Optimal production policies for multi-stage systems with setup costs and uncertain capacities

The increased complexity of modern manufacturing has led to uncertainties in production processes. Factors such as unplanned machine maintenance, tool unavailability, and complex process adjustments make it difficult to maintain a predictable level of output. To be effective, an appropriate production model must incorporate these uncertainties into the representation of the production process. This paper considers a one-time production of an application-specific product which must follow a fixed routing through the manufacturing system. The flow of items can be modeled as a multi-stage serial production line. The productive capacity is uncertain at each stage and the decision to produce at any stage incurs a significant setup cost. Semifinished products have little value and inability to satisfy the demand incurs a penalty for each unit of unmet demand. We show that the optimal production policy for this system can be characterized by two critical numbers, which can be computed a priori based on the cost parameters and distributional information for all downstream stages. Sensitivity of the critical numbers is also explored.