A Periodic Review, Production Planning Model with Uncertain Capacity and Uncertain Demand---Optimality of Extended Myopic Policies

Increasing product complexity, manufacturing environment complexity and an increased emphasis on product quality are all factors leading to uncertainties in production processes. These uncertainties are in the form of unplanned machine maintenance, varying production yields and rework, among others. In planning for production, an adequate model must incorporate these uncertainties into the representation of the production process. This paper treats the aggregate planning problem for a single product with random demand and random capacity. In the single-period problem, random capacity does not affect the optimal policy but results in a unimodal, nonconvex cost function. In the multiple-period and infinite-horizon settings order-up-to policies that are dependent on the distribution of capacity are shown to be optimal in spite of a nonconvex cost. In the infinite-horizon setting an intuitive description of the situation leads to the notion of a class of extended myopic policies, requiring the consideration of review periods of uncertain length.