Problem Reduction Approaches for Production Planning Using Clearing Functions

A limitation of many mathematical programming models for production planning is their inability to reflect the nonlinear relation between workload and cycle times. Nonlinear clearing functions (CFs) explicitly model this relationship, and have shown promise for developing effective formulations. However, the use of CFs results in much larger models, and the effort involved in estimating the CFs is also significant. This paper examines the performance of reduced models where only a subset of potentially critical workcenters is represented with CFs. We find that even when the workcenters considered involve 75% of the average work in progress (WIP) in the system, the reduced models result in substantially lower performance than the full model where CFs are fitted to all workcenters. These results suggest that interactions between workcenters are quite complex and that models focusing on a limited set of machines may give misleading estimates of system performance. We provide insight into the causes of this behavior by analyzing the dual variables associated with the workcenters.