A production-inventory system with markovian capacity and outsourcing option

We study the optimal production-inventory-outsourcing policy for a firm with Markovian in-house production capacity that faces independent stochastic demand and has the option to outsource. We find very simple optimal policy forms under fairly reasonable assumptions. In addition, when the capacity Markov process is stochastically monotone, the policy parameters decrease in the firm's current capacity level under additional assumptions. All these results extend to the infinite-horizon and undiscounted-cost cases. We analyze comparative statics and the necessity of some technical conditions, and discuss when the outsourcing option is more valuable.