A U.S. Postal Service supervisor is looking for ways to reduce stress in the sor

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 400 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 385 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 75,000 letters are to be sorted during a 12-hour shift, the safety stock policy variable, ?, is 0.15, and the average waiting time plus material handling time is 45 minutes per tub? The average processing time per tub of letters, p, is day. (Enter your response rounded to four decimal places.)

Explanation / Answer

Average processing time per tub = p = 385 seconds = 385/(12*3600) = 0.0089 days.

Average waiting time per tub = w = 45 minutes = 45/(60*12) = 0.0625 days

Container size = c = 400 letters

Daily demand = d = 75,000 letters

Number of tubs required (k) = d*(w+p)*(1+0.15)/c = 75000*(0.0625+0.0089)*1.15/400 = 15.4 or, 16 (rounded off)

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