Night patrol roster that cannot be met after a guard falls ill
Your beat has four guards - Ramesh, Suresh, Kavita and Dinesh - and the night patrol from 20:00 to 04:00 must run every night with exactly two guards. The divisional safety guideline says no guard may be detailed on two consecutive nights, every guard must get at least two nights in the week, and no guard may exceed four nights. The roster already circulated is: Monday Ramesh and Suresh; Tuesday Kavita and Dinesh; Wednesday Ramesh and Suresh; Thursday Kavita and Dinesh; Friday Ramesh and Suresh; Saturday Kavita and Dinesh; Sunday Ramesh and Suresh. At 16:00 on Wednesday, Suresh reports to you with fever; the block PHC doctor advises three days of rest, so he is unavailable for the Wednesday, Thursday and Friday nights. The Range Officer is away at a meeting and cannot be contacted before Thursday noon. You must post a revised roster before the 20:00 roll call, and the beat diary must record why.
1. Check the circulated roster against the three rules before Suresh reported sick.
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Count the nights. Ramesh: Monday, Wednesday, Friday, Sunday = 4. Suresh: the same four = 4. Kavita: Tuesday, Thursday, Saturday = 3. Dinesh: the same three = 3. Total 14 duty-nights, which equals 7 nights x 2 guards - the arithmetic matches.
Rule 1, maximum four. Ramesh 4, Suresh 4, Kavita 3, Dinesh 3. Compliant. Rule 2, at least two. Everyone has at least three. Compliant. Rule 3, no consecutive nights. Check each guard's sequence. Ramesh: Mon-Wed-Fri-Sun, all separated by a night. Suresh identical. Kavita and Dinesh: Tue-Thu-Sat. Compliant.
Conclusion. The circulated roster was valid before 16:00 on Wednesday. That matters, because it means the problem is not a badly made roster - it is the sudden loss of one person, and your note should say so rather than blaming the original plan.
2. Can Ramesh, Kavita and Dinesh cover the remaining five nights without breaking the no-consecutive rule? Prove your answer.
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First, the immediate block. Kavita and Dinesh worked Tuesday. Under the no-consecutive rule neither can work Wednesday. Ramesh can, since he last worked Monday. That gives one eligible guard for a two-guard night. Wednesday cannot be staffed under the rule at all, before any further counting.
Second, the arithmetic for the whole period. Five nights (Wed to Sun) x 2 = 10 duty-nights, to be covered by three guards. In five consecutive nights, a guard who is never on two consecutive nights can work at most three nights - pattern 1, 3, 5. So the maximum available is 3 guards x 3 = 9 duty-nights against a requirement of 10. Short by one, permanently.
Third, note that the four-night ceiling is not the problem. Even if the ceiling were raised, the no-consecutive rule keeps the capacity at 9. So the rule to relax is the rest rule, not the ceiling, and it need only be relaxed once.
Conclusion. The requirement is infeasible on the present strength. Any roster that claims to meet all three rules with three guards is arithmetically false and should not be signed.
3. You must post a roster before 20:00. Set out your options, rank them, and justify the one you choose.
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Option A - borrow one guard from the adjoining beat for Wednesday to Friday. Best option. It preserves the rest rule, keeps two-person patrols intact, and costs the neighbouring beat only three nights. It needs the Range Officer's order, so record the telephonic or verbal permission in the beat diary immediately and send written intimation on Thursday morning. If the adjoining beat is short-staffed, ask for one night only, since a single extra person removes the deficit entirely.
Option B - one guard works one consecutive pair, with compensatory rest. Acceptable fallback if no help can be reached. Choose the physically fittest and nearest-resident guard, pair him across Wednesday-Thursday or Thursday-Friday only, give him a full 24 hours off immediately afterwards, and record the deviation, the reason and the compensatory rest in the diary. This is a deliberate, documented exception, not a quiet breach.
Option C - single-guard patrol on the quieter nights. Reject. The two-person rule exists for physical safety, for wireless or mobile cover, and because a single guard's seizure and evidence are weak against a well-prepared offender. Saving a roster rule at the cost of an assault or a failed prosecution is a bad trade.
Option D - call Suresh back. Reject outright. He has a medical certificate and three days of rest; a sick guard on a four-hour night patrol in the forest is a liability and an offence against basic duty of care.
Chosen course. Try A first, fall back to B, and never C or D. Post the roster, brief both guards at roll call, log the deviation with reasons, and place the full facts before the Range Officer on Thursday as a written note.