Inventory control with Markovian capacity and the option of order rejection

We consider a stochastic inventory control problem with Markovian capacity and the option of order rejection. We show its optimal policy to be the combination of a capacity-dependent modified base-stock production policy and a capacity-dependent critical-point order acceptance policy. When capacity is stochastically monotone, we show that the policy parameters change over the current capacity level in an intuitive way. All these results can be extended to the infinite-horizon case, with or without cost discounting. Our computational study substantiates the benefits from both exploiting the Markovian behavior of the capacity and rejecting orders when necessary.