Scheduling Four Panchayat Inspections
The BDO must inspect four panchayat offices, A, B, C and D, on one day. Each inspection takes 30 minutes. Travel times are A to B 20 minutes, B to C 25 minutes, C to D 20 minutes, D to A 30 minutes, A to C 35 minutes and B to D 30 minutes. The BDO starts at A at 9:00 a.m. Office C closes at 12:00 noon. Office D's secretary is available only after 10:30 a.m. The driver must refuel at the depot beside B for 15 minutes before 11:00 a.m. The BDO needs a 20-minute lunch after 12:30 p.m. The assistant proposes the order A-C-B-D. The BDO asks the Panchayat Secretary to test the proposal, identify any conflict and suggest a workable order that finishes as early as possible without repeating an office.
1. Test the assistant's proposed order A-C-B-D and identify every conflict.
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A-C-B-D runs as follows. A: 9:00-9:30. Travel A-C 35 minutes, arrive C 10:05. C: 10:05-10:35, so C's noon closing is met. Travel C-B 25 minutes, arrive B 11:00. B: 11:00-11:30. The next required action is refuelling at B, but it would begin at 11:30, after the 11:00 a.m. deadline. That is a clear conflict.
Travel B-D 30 minutes would arrive at D at 12:15, which is after D's 10:30 availability, so D itself is not a problem. D would run 12:15-12:45, and lunch would then be at 12:45, satisfying the after-12:30 rule. The fatal defect is not C or D but the refuelling window; the proposed order cannot be approved as it stands.
2. Find a workable order and give the timeline.
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A-B-C-D works. A: 9:00-9:30. Travel A-B 20 minutes, arrive B 9:50. Refuel 9:50-10:05, before the 11:00 deadline. B: 10:05-10:35. Travel B-C 25 minutes, arrive C 11:00. C: 11:00-11:30, before C closes at noon. Travel C-D 20 minutes, arrive D 11:50. D: 11:50-12:20, after D's 10:30 availability. Inspections finish at 12:20.
Lunch must be after 12:30, so the BDO can use 12:20-12:30 for notes and then take lunch from 12:30 to 12:50. All constraints are met: C is visited before noon, D after 10:30, refuelling before 11:00, and no office is repeated. This also finishes inspections earlier than the proposed order would, even if the refuelling defect were ignored.
3. What reasoning should the Secretary give if the BDO asks whether A-B-D-C might be earlier?
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A-B-D-C appears attractive but fails C's closing time. A: 9:00-9:30. Travel A-B 20 minutes, arrive 9:50. Refuel 9:50-10:05. B: 10:05-10:35. Travel B-D 30 minutes, arrive D 11:05. D: 11:05-11:35. Travel D-C 20 minutes, arrive C 11:55. C would then run 11:55-12:25, which crosses the noon closing. Even if the office merely stops accepting new work at noon, an inspection starting at 11:55 is unsafe and likely to be refused.
The Secretary should compare constraints, not just total travel time. A route is feasible only if every fixed window is met. A-B-C-D meets the refuelling, C-closing and D-availability windows; A-B-D-C does not meet C's closing. The recommendation should therefore stay with A-B-C-D unless the C office agrees in writing to stay open.