An Inventory Model with Two Demand Classes

GUEST LECTURER
Marty Reiman

AFFILIATION
Bell Labs

ABSTRACT
In this talk I describe some results related to a variant of a standard inventory model. The model has a single item, a single location, two demand classes, and operates under discrete review. There is a fixed positive replenishment lead time and unlimited backlogging of unmet demand is allowed. There are no order setup costs, and both holding costs and backlogging costs are linear. If the backlogging costs are the same for both classes then this reduces to the classical model of Karlin and Scarf (1958), who showed that a 'base-stock' policy is optimal. We are interested in the case where the backlogging costs are different for the two classes. Although it is intuitively clear that the demand class with the larger backlog cost should be treated better, the optimal policy for operating this system is not known. The simplest way to give priority to one class is to satisfy all backlogs from that class before backlogs of the other class are satisfied. A stronger preference can be given by holding some items in reserve for the higher priority class. We present an asymptotic analysis, in the long lead time limit, of these priority policies. This analysis shows that the simple priority policy (without reservation) is asymptotically optimal. The priority policy with reservation is also asymptotically optimal if the reservation threshold does not grow too fast with the lead time.

DATE & TIME
Tuesday, May 15, 2007 -- 11:00 AM

DURATION
1 hour

LOCATION
Executive Classroom 228, Main

CONTACT PERSON
Jim Dai