Hedging-point production control with multiple failure modes

We consider the control of a production facility subject to multiple failure modes. Motivated by a work of Akella-Kumar (1986) and Bielecki-Kumar (1988) on single-failure-mode models, we study hedging-point policies, in which production is controlled to its maximum rate whenever inventory is below a critical level and set to zero whenever inventory is above that level. The maximum production rate varies with the state of the machine. Assuming that the machine state is governed by a semi-Markov process, we evaluate average and discounted inventory costs for any hedging point, thus providing a simple mechanism for identifying optimal hedging points. Our most explicit results require that intervals in which demand exceeds production are exponentially distributed. We drop the exponential assumption at the expense of obtaining asymptotics rather than exact results.