This paper deals with the inventory control problem for production system in which multiple part types are produced and the produced parts are supposed to be deteriorating with fixed rates. The capacity of the production system is assumed to be random and bounded. The inventory control problem is formulated as a stochastic optimization problem that falls into the framework of the optimization problem of the class of systems with Markovian jumps. The optimal production rates are characterized and a numerical example is worked out to show the validness of the theoretical results.