Bottleneck in a Campus Print Center
During exam week, a campus print center receives about 50 jobs per hour. Each job goes through four steps in sequence. Intake and file check takes one clerk 2 minutes per job. Printing uses three identical printers; each job occupies one printer for 5 minutes. Collation and stapling takes one worker 3 minutes per job. Payment takes one cashier 1 minute per job. The center currently staffs one intake clerk, three printers, one collation worker, and one cashier. Jobs wait in a single queue before intake. The manager can add one cross-trained worker to any one station for the week. Staff cost is the same regardless of station. The center wants to reduce the queue growth during the 10:00-12:00 peak, when arrivals are 50 jobs per hour. Assume no variability, no breaks, and steady arrivals.
1. Calculate the current process capacity in jobs per hour and identify the bottleneck. Show each station's capacity.
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Station capacities:
- Intake: 60/2 = 30 jobs/hour.
- Printing: 3 printers × 60/5 = 36 jobs/hour.
- Collation: 60/3 = 20 jobs/hour.
- Payment: 60/1 = 60 jobs/hour. The process capacity is the minimum, 20 jobs/hour, so collation is the bottleneck. At 50 arrivals/hour, the queue grows by 50 − 20 = 30 jobs/hour during the peak.
2. The manager can add one worker to a single station. Which station should receive the worker, and what will the new process capacity be? Justify with numbers.
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Test each single addition by recomputing the minimum:
- Add to collation: capacity becomes 2 × 20 = 40/hour; new minimum = min(30, 36, 40, 60) = 30/hour.
- Add to intake: 60/hour; minimum = min(60, 36, 20, 60) = 20/hour, unchanged.
- Add to payment: 120/hour; minimum remains 20/hour.
- Add a worker to printing without a fourth printer: no change to 36/hour; minimum remains 20/hour. Adding a fourth printer would raise printing to 48/hour, but collation still limits at 20/hour. Collation is the correct station: it raises process capacity from 20 to 30 jobs/hour. The center still cannot match 50 arrivals/hour.
3. After the best single addition, what is the expected queue growth per hour during the peak? What additional change would be needed to eliminate queue growth?
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After adding the second collation worker, capacity is 30 jobs/hour and arrivals are 50 jobs/hour, so the queue grows by 20 jobs/hour. One additional change is not enough. The next bottleneck is intake at 30/hour; a second intake clerk raises it to 60/hour, but printing at 36/hour then limits the process. To reach 50/hour, the center also needs printing capacity of at least 50/hour: five printers give 60/hour. Collation would then need a third worker (60/hour). So eliminating queue growth requires at least a second intake clerk, five printers, and three collation workers, unless processing times are reduced.