A make-to-order supply chain has customer orders arriving in Poisson fashion at the rate of 90 orders per day. Raw material and subassemblies are always on hand. The facility assembles these on receipt of an order and the customers receive them immediately. If the processing time is exponentially distributed with rate 96 orders per day (average processing time = 15 minutes), compute the following:
(a) Probability of at least 10 backorders
(b) Probability of no backorders
(c) Standard deviation of lead time for a typical order
(d) Fraction of orders which have lead time greater than 1 day
(e) Throughput rate of the system