Transient behavior of a single-stage kanban system based on the queueing model

We deal with a single-stage kanban system with Poisson demand arrivals and Erlang production times, and we study an optimization of the number of kanbans when a change of load to the system is planned. We formulate the system as an M/Es/1 queueing system under piecewise constant load, and propose a numerical method by transient solutions of the M/Es/1 queue. Our method reveals the transient behavior of the kanban system with respect to expected inventory level and expected waiting time to satisfy demand. We suggest the required number of kanbans, and the time required to change to this required number, to optimize these criteria.