The deadline disappears
A hotel manager is setting tomorrow’s cleaning roster. An accurate forecast makes minimum staffing look safe, but guests pay for rooms ready when promised.
In this hypothetical example, all figures are assumed. At 10 a.m., 24 vacant rooms need cleaning, matching the forecast. Each needs 20 minutes, including setup. Booking records mark 16 rooms as ready_by: noon; the other eight are due at 2 p.m.
Four rooms miss noon
Aggregating those records into a daily count removes ready_by. Two cleaners provide 2 × 4 = 8 staff-hours, matching 24 × 20 ÷ 60 = 8 hours of work. Yet by noon they can finish only 2 × 120 ÷ 20 = 12 rooms. Four promised rooms remain unready.
The forecast passes its total-count test; the staffing rule ignores timing. Like an occupancy figure, the total describes volume without scheduling the work.
Two rosters fit the budget
Assume the hotel pays €18 per cleaner-hour, can book two-hour shifts, and has a €220 morning labour budget. Option A keeps three cleaners for four hours: 3 × 4 × €18 = €216. Option B keeps two for four hours and adds one until noon: (2 × 4 + 2) × €18 = €180.
Both have capacity for 18 rooms before noon. B adds capacity for 12 afterward, covering the remaining eight. Choose B: it meets both deadlines at €36 less labour cost. Room revenue is unchanged.
Let the records change the choice
Sort bookings by ready_by and assign the earliest deadlines first. At each deadline, compare all rooms due so far with available cleaner-minutes so far divided by 20. Missing deadlines or excess demand require correcting records or changing coverage before confirming shifts.
Now change the hypothetical bookings: all rooms are due at 2 p.m. Two cleaners then cost 2 × 4 × €18 = €144 and fit exactly. The original lean roster works if no other tasks consume that capacity.