Range, work in progress and utilization

For the design of a supply chain as well as for a production system, the relationship between utilization, range, lead time and work in progress is very important. Because of the cost of the available capacity, the utilization should be high, but on the other hand full utilization has a negative impact on the lead time and work in progress. In this paper, some relationships for a continuous production system are formulated and theoretically proven between average lead time, average range, average work in progress and average utilization for a multi-item system with a dynamic demand. The basic equation that is developed is the continuous and deterministic analogous relationship to the well-known Little Law based on queuing theory. The theoretically deduced and proven logistical curves are similar to the results of the funnel model based on empirical studies and simulation. One interesting result is that the variability of the inventory or of the production load causes a waste of capacity and therefore a reduced utilization and an increased lead time. With the help of the deduced relationships, rules for the design and control of a production system are introduced.