Deployment Arithmetic for a Fourteen-Day Mela
A sub-divisional police officer must plan static deployment for a 14-day fair. Effective strength available to him is 6 head constables and 44 constables; three more constables are on medical leave, and one SI is held back for supervisory rounds and is not counted in static deployment. Standing orders require, in every 8-hour shift: 5 nakas (barriers) with 2 constables each, 1 mobile patrol party of 3, and 4 constables for the station/control-room guard. A reserve equal to 15% of that shift's deployment must be kept, rounded up to the next whole person, for emergencies. Departmental rules permit only one rest day in seven per person, and in normal deployment not more than 8 hours of duty a day. The SP says he can release 12 constables from the district reserve, but no more. The fair opens in four days, and the deployment order must be in writing before the first VIP visit.
1. Compute the minimum person-shifts required per day under standing orders, the effective availability per day, and the size of the gap in both person-shifts and headcount.
Read the worked answer
Per-shift requirement (5 nakas):
- Nakas: 5 × 2 = 10
- Mobile patrol: 3
- Station/control-room guard: 4
- Sub-total = 17
- Reserve: 15% of 17 = 2.55 → rounded up = 3
- Total per shift = 20
Per day (3 shifts of 8 hours): 20 × 3 = 60 person-shifts per day.
Availability: deployable strength is 6 HC + 44 constables = 50. With one rest day in seven, each person gives 6/7 of a shift per day: 50 × 6/7 = 42.86 → 42 person-shifts per day (round down; you cannot deploy 0.86 of a person).
Gap: 60 − 42 = 18 person-shifts per day.
In headcount: each additional person supplies 6/7 of a person-shift per day, so 18 ÷ (6/7) = 21 additional personnel.
Reading: the standing order as written cannot be executed with this strength at 8-hour shifts - it needs roughly 21 more persons, not 12. The 8-hour rule and the reserve rule are both mandatory, so the shortfall must be closed by extra force, by a formally approved relaxation, or by cutting the deployment; doing nothing and letting constables work double shifts is not an option the rules allow.
2. The SP releases 12 constables. Is the full 5-naka plan now feasible at 8-hour shifts? If not, what is the maximum number of nakas that can be manned while still keeping the 15% reserve and the rest-day rule?
Read the worked answer
New availability: 50 + 12 = 62 personnel → 62 × 6/7 = 53.14 → 53 person-shifts per day.
Testing naka counts (requirement = 3 × [2N + 3 + 4 + ceil(0.15 × (2N + 7))]):
- N = 5: base 17, reserve 3, per shift 20 → 60 per day. Short by 7.
- N = 4: base 15, reserve ceil(2.25) = 3, per shift 18 → 54 per day. Short by 1.
- N = 3: base 13, reserve ceil(1.95) = 2, per shift 15 → 45 per day. Surplus of 8.
Answer: 5 nakas is still not feasible; 4 nakas is feasible only if one extra person-shift per day is found; 3 nakas is comfortably feasible.
How to use the finding: the honest recommendation is to man 4 nakas and cover the single missing person-shift by putting the supervisory SI into the reserve slot for one shift - accepting that he then does not do rounds - or by asking for one Home Guard. Manning 3 nakas and banking the surplus of 8 is the safer option if the approach roads are low-risk: that surplus can become a second patrol party or a women's help desk, which the mela actually needs. What the officer must not do is quietly plan 5 nakas knowing the reserve will be emptied on day one; the reserve is the only cushion when an incident happens.
3. Write the core of the officer's recommendation to the SP. Include the 12-hour-shift alternative and the risk you must flag with it.
Read the worked answer
Recommendation (three options, with arithmetic):
- Option A - full compliance with standing orders: requires 21 additional personnel beyond present strength. Cannot be met from the 12 released.
- Option B - 12-hour shifts (two shifts a day) with 5 nakas: requirement = 2 × 20 = 40 person-shifts per day against a present capacity of 42 (before the 12 extras). This is feasible today, and with the 12 extras (53 available) it leaves a real cushion. But it breaches the 8-hour norm and must be approved in writing by the SP, not assumed by the SI.
- Option C - 8-hour shifts with 4 nakas and the single gap plugged as shown.
Risk to flag with Option B: twelve hours on a barrier produces exactly the failure the deployment is meant to prevent - a tired constable misses a vehicle check at 4 a.m., or overreacts at a crowding point. The recommendation should therefore carry conditions: rotate night shifts so no one does more than two consecutive nights, give a genuine 12-hour rest between shifts, keep the reserve intact rather than borrowing from it, and brief the men that fatigue is a reportable condition. Note also that a 12-hour pattern leaves no surge capacity for the 20:00 VIP movement, so the reserve must be protected.
Framing: present this as options with numbers, not as a complaint. The SI's duty is to tell the SP what the standing order costs in manpower and what the cheaper alternative costs in risk; the choice, and any relaxation, must be recorded in writing.