Secondary Inspection Staffing: Workload, Emergency Coverage, and Overtime
Secondary inspection at a small port operates from 14:00 to 18:00. Records show 120 travelers require secondary processing in that window. Arrivals are even except that 35% arrive between 16:00 and 18:00. Each inspection consumes an average of 8 minutes of officer time, and each officer can inspect only one traveler at a time. Policy requires at least two officers on duty at all times, one of whom must remain free for emergency response. Any officer scheduled more than 5 hours receives a 30-minute unpaid meal break. Four officers are available: two can work 14:00-18:00 and two can work only 16:00-20:00. Overtime is authorized at 1.5 times a base rate of $38 per hour. The shift supervisor must submit a written staffing plan by 12:00.
1. Compute the total inspection workload in officer-hours and the effective inspection capacity of the four available officers between 14:00 and 18:00. Does the plan meet demand?
Read the worked answer
Workload: 120 travelers × 8 minutes = 960 minutes = 16 officer-hours of inspection work.
Effective capacity: from 14:00 to 16:00, two officers are on duty. Because one must remain free for emergency response, only one officer can inspect: 1 officer × 2 hours = 2 officer-hours. From 16:00 to 18:00, four officers are on duty; after reserving one for emergency response, three can inspect: 3 officers × 2 hours = 6 officer-hours. Total effective inspection capacity = 8 officer-hours.
Result: the plan is 8 officer-hours short of the 16-hour workload. The four officers are not idle, but the emergency-response requirement removes one officer from inspection at all times, and the two late officers are unavailable during the first two hours. No meal break applies because no one is scheduled for more than 5 hours.
2. Where is the shortfall concentrated? Using the 35% arrival figure, show whether 16:00-18:00 is actually the busiest period.
Read the worked answer
The 35% figure does not make 16:00-18:00 the busiest period; it leaves 65% of arrivals in 14:00-16:00.
14:00-16:00: 65% × 120 = 78 travelers. 78 × 8 = 624 minutes = 10.4 officer-hours over 2 hours, or 5.2 inspectors on average. Adding the emergency officer means about 6.2 officers should be on duty. Only 2 are available, so the shortage is about 4.2 officers, or 8.4 inspection officer-hours.
16:00-18:00: 35% × 120 = 42 travelers. 42 × 8 = 336 minutes = 5.6 officer-hours over 2 hours, or 2.8 inspectors on average. Adding the emergency officer means about 3.8 officers; the 4 available officers just meet that demand.
The real shortfall is concentrated in the first two hours, not the later period with the higher percentage.
3. What is the least costly overtime addition that covers the 14:00-16:00 shortfall while preserving the emergency officer, and what does it cost? State your assumptions.
Read the worked answer
At 14:00-16:00, demand is 10.4 inspection officer-hours. The single available inspecting officer supplies 2 officer-hours, leaving a shortfall of 8.4 inspection officer-hours.
Assume added officers must work the full 2-hour block and are paid overtime at 1.5 × $38 = $57 per hour.
- Four added officers supply 4 × 2 = 8 officer-hours, for a total of 10 officer-hours. That is still 0.4 officer-hours short.
- Five added officers supply 10 officer-hours, for a total of 12 officer-hours, which covers demand with a small margin.
Cost for five added officers: 5 × 2 hours × $57 = $570.
If fractional scheduling were practical, four officers plus 24 minutes of a fifth would cost 8 × $57 + 0.4 × $57 = $478.80. With whole 2-hour blocks, $570 is the least costly compliant option. The emergency officer remains free throughout.