The roster that will not fit: manpower and overtime arithmetic before a festival bandobast
You are the Station House Officer of a rural police station in Jammu province with 46 sanctioned constable posts. On 1 October, six posts are vacant, four constables are on long medical leave, and two are attached to the district headquarters for a special investigation. The station runs three eight-hour shifts every day of the month. Each shift needs nine constables on beat patrol and two on station-house duty, and all eleven posts must be manned for all 30 days. Every constable is entitled to one weekly off, which comes to four off-days in a 30-day month. The station's monthly overtime budget is ₹1,80,000. A constable called for an extra shift beyond his roster is paid ₹450 per shift, and any constable who works a night shift also draws ₹150 as night allowance. No constable may be placed on more than two consecutive night shifts. On 5 October, three more constables apply for 15 days' leave beginning 10 October.
1. Calculate the station's deployable strength on 1 October and the monthly shortfall in constable-shifts. Can the gap be closed by cancelling weekly offs?
Read the worked answer
Step 1 – Deployable strength. 46 sanctioned − 6 vacant = 40 present. Of these, 4 are on long medical leave and 2 are attached outside the station: 40 − 4 − 2 = 34 constables actually available.
Step 2 – Requirement. Each shift needs 9 (beat) + 2 (station house) = 11 constables. Three shifts a day = 33 constable-shifts per day. For 30 days: 33 × 30 = 990 constable-shifts.
Step 3 – Supply without overtime. Each constable works 30 − 4 = 26 days. 34 × 26 = 884 constable-shifts.
Step 4 – Gap. 990 − 884 = 106 constable-shifts per month, roughly 3.5 shifts per day.
On cancelling weekly offs: cancelling all 136 off-days would nominally yield 1,020 shifts and appear to close the gap, but it is not a lawful routine fix. Weekly rest is a service condition, and mass cancellation exposes the department to claims and to fatigue-related error. It can be used only for a declared emergency, for the specific days of the bandobast, with compensatory rest recorded. The realistic options are sanctioned overtime, recall of the two attached constables, and temporary manpower (Home Guards/SPOs) for static duty.
2. Cost the overtime and night allowance for October and rule on whether the budget holds.
Read the worked answer
Overtime. 106 extra shifts × ₹450 = ₹47,700.
Night allowance. The night shift is one of the three daily shifts, so 11 night posts must be filled every night: 11 × 30 = 330 night-shift instances. Each attracts ₹150: 330 × ₹150 = ₹49,500. This is paid to whoever works the night shift, including a constable working his normal roster - it is an allowance, not overtime.
Base total: 47,700 + 49,500 = ₹97,200, against a budget of ₹1,80,000. Headroom = ₹82,800.
The trap to flag: if extra shifts themselves fall at night, each also draws ₹150. If all 106 extra shifts were night shifts, add 106 × ₹150 = ₹15,900, giving a worst case of ₹1,13,100. Even the worst case stays inside ₹1,80,000, so the roster is financially feasible for October.
But feasibility is not only financial. Check the consecutive-night rule: 330 night instances spread over 34 constables is about 9.7 nights each per month, so a rotation of two nights followed by a day/night change is workable. Record the rotation in the duty order, maintain a fatigue register, and keep overtime within about one extra shift per constable per week so that the 24-hour rest rule is not breached.
3. Three constables take 15 days' leave from 10 October. Recompute the shortfall and give the deployment you would actually issue.
Read the worked answer
Recalculation with an explicit assumption. For 15 days the three constables are unavailable: 3 × 15 = 45 person-days lost. But each would have had about two off-days in that 15-day window, so the net loss is 45 − 6 = 39 working days. Revised supply = 884 − 39 = 845; requirement stays 990; shortfall = 145 constable-shifts (about 4.7 extra shifts per available constable for the month).
Cost: 145 × ₹450 = ₹65,250, plus night allowance ₹49,500 = ₹1,14,750. If a large share of the extra shifts is at night, the figure can rise by up to 145 × ₹150 = ₹21,750, i.e. about ₹1,36,500 - still within ₹1,80,000.
Deployment I would issue:
- Recall the two attached constables for the 15-day window, with written intimation to the district headquarters.
- Request six Home Guards/SPOs for static station-house duty; they do not go on beat.
- Stagger weekly offs so that no more than four constables are off on any single day, and freeze leave for the rest of the month.
- Publish a night rotation in writing that honours the two-consecutive-night limit, and name a reserve constable for each shift.
- Record in the order why overtime, and not cancellation of weekly rest, was chosen.