A time-continuous analytic production model for service level, work in process, lead time and utilization

Because of the fact that some logistical objectives are controversial, a trade-off between short actual lead times, low inventories, high utilization, high service levels and low backorders is necessary. To make good decisions in the design and, in particular, the optimization of a production system or supply chain a deep understanding of the relationship between the logistical figures is essential. In this article relationships between these logistical figures are developed by an analytical approach for a time-continuous multi-item production model. Furthermore, the deviation of work in process is used to describe the fluctuation and disturbances of real systems.