The Overtime Roster
A station has 12 officers available for patrol over a 24-hour period. Policy requires a minimum of 3 officers on patrol at all times. Each officer can work a maximum of 8 hours in the 24-hour period and must have at least 8 hours rest between shifts. Six of the officers have already worked an 8-hour shift ending at 18:00 and cannot work again until at least 02:00. The remaining six are fresh and available from 18:00. The station commander wants to know whether the minimum can be met through the night and where the gaps are.
1. Determine whether the 3-officer minimum can be maintained from 18:00 to 06:00, showing your reasoning.
Read the worked answer
Officers available:
- 6 tired officers: off until 02:00, then available for up to 8 hours (02:00–10:00).
- 6 fresh officers: available from 18:00 for up to 8 hours each.
Coverage needed: 3 officers × 12 hours (18:00–06:00) = 36 officer-hours.
Fresh officers can supply: 6 × 8 = 48 officer-hours, but only within their 8-hour window. If all six start at 18:00 they finish at 02:00, leaving 02:00–06:00 uncovered by fresh officers.
Better plan: Split the six fresh officers into two groups of three. Group A works 18:00–02:00; Group B works 22:00–06:00 (staggered starts keep 3 on patrol). Check: 18:00–22:00 Group A only = 3 ✓; 22:00–02:00 A+B = 6 (more than minimum, fine); 02:00–06:00 Group B = 3 ✓.
Conclusion: The minimum can be met 18:00–06:00 using staggered shifts among the six fresh officers, without touching the tired officers. The tired officers are then available from 02:00 as reserve.
2. The commander wants to also cover 06:00–10:00 at the minimum. Using the tired officers, explain the constraint and one risk.
Read the worked answer
Constraint: The six tired officers become available at 02:00 and can work up to 8 hours, i.e. until 10:00. To cover 06:00–10:00 at 3 officers, three of them can start at 02:00 (after their rest) and work to 10:00 - but that means they have worked a full 8 hours again with only 8 hours' rest. Alternatively, they start at 06:00 and work to 14:00, which covers the gap but leaves 02:00–06:00 to be covered by the fresh Group B (which finishes at 06:00), so a handover must be arranged at 06:00.
Risk: Fatigue. Officers working an 8-hour shift, resting 8 hours, then working another 8 hours accumulate fatigue, which degrades judgement, reaction time, and decision-making - exactly the qualities patrol work depends on. The roster meets the letter of the policy but may not meet its purpose. The commander should monitor fatigue, rotate duties, and treat the minimum as a floor, not a target.