Question

A U.S. Postal Service supervisor is looking for ways to reduce stress in the sorting department. With the existing arrangement, stamped letters are machine-canceled and loaded into tubs with 325 letters per tub. The tubs are then pushed to postal clerks, who read and key zip codes into an automated sorting machine at the rate of one tub per 425 seconds. To overcome the stress caused when the stamp canceling machine outpaces the sorting clerks, a pull system is proposed. When the clerks are ready to process another tub of mail, they will pull the tub from the canceling machine area. How many tubs should circulate between the sorting clerks and the canceling machine if 85,000 letters are to be sorted during a 9-hour shift, the safety stock policy variable, a, is 0.05, and the average waiting time plus material handling time is 30 minutes per tub? The average processing time per tub of letters, p, is day. (Enter your response rounded to four decimal places.) The average waiting time per tub of letters, w, is day. (Enter your response rounded to four decimal places.) Therefore, the number of tubs that should circulate between the sorting clerks and the canceling machine is tubs. (Enter your response rounded up to the next whole number.)

Answer 1

(A)

Processing time per tub = 425 seconds

Working hours in a day = 9 hours

Processing time per tub = 425 / (9×60×60)

Processing time per tub (p) = 0.0131 days

(B)

Waiting time per tub = 30 minutes

Working hours in a day = 9 hours

Waiting time per tub (w) = 30/ (9×60)

Waiting time per tub (w) = 0.0556 days

(C)

Capacity of tub (C) = 325

Daily demand (d) = 85,000

Policy Variable ($\alpha$) = 0.05

K d'w+p)(1+ a) C

K = [85,000 × (0.0131+0.0556)(1+0.05)] / 325

K = 18.86 containers

K = 19 containers (rounded off)