Household Survey After Enumerator Transfers and Rain Losses
A block office must complete a household survey of 10,800 households in 20 working days. It deploys 45 enumerators, each expected to cover 12 households per day. After 8 working days, 8 enumerators are transferred and cannot be replaced from the existing pool; separately, 3 working days are lost to heavy rain. The district deadline cannot move. The office can hire temporary enumerators at ₹650 per enumerator per day, or extend the existing team's working days at the same daily rate but only up to 6 extra days before the data quality audit. Daily supervision costs ₹2,000 regardless of team size. Data quality falls sharply if any enumerator is asked to cover more than 14 households per day. The first 8 days met the 12-household target exactly.
1. Calculate the number of households remaining and the daily output required. How many additional enumerators are needed to finish on time without exceeding the 14-household quality limit?
Read the worked answer
Work completed in 8 days = 45×12×8 = 4,320 households. Remaining = 10,800 − 4,320 = 6,480. Remaining working days = 20 − 8 − 3 = 9. Required output = 6,480/9 = 720 households/day. At the quality ceiling of 14 per enumerator per day, the minimum team is 720/14 = 51.43, so 52 enumerators. The existing team is 45 − 8 = 37, so 15 temporary enumerators are needed. If you instead hold the original 12/day norm, you need 720/12 = 60, i.e. 23 temporaries, but that is not required by the stated quality constraint. State the assumption: 14/day is a ceiling, not a target, so schedule 52 with daily monitoring and do not let individual totals exceed 14.
2. The accountant says extending the 37 remaining enumerators by a few days is cheaper than hiring 15 temporaries. Evaluate the claim and recommend.
Read the worked answer
With 37 enumerators at 12/day, output is 444/day; 6,480/444 = 14.6, so 15 days are needed, which is 6 extra days beyond the 9 remaining. Cost = 37×15×650 + 15×2,000 = 360,750 + 30,000 = ₹3,90,750. At 14/day, output is 518/day; 6,480/518 = 12.5, so 13 days, 4 extra days. Cost = 37×13×650 + 13×2,000 = 312,650 + 26,000 = ₹3,38,650. Hiring 52 for 9 days costs 52×9×650 + 9×2,000 = 304,200 + 18,000 = ₹3,22,200. The temporary option is cheaper by ₹68,550 at 12/day and by ₹16,450 at 14/day, and it meets the fixed deadline. Extension also misses the district deadline even if the quality audit would allow it, so it is not a feasible alternative unless the deadline is renegotiated.
3. What daily control would you use to keep quality from collapsing when 15 new enumerators join?
Read the worked answer
Pair each temporary with an experienced enumerator for the first two days, cap every person at 14 households and visibly track the daily count. Require a 10% random back-check of completed households, compare refusal and replacement rates by enumerator, and review any list with more than 14 entries or an unusual completion time. Hold a 15-minute morning huddle on the definition of a household and the replacement rule. If error rates rise, reduce the tempo and add a day only through the approved extension, not by silently pushing individual output above 14.