Fill Time, Inventory and Capacity in a Multi-Item Production Line under Heijunka Control

The concept of production levelling (or Heijunka), which is part of the Toyota Production System, aims at reducing the variance of upstream material requirements and of workload utilization.When using Heijunka control, however, the fluctuation of the external demand has to be compensated by the fill time (the time from demand arrival until fulfilment) and/or end product inventory and/or reserve capacity. The inventory is usually controlled by Kanban loops. But precise statements on the necessary number of Kanban to guarantee a certain fill time are missing in literature.We consider a multi-item production line with a given Heijunka schedule and Poisson demand.We derive approximate analytic relationships between fill time, inventory and capacity for three different planning situations.