The Certification Puzzle on Line 2
At a two-machine plant, each shift must run M1 and M2 with exactly two operators: one certified on M1 and one certified on M2. Asha and Chetan are certified only on M1; Bilal and Divya are certified only on M2. No operator may work both the day and night shift on the same day. Divya is unavailable every Friday; Bilal cannot work nights for medical reasons. A buddy waiver allows an M1-certified operator to run M2 for one shift only if an M2-certified operator is physically present on the same shift. On a normal Tuesday, all four are available. On the coming Friday, Divya calls in sick, and the night shift has a customer-critical M2 batch that cannot be moved to another week without a ₹40,000 penalty. The supervisor may reschedule within Friday and Saturday, but cannot hire or waive the medical restriction. The plant manager asks for the smallest feasible change that avoids the penalty.
1. On a normal Tuesday, which assignments are forced and which are flexible? Explain.
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Bilal cannot work nights, so he must take the day shift on M2. That forces Divya onto the night shift on M2, because she is the only other M2-certified operator. The M1 pair, Asha and Chetan, can split between day and night in either order. So the forced core is Bilal on day M2 and Divya on night M2; the only flexibility is which of Asha or Chetan works day M1 and which works night M1. There are two valid Tuesday schedules, not four, because Bilal's medical restriction removes the option of putting him on nights. Any schedule that puts Bilal on nights or leaves an M2 machine without Bilal or Divya violates a hard rule.
2. Divya calls in sick on Friday. Can the Friday night shift run both machines? If not, what is the smallest feasible change that avoids the ₹40,000 penalty?
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No. On Friday night, M2 needs Bilal or Divya. Bilal cannot work nights, and Divya is sick. The buddy waiver does not help because it requires an M2-certified operator to be physically present on the same shift; no such operator is available. Therefore the Friday night M2 batch cannot legally run. The smallest change is to move that night shift to Saturday night, when Divya is available: assign Divya to M2 and one of Asha or Chetan to M1. This stays within the same week, so the ₹40,000 penalty is avoided. It does not require hiring, waiving the medical restriction, or double-shifting anyone. Friday day can still run with Bilal on M2 and an M1-certified operator.
3. The plant manager proposes that Asha run M2 on Friday night under the buddy waiver, with Bilal supervising by phone. Evaluate this proposal against the rules.
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Reject it. The waiver has two conditions: the operator must be M1-certified, which Asha is, and an M2-certified operator must be physically present on the same shift. Bilal by phone is not physically present, so the second condition fails. The proposal also strains the medical restriction: even if phone supervision were not 'night work' in a formal sense, it places Bilal in the night operating loop and normalises a workaround. The rule exists because M2 has hazards that need on-site certified judgement. The correct answer is to move the batch to Saturday night with Divya, not to convert a hard safety rule into a telephone exception.