The schedule is a hidden capacity.

Scheduling and capacity · Research direction

The problem

Empty appointment slots, double-booked rooms, missed follow-ups and a waiting list that nobody can see are the same problem seen from four sides. Capacity is rarely missing. It is trapped in rules nobody wrote down.

The question

Can scheduling be modelled as what it is, a constraint problem with people on both sides, and explained back to staff in terms they can overrule?

The schedule is a hidden capacity

On empty slots, long waits and the rules nobody wrote down.

Every clinic has the same two complaints at once: nobody can get an appointment, and there are empty slots on Thursday. Both are true. The slots are not usable because of rules that live in the heads of the people who run the diary.

One slot is reserved for urgent cases, but nobody remembers what counts as urgent. One room only fits a certain procedure. One clinician does not see certain patients on certain days. None of that is wrong. It is just not written down anywhere a system, or a new colleague, could read.

The first piece of work is therefore not optimisation. It is writing the constraints down in plain language and having the people who live with them correct them. A front-desk lead should be able to read the list and say: that one is wrong, that one is missing.

Only then does it make sense to let software propose changes. And every proposal should say what it moves. Moving one person earlier moves someone else later. Naming that trade is what allows a human to accept it, refuse it or change it.

Fairness belongs in the model as a named constraint, not as an afterthought. Who waits, and why, should be something a manager can inspect. If the only way to understand why a person waited is to trust the system, the system is not ready.

We make no claim about how much capacity this frees. We do not know. We will publish the model and the test data first, and the numbers only if they survive.

Test design

• Constraints are written in plain language that a front-desk lead can read and correct.
• Every proposed change shows who it affects and what it displaces.
• Fairness is a stated constraint: who waits, and why, is inspectable.

Protocol: Constraint legibility test