Impacts of random capacity and fluctuating environment on inventory systems

In this paper, we consider an inventory problem with random demand and random capacity in a fluctuating environment. Our objective is to minimize the total discounted cost during the whole sales horizon by choosing an appropriate replenishment policy. We show that the optimal ordering policy has an extended order-up-to type. The optimal cost function and the optimal ordering policy both have some stochastically monotone relationships with the random capacity under some mild conditions.