Modeling Cycle Times in Production Planning Models for Wafer Fabrication

A key parameter of the linear programming (LP) models widely used for production planning in industry and academia are the lead times, the estimated delay between material becoming available to a resource and its completion at that resource. Lead times are commonly treated as exogenous, workload-independent parameters and assumed to be integer multiples of the planning period. Although formulations with non-integer lead times have been implemented in industry, we are unaware of any studies systematically evaluating their performance. In this paper, we compare the performance of LP models with and without non-integer lead times by simulating the execution of the resulting release plans. We also compare their performance to that of a formulation incorporating workload-dependent lead times using nonlinear clearing functions. We find that the performance of the models with non-integer lead times is substantially better than those with integer lead times, and often superior to that of the much more complex clearing function models. These results suggest that whenever reasonable estimates of the lead times are available, non-integer lead times should be used due to their simplicity of implementation and excellent performance.