Inventory models with random yield in a random environment

We consider a single item inventory model which is observed periodically in a randomly changing environment. All model parameters are specified by the state of the environment which is assumed to be a time-homogeneous Markov chain. Yield is random due to the random capacity of the vendor, i.e., a given order is fully received if the order quantity is less than this capacity. Otherwise, the quantity received is equal to the available capacity. The problem is analyzed in single, multiple and infinite periods and it is shown that in all cases, the optimal policy is the well-known base-stock policy where the optimal order-up-to level depends on the state of the environment. The results are compared with the solutions of the certain yield model when there is infinite capacity. We show that the order-up-to levels are equal in the single period case. However, in multiple and infinite periods, we order the same or more if the yield is random.