Case 09 · scheduling · Medium · About 6–10 minutes
A frame restorer has one workbench and a full day's order. Five jobs must fit between nine and four. The inspection has a fixed appointment, and the other jobs have a few dependencies.
Make a timetable that uses every hour. There is no extra drying time or second worker to rescue an impossible plan.
The workday runs from 9:00 a.m. to 4:00 p.m. The restorer performs these five jobs, each exactly once:
| Job | Duration |
|---|---|
| Polish | 2 hours |
| Label | 1 hour |
| Mount | 2 hours |
| Inspect | 1 hour |
| Pack | 1 hour |
Jobs cannot overlap or be split. They begin on whole hours. There are no idle gaps, and one job starts as soon as the previous job finishes.
- Mount begins after both Polish and Label have finished.
- Inspect begins at exactly 2:00 p.m.
- Pack begins after Mount has finished.
- Label cannot begin at 9:00 a.m.
What is the complete timetable? “After” allows the next job to begin at the exact finishing time of the earlier job. No unlisted task is required between jobs.
Try blocking the fixed inspection hour first. Then consider which job is actually allowed to start the morning.
Hint 1 - reveal when you want a nudge
Mount cannot be first because it needs two earlier jobs. Pack cannot be first because it needs Mount. Inspect is fixed in the afternoon.
Hint 2 - reveal when you want a nudge
Label cannot start at 9, so Polish must fill 9–11. What can legally begin at 11?
Reveal the solution and explanation
The only timetable is:
- 9:00–11:00: Polish
- 11:00–12:00: Label
- 12:00–2:00: Mount
- 2:00–3:00: Inspect
- 3:00–4:00: Pack
At nine, Mount is blocked by its prerequisites, Pack is blocked by Mount, and Inspect cannot begin until two. Label is explicitly forbidden at nine. Therefore Polish must come first.
At eleven, Mount still needs Label. Pack still needs Mount, and Inspect still has its appointment. Label is the only available next job.
At noon, Mount is ready and has exactly two hours before inspection. Packing is not ready, and a gap is forbidden, so Mount must occupy noon to two. Inspect follows at its fixed time, leaving Pack for the last hour.
The durations sum to seven hours, matching the whole workday. Each step has only one legal next job, so the timetable is unique without any hidden assumptions about how real restoration work is done.
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