The authors reported that for identical workstations, if
WIP is to be ignored, allocating Kanbans as evenly as possible and spreading the remaining ones over the line with reference toward the center will maximize the average throughput rate. However, if the cost of WIP is signifi-- cant, allocating more Kanbans to the down-
stream workstations towards the end of the
line will maximize the marginal beneit. Tayur [21] considered a serial production line with a single server in each workstation. For maximizing the average throughput rate of a production line, given a fixed total num-ber of Kanbans, he stated the following corol-laries:
(1) Increasing the number of Kanbans inany workstation decreases the waitingtime.
(2) A uniform allocation of Kanbans to workstations is not optimal.
(3) In systems with three or more worksta-tions, optimal allocations have exactly one Kanban in each of the two end
workstations.
(4) In a two workstation system, every allo-cation of a ®xed number of Kanbans yields the same throughput.
(5) In a three workstation system with N Kanbans, the optimal allocation is (1,N ÿ 2, 1).
Muckstadt and Tayur [15, 16] investigated a system similar to the one given by Mitra and Mitrani [14]. Muckstadt and Tayur suggested a heuristic procedure to achieve a given target throughput rate. Their objective was to mini-mize the average WIP. The heuristic procedure is as follows: begin with a total of N Kanbans, one in each workstation, and gradually increase the total number of Kanbans until the target average throughput is met. They indicated that each of the end workstations needs only one Kanban, but the additional Kanbans are allocated to the interior worksta- tions in the following way.