Reducing the cost of defects in multistage production systems: A budget allocation perspective

Manufacturing firms are frequently concerned with operational improvements of their production system. As such, firms are often called to address the following question: How should they allocate their limited capital resources to the various stages of a multistage production system in order to improve the yield of the production stages and, at the same time, minimize the annual cost incurred from defects? In this paper, we provide a mathematical foundation for managerial decision making, which addresses this important operational problem. The approach we present is generalizable to any multistage production system, including existing and start-up systems, and considers the interplay of four factors on the allocation of capital resources. For each stage, these factors include the current mean yield, the cost of achieving the yield improvement, the cost incurred to the firm from a defect observed at each production stage, and the annual number of products processed. The formulation results in a budget allocation tool that allows managers to consider tradeoffs on the aforementioned factors across all stages. A sensitivity analysis identifies cases where a particular production stage is more likely to have a higher yield improvement compared to other stages. The sensitivity analysis is particularly useful for decision making in cases where the model parameters can not be accurately estimated, and management can only provide an estimate of a range of possible values. We demonstrate the applicability of the budget allocation approach using data from a real life multistage production system.