Queueing models of Kanban and MRP controlled production systems

The impact of stochastic demand and stochastic processing times on the performance of production systems controlled using Kanbans or MRP is considered. A linked queueing network model is developed to describe the behaviour of Kanban controlled systems. Next it is shown that the linked model is equivalent to multiple server queues in series with a blocking mechanism that depends on the features of the system. If there are reserve stocks in the system then the blocking mechanism is the conventional blocking of service because the next queue is full. However, if Kanbans can be triggered by backorders, then the blocking mechanism is more complex and requires looking at the number of customers in following stages. Next, it is shown that MRP systems are also equivalent to series queues but with the rules for determining release of jobs into service now involving forecasts of future demand. Based on the insights from the queueing models, a general approach to production control incorporating both Kanban and MRP systems as special cases is proposed.