1. Introduction

We consider a single-stage production--inventory system that operates in a make-to-stock mode. The system consists of a manufacturing facility where parts are processed, and an output store where finished parts are stored. Parts in the manufacturing facility are called Work-In-Process or WIP, and parts in the output store are called Finished Goods or FG. We make the following assumptions:

1. There is an infinite supply of raw parts and a single type of parts produced.

2. Demands for FG inventory arrive randomly, one at a time.

3.

4. There is no setup cost or setup time for placing an order to the manufacturing facility.

5. There is no limit on the number of orders that can be placed per unit time. FG inventory levels are followed continuously, and replenishments of FG inventory may be ordered from the manufacturing facility at any time.

Under the above assumptions there is no incentive to replenish FG inventory by anything other than a continuous review, one-for-one replenishment policy. For such a system, Rubio and Wein (1996) proposed and analyzed a classical base stock replenishment policy, according to which, whenever the inventory position of the output store (i.e., WIP + FG - BD) falls below a specified level, called base stock, a new part is released into the manufacturing facility. A replenishment policy that has attracted considerable attention is the make-to-stock analog to a CONWIP policy proposed by Spearman et al. (1990). According to this policy, whenever the inventory in the system (i.e., WIP + FG) falls below a specified level, a new part is released into the manufacturing facility (e.g., see Veach and Wein, 1994). Tardif and Maaseidvaag (2001) proposed and studied an adaptive make-to-stock CONWIP policy, according to which, the level of inventory in the system that triggers the release of a new part into the manufacturing fa cility is allowed to change depending on the inventory and backorder levels.

Motivated by the base stock and the make-to-stock CONWIP policies, both of which depend on a single parameter, we focus on a slightly different two-parameter replenishment policy, which we call "base stock with WIP cap" policy. According to this policy, whenever the inventory position of the output store (WIP + FG - BD) falls below a specified level, called base stock, an order for the release of a new part in the system is issued. If the WIP inventory is below a different specified level, called WIP cap, the order goes through and a new part is released into the manufacturing facility; otherwise, the order is put on hold until the WIP inventory drops below the WIP cap.