Noah is qualified to prepare the report. Maya is qualified to review it. Those checks are necessary, but they leave important questions unanswered. Will Noah finish before Maya starts? Is Maya reviewing someone else's work? Has that same hour already been promised to another report?

A person's qualifications describe what they can do. Whether an arrangement works also depends on how their assignment relates to the other choices.

In our report example, some conditions concern a single assignment: Noah must be qualified to prepare the report. Others connect assignments: review must follow preparation, and the reviewer must differ from the preparer. Each condition limits which combinations are acceptable. We will call these conditions constraints.

Now suppose the team needs three reports prepared and reviewed by noon. Noah and two other qualified writers each finish a report at 11. Maya and a second reviewer, Eli, are the only qualified reviewers available from 11 to noon. Neither prepared any of the reports. Each review takes one uninterrupted hour, and each reviewer can handle only one report at a time.

Look at any report by itself. Maya could review it. Eli could review it. It has qualified, independent reviewers available before the deadline.

Look at any two reports together. Maya can review one while Eli reviews the other. That pair also fits.

Then include all three: three review-hours are needed, but only two reviewer-hours are available.

No assignment of the three reviews to Maya and Eli can satisfy the deadline under these conditions. The map below shows one attempt. Its missing assignment becomes a missing place in the schedule.

An open reviewer link leaves C without a scheduled hour Maya is assigned to Review A and Eli is assigned to Review B. Review C points to an unassigned reviewer placeholder. In the schedule Maya reviews A and Eli reviews B from 11 am to noon. C has no available reviewer row for its required hour. The open placeholder is not a person or an extra hour of capacity. Relationships Maya Review A Eli Review B Reviewer unassigned Review C assigned to assigned to needs a reviewer Schedule 11 am Noon Deadline Maya Review A Eli Review B Review C has no reviewer available for its required hour.

A relationship map assigns Maya to review A and Eli to review B, while Review C has an open reviewer connection. The matching schedule shows Maya reviewing A and Eli reviewing B concurrently from 11 am to the dashed noon deadline. A note states that Review C has no reviewer available for its required hour. The missing connection is a capacity shortage, not another available reviewer row; swapping the reports leaves the same shortage.

One attempted allocation shown in two views. Each review needs one hour. The open link for C has no available reviewer row in the schedule; swapping reports leaves the same shortage.

The failure appears only when we account for the combined demand. If you approve each report separately because a reviewer could handle it, you can promise the same capacity several times. Every individual approval looks reasonable while the overall commitment is impossible.

This is why checking an arrangement requires us to follow the relationships between its choices. Some constraints concern one assignment, some connect two, and others apply to a whole group. Shared staff time, a common budget, or a limit on simultaneous work can make the group's total demand decisive.

For your own plan, look for anything that several choices rely on. Count the total demand on that shared resource within the relevant time window. Check who has already claimed it. A resource that supports any one choice may still be insufficient for the complete arrangement.

Next: What Does It Mean When No Arrangement Works? We will examine what an impossible combination tells us about the requirements and available options.