March Review: Staffing, Fuel Arithmetic and an Argument That Proves Nothing
The head of a sûreté unit reviews March before signing the monthly report. Establishment: 12 officers, of whom 1 is on annual leave and 1 at a training course for the whole month, leaving 10. Cover required: three shifts a day (06–14, 14–22, 22–06) with two officers per shift, every day, including weekends. Rules: no officer may work more than 5 shifts a week, and no officer may take a shift beginning less than 8 hours after the end of the previous one. Fuel: one patrol shift covers 150 km, the two vehicles average 12 L/100 km, diesel is booked at 29.00 DA per litre, the month has 30 days, and the allocated fuel budget is 95,000 DA. In the fuel log, 60 litres are missing between two tank readings, and three officers held the tank key. The unit chief says: 'We stayed inside the fuel budget, so nothing was taken.'
1. Show whether the staffing plan is workable, then state the exact condition under which it stops being workable.
Read the worked answer
Demand: 3 shifts × 2 officers = 6 officer-shifts per day, so 42 per week.
Capacity: 10 officers × 5 shifts maximum = 50 officer-shifts per week. Margin: 8 shifts. The plan is therefore workable, with every officer averaging 4.2 shifts a week.
The 8-hour rule does not reduce this capacity but constrains the rotation: an officer on 22–06 cannot take the 06–14 shift the same morning. The safe construction is to work in fixed pairs and move pairs forward by one shift each day - pair 1 morning, pair 2 afternoon, pair 3 night on day 1; pair 4 morning, pair 5 afternoon, pair 1 night on day 2, and so on. Each pair returns to the same shift about every two and a half weeks, and no officer ever follows a night with a morning.
Break point: two more absences. With 8 officers, capacity is 40 shifts against a demand of 42 - the plan fails by 2 shifts a week, and no rotation can repair it, because the 8-hour rule cannot be traded away. The answer is a written request for reinforcement or a formal reduction of cover, decided by the head of unit, not improvised in the roster.
2. Compute the monthly fuel requirement and cost, and say precisely how much room the budget leaves.
Read the worked answer
Per patrol shift: 150 km × 12 L/100 km = 18 litres.
Per day: 6 shifts × 18 L = 108 litres. Per 30-day month: 108 × 30 = 3,240 litres. Cost: 3,240 × 29.00 DA = 93,960 DA.
The budget is 95,000 DA, so the margin is 1,040 DA, i.e. 1,040 ÷ 29.00 ≈ 35.9 litres - one day and a bit of buffer, less than two full patrol shifts.
Two consequences follow. First, the plan is affordable but with almost no slack: a single extra patrol shift beyond the schedule consumes 18 L, i.e. half the margin. Second, and more important for the review, the margin is not a safety cushion against losses; it is smaller than the 60 litres reported missing, which is exactly why the chief's sentence needs to be tested rather than signed.
3. Evaluate the chief's argument: 'We stayed inside the fuel budget, so nothing was taken.'
Read the worked answer
The argument is invalid as it stands: staying inside the budget is compatible with a loss, provided the vehicles drove less than planned - and it is also incompatible with a 60-litre loss at the planned distance. The figures must be made to speak.
Budget in litres: 95,000 ÷ 29.00 ≈ 3,275.9 litres. If 60 litres disappeared in addition to normal consumption, spend would be (3,240 + 60) × 29.00 = 3,300 × 29.00 = 95,700 DA, i.e. 700 DA over budget. So a real 60-litre loss at planned distances could not have stayed inside the budget.
To fit both the budget and a 60-litre loss, actual patrol consumption could not exceed 3,275.9 − 60 = 3,215.9 litres, corresponding to 3,215.9 ÷ 0.12 ≈ 26,799 km, roughly 201 km less than the 27,000 km planned - about 1.3 shifts of driving. Therefore either the distances were lower than planned, the real consumption differs from 12 L/100 km, one of the two tank readings is wrong, or the budget line was topped up.
Conclusion to write in the report: the budget statement does not clear anyone. Reconcile fuel drawn against odometer readings and shift records for the period between the two readings, then hear the three key-holders. Sign nothing until that reconciliation is attached.