Control-Room Roster with Two Operators Unavailable
A 2×210 MW station control room must be manned by exactly three operators in each of three 8-hour shifts - A (06:00–14:00), B (14:00–22:00) and C (22:00–06:00) - on all seven days of the week. The approved panel is 12 operators, of whom one is on 30 days' medical leave and one is away on a training programme, leaving 10 physically available. Station rules require a maximum of six consecutive working days followed by at least 24 hours off; not more than two consecutive C shifts; at least 16 hours between the end of a C shift and the start of the next duty; and at least two of the three operators in any shift must be senior (8 of the 10 available are senior). Operator Yadav holds a medical certificate restricting him to A shift only. One of the available operators is a newly promoted trainee who must never be posted without a senior. The shift in-charge proposes to cover the week with no overtime, arguing that 11 × 6 = 66 operator-shifts is more than the 63 required.
1. Test the shift in-charge's arithmetic and state whether a compliant roster with no overtime actually exists.
Read the worked answer
Requirement: 3 shifts × 3 operators × 7 days = 63 operator-shifts per week. Correct so far.
Capacity: the in-charge has used 11 available operators, but the operator on the training programme is not physically available for duty. The correct figure is 10, and each must have at least one rest day in seven, so capacity is 10 × 6 = 60 operator-shifts.
60 < 63, so a compliant roster without overtime does not exist. The deficit is at least three operator-shifts per week, and it is structural, not a rounding error.
Additional binding constraints:
- Senior cover needs 2 × 3 × 7 = 42 senior-shifts. Yadav supplies only 6, all on A shift, leaving 36 to come from the other 7 seniors - about 5.1 each against a capacity of 6, so a single unplanned absence of a senior on a day when Yadav is off breaks the two-senior rule.
- The trainee occupies one of the three seats in whichever shift he works, reducing flexibility on the night shift where senior cover is hardest to arrange.
So the honest answer to the in-charge is: the arithmetic is right in principle but wrong in inputs, and the roster as proposed will breach either the rest rule or the senior-cover rule within the first week.
2. Cost the minimum remedy: overtime at twice the normal shift wage (normal shift wage ₹1,850) against a contract operator at ₹1,200 per shift. Recommend one.
Read the worked answer
Deficit: 3 operator-shifts per week.
Option 1 - overtime. 3 × (2 × ₹1,850) = ₹11,100 per week.
Option 2 - contract operator. 3 × ₹1,200 = ₹3,600 per week.
On pure cost the contract option is cheaper by ₹7,500 a week, but cost is not the deciding test here. A contract operator cannot be counted as one of the three control-room operators: the post requires a certified, station-familiar operator who can act on a unit trip without supervision, and a contract man without that certification leaves the shift legally and technically short even if physically present. He can be used only as an additional helper, which does not close the deficit.
Recommendation: sanctioned overtime for one week - three extra shifts, with the six-consecutive-day rule still enforced on the individuals concerned - while in parallel recalling the operator from training or bringing a reliever of the same grade from the station pool. Overtime beyond one week starts to erode the rest rule and is exactly the fatigue risk the rule is written to prevent.
3. Explain why rotations are run forward (A then B then C) and how Yadav's restriction changes the way the night-shift senior cover must be planned.
Read the worked answer
Forward rotation gives increasing rest. In an A→B→C rotation each changeover pushes the reporting time later: an operator finishing A at 14:00 starts B at 14:00 the next day (24 hours of rest), and one finishing B at 22:00 starts C at 22:00 the next day (24 hours). The rest interval therefore always exceeds the 16-hour minimum.
Backward rotation is the dangerous one. Going C→A, a man who finishes the C shift at 06:00 on Tuesday and is rostered for A on Tuesday would report at 06:00 with zero rest; even with a day in between, the interval is only 24 hours and the body clock shifts backwards, giving poorer alertness in a control room where the night shift carries the highest error risk.
Effect of Yadav's restriction: he must be counted as zero for night-shift senior cover, so the eight night-shift senior seats per week (2 per night × 7) must come from the remaining seniors. His weekly off must be placed on a day when A shift can be staffed by two other seniors, and it must never coincide with the planned off-day of the senior who is backing up the night shift - otherwise the two-senior rule fails on a shift where the trainee is also posted.