Lead time modeling in production planning

We use two mathematical models to represent the dependency between workload releases and lead times: a linear programming model with fractional lead times (FLT) and a clearing function (CF) based nonlinear model. In an attempt to obtain a reference solution, a gradient based simulation optimization procedure (SOP) is used to determine the lead times that, when used in the FLT model, yield the best performance. Results indicate that both FLT and CF models perform well, with CF approach performing slightly better at very high workload scenarios. The SOP is able to improve upon the performance of both models across all experimental conditions, suggesting that FLT and CF models are limited in representing the lead time dynamics. All three models yield quite different lead time patterns at critical machines, suggesting the need for further study of the behavior of these models.