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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.

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Abstract:We study the problem of recovering a production plan after a disruption, where the disruption may be caused by incidents such as power failure, market change, machine breakdown, supply shortage, worker no-show, and others. The new recovery plan we seek after has to not only suit the changed environment brought about by the disruption, but also be close to the initial plan so as not to cause too much customer unsatisfaction or inconvenience for current-stage and downstream operations. For the general-cost case, we propose a dynamic programming method for the problem. For the convex-cost case, a general problem which involves both cost and demand disruptions can be solved by considering the cost disruption first and then the demand disruption. We find that a pure demand disruption is easy to handle; and for a pure cost disruption, we propose a greedy method which is provably efficient. Our computational studies also reveal insights that will be helpful to managing disruptions in production planning.

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