Peak-Load Desk Allocation at Port Meridian
Port Meridian's air terminal handles a single morning shift, 06:00–14:00. Six primary inspection desks are rostered, each officer processing a passenger in an average of 1.2 minutes, or 50 passengers per desk-hour. Two desks close from 10:00 to 12:00 for mandatory training, leaving four open during that period. Total arriving passengers for the shift are forecast at 1,920, distributed evenly across the eight hours except for a peak of 300 passengers per hour between 10:00 and 12:00. The service standard requires 95% of passengers to reach a decision within 45 minutes of joining the queue. Secondary inspection refers 6% of arrivals, each taking an average of 14 minutes; four secondary desks are staffed for the full shift. Last Tuesday the queue at 12:00 reached 210 passengers and 14 people missed connecting flights, prompting a complaint from the airport operator.
1. Calculate primary inspection capacity for the shift and the utilisation rate. Does aggregate capacity prove the roster is adequate? Show your working.
Read the worked answer
Capacity. 6 desks × 8 hours = 48 desk-hours. Training removes 2 desks × 2 hours = 4 desk-hours, leaving 44 desk-hours. At 50 passengers per desk-hour, capacity is 44 × 50 = 2,200 passengers. Forecast demand is 1,920, so aggregate utilisation is 1,920 ÷ 2,200 = 87.3%, with 280 passenger-spaces (5.6 desk-hours) spare.
Why the aggregate is misleading. Between 10:00 and 12:00 only four desks are open: capacity is 4 × 50 = 200 passengers per hour against 300 arriving, a shortfall of 100 per hour and a backlog of 200 after two hours. Outside the peak, arrivals are (1,920 − 600) ÷ 6 = 220 per hour against 300 capacity, a surplus of 80 per hour. Clearing 200 at 80 per hour takes 2.5 hours, so the queue persists until about 14:30, beyond the shift. The 45-minute standard cannot be met at the peak.
Aggregate utilisation of 87% therefore does not prove the roster is adequate; the timing of capacity matters more than the daily total.
2. Calculate the secondary inspection workload and utilisation. Do four desks suffice? Explain the peak risk.
Read the worked answer
Workload. 6% × 1,920 = 115.2, so about 116 passengers. Work = 116 × 14 = 1,624 minutes = 27.1 desk-hours. Capacity = 4 desks × 8 hours = 32 desk-hours. Utilisation = 27.1 ÷ 32 = 84.6%, leaving 4.9 desk-hours.
Does four suffice? On a whole-shift average, yes. The peak exposes the risk: 6% of the 600 peak arrivals = 36 referrals. At 14 minutes each, that is 504 minutes = 8.4 desk-hours, but four desks deliver only 8 desk-hours in the two-hour window. Secondary is therefore over 100% utilised during the peak and a queue forms.
Because referrals are not evenly spaced, a cluster of two or three complex cases can breach the standard even when the shift total looks comfortable. The last Tuesday queue of 210 at 12:00 is consistent with primary congestion, but secondary should be modelled hourly rather than as a daily total. A queue in secondary feeds back into primary, because referred passengers occupy primary desks until a secondary space is free.
3. Recommend two roster or process changes to protect the 45-minute standard, justifying each with numbers.
Read the worked answer
Option A: move the training. Reschedule the two-desk training to 06:00–08:00 or after 14:00. That restores six desks throughout the peak: capacity 300 per hour against 300 arriving, eliminating the 200 backlog and protecting the 45-minute standard. Training hours are unchanged and no overtime is required.
Option B: stagger and surge. Keep four desks training but open a fifth and sixth desk between 10:00 and 12:00 using overtime or a later shift, and stagger the training across four days so only one desk closes at a time. A one-desk closure costs 50 passengers per hour of capacity; the peak shortfall then falls to 50 per hour and clears in about 40 minutes.
Recommendation. Option A is the lower-cost fix because it removes the cause rather than buying capacity. Pair it with hourly queue monitoring and a trigger: if the queue exceeds 120, open a fifth primary desk and move one secondary officer to triage. Record the reasoning so the airport operator's complaint receives a specific, numerical response rather than a general assurance.