Impulse control of a brownian inventory system with supplier uncertainty

In this paper we consider an inventory system which is driven by several types of uncertainties. First, we assume that when an order is placed, it may not always be available, perhaps due to strikes or embargoes. The durations of the available/unavailable periods are assumed to be random. Second, it is assumed that the inventory level process is a Brownian motion with negative drift. We develop the discounted cost for the infinite horizon problem using renewal arguments. The resulting objective function of two decision variables is minimized for different values of the problem parameters and a sensitivity analysis is provided. In this paper we have considered an inventory model with supplier uncertainty where orders placed may not always be received due to strikes, embargoes, etc. This assumption of supply uncertainty was similar to the one in Parlar and Berkin [10] who had assumed demand to be deterministic. In the current paper inventory level process (driven by the demand process) was modeled as a Brownian motion. Objective function of discounted cost over an infinite horizon was constructed using renewal arguments. Two decision variables b and y were introduced where b was the total capacity of the inventory system and y was the quantity to be ordered when inventory level reaches zero. We were able to obtain exact expressions for all the terms appearing in the objective function using the theory of reflected and absorbed Brownian motion. Numerical examples and a sensitivity analysis of all the problem parameters was provided.