Kanban, a pull system for inventory control is in direct contrast to conventional push systems. In the pull system, the kind and quantity of items needed by the succeeding stage are withdrawn from the preceding stage, only at the rate and at the time they are consumed. In this paper, lot size models are formulated in two special cases of practical interests and simple solution procedures are adapted to minimize the total cost of the kanban system. An numerical example is solved to illustrate the method.