes with stochastic replenishment lead-times. Moreover, he considers a non-stationary critical-level policy that provides a benchmark to evaluate the stationary critical-level policy employed by Nahmias and Demmy (1981), Melchiors et al (2000), and Deshpande et al (2003). Dekker et al (1998) study an inventory model with two demand classes and one-for-one replenishment policy.…”

“…Our work is most closely related to that of Nahmias and Demmy (1981) and Deshpande et al (2003). However, whereas their work considers two demand classes, we have no restriction on the number of demand classes.…”