The order of play looks like a list. It is the output of an assignment problem with more constraints than most people realize, solved fresh every evening.
The constraints are hard and numerous
Players need minimum rest between matches, doubles entrants cannot be scheduled in two places, and broadcast partners have contracted windows for certain matches.
Court capacity differs, so match selection is partly a demand forecast. Putting a high-demand match on a small court creates a crowd management problem.
Grass adds a constraint other surfaces do not, since court wear accumulates and the schedule has to distribute usage across the fortnight.
Every constraint is a recorded fact
The scheduler works from data: match completion times, which players are still in which events, court usage totals, and previous days' assignments.
None of that is guesswork, which is why the exercise is tractable. The difficulty is the number of interacting constraints rather than uncertainty about the inputs.
Weather is the one genuinely uncertain input, and it is the reason schedules are built with contingency rather than optimized tightly.
Why the schedule is published late
The order of play for the following day is released in the evening because it depends on results that are still being decided.
A late finish can invalidate a draft schedule entirely if it leaves a player without adequate rest, forcing reassignment across several courts.
Publishing early would mean publishing something likely to change, which is worse for spectators than publishing accurately and late.
Timing is deliberately vague
Matches after the first on a court are listed as following rather than at a stated time, because tennis has no fixed duration.
This is a record-keeping decision as much as a practical one. Publishing a specific time would create an expectation the tournament cannot meet.
Actual start and finish times are logged precisely, and that log is what feeds the next day's scheduling. The precision exists internally and not publicly.
What the logs make possible afterward
Accumulated timing data lets a tournament measure how long matches actually take by round, surface condition and time of day.
Those measurements feed session planning and roof usage decisions in subsequent years, so the archive is an operational input rather than a historical curiosity.
Scheduling improves through this feedback rather than through intuition, which is why long-running events schedule more accurately than new ones.

