Historical data indicate that the interarrival time of job orders to a Kanban system for precision-motor assembly follows an exponential distribution with a mean of 1.25 h. The cycle time for the Kanban system to fill each job order is exponential with a mean of 1.10 h.

(a) Compute the probability of a total of 15 job orders in progress in the Kanban system (including those being processed, and those waiting in buffers).

(b) Compute the expected total number of job orders in progress (i.e., WIP)

in the system, and the expected flow-time of each car (queuing time plus service time).

(c) Given a 10 percent safety factor and a container size of 1, calculate the number of Kanbans to be launched into the system.