Window Staffing and Break Decision
A retail window has three clerk stations. Between 10:00 and 12:00, customer arrivals average 42 per hour. Each transaction averages 4 minutes, so one clerk serves 15 customers per hour. Two clerks are scheduled from 10:00; the third is on a 30-minute break from 10:30 to 11:00. The office policy is a 10-minute average wait target, and breaks may be rescheduled but not skipped. At 10:00 there is no backlog. A customer complaint about waiting was filed yesterday.
1. Calculate the backlog at 12:00 assuming no one adjusts the schedule. Show capacity and demand for each half-hour block.
Read the worked answer
One clerk = 60 ÷ 4 = 15 customers/hour, or 7.5 per half hour. Demand = 42/hour, or 21 per half hour.
- 10:00–10:30: 2 clerks. Capacity 15; demand 21. Backlog +6 → 6.
- 10:30–11:00: 2 clerks (third on break). Capacity 15; demand 21. Backlog +6 → 12.
- 11:00–11:30: 3 clerks. Capacity 22.5; demand 21. Backlog −1.5 → 10.5.
- 11:30–12:00: 3 clerks. Capacity 22.5; demand 21. Backlog −1.5 → 9.
At 12:00 roughly 9 customers are waiting, and the queue is shrinking by only about 3 per hour.
2. The third clerk offers to skip the break. Using the numbers and policy, propose a better option and show its effect.
Read the worked answer
Better option: move the break to 11:00–11:30 and keep three clerks through the 10:00–11:00 peak.
Effect:
- 10:00–11:00: 3 clerks, capacity 45/hour vs demand 42. Backlog falls by 3 over the hour, ending at 0.
- 11:00–11:30: 2 clerks, capacity 15 vs demand 21. Backlog +6 → 6.
- 11:30–12:00: 3 clerks, capacity 22.5 vs demand 21. Backlog −1.5 → 4.5, about 4–5 waiting.
This roughly halves the noon backlog, satisfies the break requirement, and avoids the policy violation of skipping it. Skipping the break would help, but it breaks policy and creates a fatigue and morale cost that the numbers do not capture.
3. What is the minimum staffing needed to meet the 10-minute wait target at 42 arrivals per hour, and what does that imply about yesterday's complaint?
Read the worked answer
Workload = 42 customers × 4 minutes = 168 clerk-minutes per hour = 2.8 clerks of continuous work.
Three clerks (3.0) is the minimum whole-number staffing that keeps utilization below 100%. But 2.8 of 3.0 is about 93% utilization, which leaves almost no cushion; queues and waits grow sharply at that level. Four clerks gives about 70% utilization, which is the realistic way to hold a 10-minute average wait.
Implication: with only two clerks for part of the morning and no backlog allowance, the complaint is structurally predictable rather than a single slow clerk. The fix is schedule design, not individual blame.