Scheduling e-KYC Camps Across Three Villages
The block office must hold one e-KYC camp in each of three villages - Nuagaon, Kadamba and Bahal - on Monday, Tuesday and Wednesday, one camp per day. Three officers, Meena, Rakesh and Sulochana, will each run exactly one camp. Constraints: Kadamba cannot be on Monday because of the weekly haat; Rakesh's camp is on Tuesday; Nuagaon's camp must come before Kadamba's; Meena will not go to Kadamba; Sulochana cannot work on Wednesday.
Each camp runs from 10:00 to 16:00 with a one-hour lunch break and has five registration counters, each taking 8 minutes per beneficiary on average. Expected turnouts are Nuagaon 180, Kadamba 150 and Bahal 210. The office has one vehicle, which is booked for election material on Thursday and Friday. A group from a fourth village, Tentuligaon, with 90 beneficiaries, has asked for a camp on Thursday.
1. Work out the full schedule and show why the other possible arrangements fail.
Read the worked answer
Rakesh is fixed on Tuesday, so the village held on Tuesday is Rakesh's.
Test Nuagaon on Tuesday. Then Kadamba must be Wednesday (it must follow Nuagaon and cannot be Monday), leaving Bahal on Monday. Monday and Wednesday must be shared by Meena and Sulochana. Sulochana cannot take Wednesday, so she takes Monday (Bahal) and Meena takes Wednesday (Kadamba). But Meena will not go to Kadamba. Fails.
Test Nuagaon on Monday. Kadamba is Tuesday or Wednesday.
- If Kadamba is Wednesday, Bahal is Tuesday, so Rakesh is at Bahal. Monday and Wednesday go to Meena and Sulochana; Sulochana cannot take Wednesday, so she takes Monday (Nuagaon) and Meena takes Wednesday (Kadamba). Meena refuses Kadamba. Fails.
- Therefore Kadamba is Tuesday and Bahal is Wednesday. Tuesday is Rakesh, so Rakesh is at Kadamba. Sulochana cannot take Wednesday, so she takes Monday (Nuagaon), and Meena takes Wednesday (Bahal). Works.
Final schedule: Monday - Nuagaon, Sulochana; Tuesday - Kadamba, Rakesh; Wednesday - Bahal, Meena. The solution is unique.
2. Using the camp timings and counter rate, identify which village cannot be fully covered and propose the least disruptive fix.
Read the worked answer
Working time per camp = 10:00 to 16:00 minus a one-hour lunch = 5 hours = 300 minutes.
Per counter: 300 / 8 = 37.5, so 37 completed registrations per counter (a half-finished registration is not a registration).
Five counters give 5 x 37 = 185 beneficiaries per day.
Compare with turnout:
- Nuagaon 180 - 5 places spare.
- Kadamba 150 - 35 places spare.
- Bahal 210 - short by 25.
The constraint binds at Bahal. Options, in order of least disruption:
- Add a sixth counter at Bahal for that day only - capacity becomes 6 x 37 = 222, covering 210 with 12 spare. Costs one extra staff member and one laptop.
- Extend the camp by 45 minutes: 345 / 8 = 43 per counter, 5 x 43 = 215, but the last 5 places are marginal and staff overtime and return travel after dark must be considered.
- Extending by only 30 minutes gives 330 / 8 = 41 per counter, 205 in total - still 5 short. This option fails arithmetic and should not be proposed.
Recommend option 1, plus token distribution from 9:30 so that the 25 overflow cases are known early and given a fixed slot instead of being turned away.
3. Tentuligaon (90 beneficiaries) asks for a Thursday camp. Decide whether to accept and justify the decision with figures.
Read the worked answer
Capacity is not the obstacle: 90 x 8 = 720 counter-minutes; spread over five counters that is 144 minutes, about 2 hours 24 minutes, comfortably inside a half-day. The obstacles are the single vehicle, which is committed to election material on Thursday and Friday, and staff fatigue after three consecutive camp days.
Options:
- Hold it Thursday by hiring a vehicle. Feasible if the hire cost is low and two officers are free; the half-day camp would finish well before dusk. But it breaks the same vehicle-and-staff plan that the election work depends on, and a hired vehicle may not be available at short notice.
- Attach it to Wednesday at Bahal. Reject: Bahal is already short by 25 places, and adding 90 would need a second extra counter and a longer day.
- Defer to the following Monday and intimate in writing. This is the sound default. Meanwhile, collect names and documents at the Tentuligaon panchayat so that the actual camp is a verification exercise rather than a queue.
Recommended decision: defer with a dated written slip to every applicant, and hold a pre-verification camp at the panchayat on Thursday using two staff who can travel by the regular bus. If a rented vehicle is in fact available cheaply, a Thursday half-day camp with five counters is arithmetically safe and may be approved in writing.