The Roster That Does Not Add Up
A police station has 18 constables sanctioned for shift duty. Daily requirement: Shift A (06:00–14:00) 6 constables, Shift B (14:00–22:00) 5, Shift C (22:00–06:00) 4 - 15 posts a day. Three constables are on sanctioned leave for the next 7 days, and one of the remaining constables is on light duty and cannot be assigned night shift. Every constable is entitled to one weekly off. A constable who finishes Shift C cannot be placed in Shift A the next day. The station has an overtime budget of 40 hours per constable per month; two constables have already completed 30 overtime hours this month. The inspector asks whether the roster can be run for the next 7 days without violating the rest rule or the budget.
1. Calculate the weekly shift requirement and the available shift capacity. Is the roster feasible without overtime? Show your working.
Read the worked answer
Requirement: 6 + 5 + 4 = 15 posts per day × 7 = 105 eight-hour shifts per week.
Availability: 18 sanctioned − 3 on leave = 15 constables. With one weekly off, each gives 6 shifts, so 15 × 6 = 90 shifts. Gap = 105 − 90 = 15 shifts.
The light-duty constable cannot cover C, but C needs 4 × 7 = 28 night shifts and the other 14 constables can supply up to 14 × 6 = 84 night-capable shifts, so night coverage is not the binding constraint. The binding constraint is total shifts: 90 available against 105 required.
Therefore the roster is not feasible without overtime, a temporary reduction in posts, or additional staff. The rest rule (no C followed by A next day) must be checked when assigning the 90 shifts, but it does not remove the 15-shift gap.
2. How many overtime hours are needed to cover the gap, and is the station within its overtime budget?
Read the worked answer
15 shifts × 8 hours = 120 overtime hours.
Budget: 13 constables have 40 hours each = 520 hours; 2 constables have 10 hours each left (40 − 30) = 20 hours; total 540 hours. 120 < 540, so the station is within the monthly budget.
But budget availability does not prove feasibility: the 120 hours must be distributed without breaching the C-to-A rest rule, without pushing any constable beyond 40 hours, and without putting all extra load on the same few people. A safe plan is to add overtime mainly to B and A shifts and to use a rest day after a night shift. I would also check daily rest of at least 8 hours between shifts. If the inspector wants zero overtime, the only alternatives are temporary deputation or reducing posts.
3. The inspector wants to reduce one shift's strength instead of paying overtime. Which shift should not be reduced, and what is the least harmful reduction?
Read the worked answer
Shift C should not go below 4. Night duty covers the station's perimeter, lock-up, and emergency response; reducing it creates a safety and escape risk that no overtime saving justifies. Shift A has the highest public footfall and court/record work, so cutting it also causes visible harm. Shift B is busy in the evening but has more supervisory overlap with A.
The least harmful single reduction is one post from B for the seven days: that saves 7 shifts, leaving 8 shifts (64 hours) to cover by overtime. This keeps A at 6 and C at 4, stays within the 540-hour budget, and limits the cut to the shift with the most fallback. I would record the risk assessment and review it after seven days rather than make the cut permanent.