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