Sequencing a Held Shipment
A commercial shipment is held pending three sequential steps before release. Step 1, a physical examination, takes 45 minutes and cannot begin before 09:15, when the dock crew is available. Step 2, uploading the exam report, takes 15 minutes and starts the moment the exam ends. Step 3, a compliance review, takes 30 minutes, cannot start until the upload is complete, and can only run inside the compliance officer's windows: 10:30–12:00 and 13:00–14:30. The supervisor's sign-off takes 10 minutes and can only follow a completed compliance review; the supervisor is in a meeting from 11:00 to 11:40 and is otherwise free. Release occurs the instant sign-off ends. No step can be shortened, overlapped, or moved to another day.
1. What is the earliest possible release time? Show the chain step by step.
Read the worked answer
| Step | Earliest start | Duration | Ends |
|---|---|---|---|
| 1. Examination | 09:15 | 45 min | 10:00 |
| 2. Upload | 10:00 | 15 min | 10:15 |
| 3. Compliance review | 10:30 (window opens) | 30 min | 11:00 |
| 4. Supervisor sign-off | 11:40 (meeting ends) | 10 min | 11:50 |
Earliest release: 11:50.
The two traps
- Compliance at 10:15. The upload finishes at 10:15, but the compliance officer's window does not open until 10:30. Fifteen minutes of dead time here is unavoidable.
- Sign-off at 11:00. The review finishes at 11:00 - exactly when the supervisor's meeting begins. The 40-minute meeting is a hard block, so sign-off is 11:40–11:50, not 11:00–11:10.
A common wrong answer is 11:10, produced by ignoring the supervisor's meeting.
2. What is the latest exam start time that still achieves release before 13:00? Justify the limit.
Read the worked answer
Work backwards from the two constraints that can fail.
Constraint A - the 12:00 close of the compliance window. The review is 30 minutes and must fit inside 10:30–12:00, so it must start by 11:30.
- Upload complete by 11:30
- Exam ends by 11:30 − 15 = 11:15
- Exam starts by 11:15 − 45 = 10:30
Constraint B - the supervisor. Sign-off needs the supervisor free. Any finish from 11:40 onward is fine; a finish between 11:00 and 11:40 is blocked. At a 10:30 start the review runs 11:30–12:00, so sign-off is 12:00–12:10 - inside Constraint B.
Latest exam start: 10:30.
Justify the limit from below: at 10:31 the exam ends 11:16, upload completes 11:31, the review misses its window by one minute and falls to 13:00–13:30, with sign-off 13:30–13:40. A one-minute slip costs 90 minutes. Release at a 10:30 start is 12:10, comfortably before 13:00.
3. Which single constraint, if relaxed, would advance the earliest release the most? Compare the two realistic candidates and quantify.
Read the worked answer
Candidate 1 - open the compliance window at 10:15 instead of 10:30
Review 10:15–10:45, supervisor free until 11:00, sign-off 10:45–10:55. Release 10:55, a gain of 55 minutes.
Candidate 2 - cancel the supervisor's meeting
Review still runs 10:30–11:00 (unchanged - the compliance window, not the supervisor, gates the review). Sign-off 11:00–11:10. Release 11:10, a gain of 40 minutes.
Comparison
Relaxing the compliance window gains 55 minutes; relaxing the supervisor constraint gains 40. So the compliance window is the better single change.
The interaction matters. The two blocks operate in series, so relaxing both yields 10:55, not 55 + 40. Once the window opens at 10:15, the supervisor constraint never binds at all, because the review finishes at 10:45 - before the 11:00 meeting. The marginal value of the supervisor change, given the window change, is zero.
Rule of thumb this illustrates: in a serial chain, the binding constraint is the one whose relaxation moves the finish line. Here it is the compliance window, and the 15-minute upload gap is a decoy that looks like the problem but is not.