Duty roster with a hospital emergency on Monday morning
Your office must publish a duty roster for the reconciliation desk for Monday to Friday, one clerk per day, for five clerks: Anil, Bhavna, Chetan, Deepa and Eknath. Each clerk is to be given exactly one day. The rules agreed at the staff meeting are: (i) Deepa can attend only on Wednesday, because she is on a training programme the other four days; (ii) Anil cannot take Monday or Friday because of a school drop-off commitment; (iii) Bhavna must be posted on the day immediately after Eknath, since she takes over cash verification from him; (iv) Chetan's day must fall before Deepa's day. On Monday at 8.40 a.m. Chetan telephones to say he has been admitted to hospital and cannot attend. The Assistant Engineer asks you to 'adjust someone into Monday' and publish the roster before 10 a.m. so that the counter opens on time. The counter cannot remain unmanned, and the published roster is the record against which attendance is marked.
1. Derive the original roster for Monday to Friday, showing how each rule eliminates the alternatives.
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Fix Deepa on Wednesday (rule i).
Place the Eknath–Bhavna pair (rule iii: Bhavna is the day after Eknath). The possible pairs are (Mon, Tue), (Tue, Wed), (Wed, Thu) and (Thu, Fri).
- (Tue, Wed) and (Wed, Thu) fail because Wednesday is Deepa's.
- (Mon, Tue) fails on rule (iv): Chetan must be before Deepa (Wednesday), so Chetan would need Monday or Tuesday, but Monday is Eknath and Tuesday is Bhavna. No day is left for Chetan before Wednesday.
- Therefore the pair must be (Thu, Fri) - Eknath Thursday, Bhavna Friday.
Fill Monday and Tuesday with Anil and Chetan. Rule (ii) bars Anil from Monday and Friday, so Anil takes Tuesday and Chetan takes Monday. This also satisfies rule (iv), since Monday is before Wednesday.
Final roster: Monday - Chetan; Tuesday - Anil; Wednesday - Deepa; Thursday - Eknath; Friday - Bhavna.
Note that the pair placement is the pivot: once Wednesday is fixed, the only pair position that leaves a day before Wednesday for Chetan is Thursday–Friday.
2. Can any clerk be shifted to Monday without breaking a rule? Test each candidate and state the conclusion.
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Test each clerk in turn.
- Anil to Monday: barred outright by rule (ii). Rejected.
- Bhavna to Monday: rule (iii) would place Eknath on Sunday, outside the roster week. Rejected.
- Deepa to Monday: barred by rule (i), she can attend only Wednesday. Rejected.
- Eknath to Monday: then Bhavna must be Tuesday and Deepa is Wednesday; Chetan, who must be before Wednesday, has only Monday and Tuesday available, both now taken. Anil would be left with Thursday or Friday, and rule (ii) bars him from Friday, so the schedule collapses. Rejected.
- Swapping Anil to Monday: the same bar as above; Anil cannot take Monday.
Conclusion: no single move satisfies all four rules. The constraint that bites is rule (iii) - it fixes an adjacent pair - combined with rule (iv), which needs a free day before Wednesday for Chetan. So the request to 'adjust someone into Monday' cannot be met within the agreed rules; a rule must be formally relaxed in writing, or cover must come from outside the roster.
3. What will you do and record before 10 a.m.? Give the options in the order you would try them and say what must appear on the record.
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Option 1 - obtain a written relaxation of rule (ii). Ask the Assistant Engineer to permit Anil on Monday and shift Anil's Tuesday slot to nobody (Tuesday would then be vacant), which still leaves a gap. A cleaner relaxation is to post Anil on Monday and move the counter's Tuesday work to the Thursday/Friday pair by written order. Any relaxation must be recorded with the rule waived, the reason, the approving officer and the date.
Option 2 - deployment from another section. Request a clerk from an adjacent section for Monday only, with the AE's approval, and enter the name in the roster with the remark 'deployed vide AE's order dated ____'.
Option 3 - the AE or head clerk mans the counter for Monday, recorded in the same manner.
Record to be kept: an office note stating that Chetan is on medical grounds, the roster as originally approved, the specific rule relaxed or the outside deployment, the approving authority, and the attendance marking for Monday. The published roster must not simply show a different name with no explanation, because attendance and any later query will be checked against it.