There is an alogrithm.

It takes the TOBT (target off blocks time) reported by the airline which may / may not be the same as the schedule. This is the time the flight is expected to be ready to depart.
The alogrithm then adds in a load of variables (aircraft type, flight plan, stand, runway in use, estimated taxi time etc) and looks at everything else wanting to leave around that time and builds a departure sequence.
This determines the TTOT (target take off time) and displays the TSAT (target start approval time) to the flight deck on the screens in front of the aircraft
If there is regulation either locally or in wider EU airspace then a CTOT may be issued which is fed into the algorithm to determine the optimal time to release the aircraft from the stand - if there's a shortage of stand space you can be moved to a remote holding point.

Assuming the flight deck call ready at TOBT (there is a +/- 5 minute leeway) then the aircraft will either get immediate push back approval or be held on stand until TSAT. If the CTOT is generating a much later TSAT then the ready call gets fed into the wider system at Eurocontrol to push for an improvement and reduce the delay.

Some airlines try to game the system by moving TOBT by 5 minutes every 5 minutes when they have a delay but that is actually self-defeating as it creates instability in the departure sequence and can lead to delays for other flights as the algorithm tries to fit them in.

Have a look at ACDM on the Eurocontrol website; it's interesting stuff (and something I worked on with Heathrow and, to a much lesser extent, at Gatwick many years ago).

EDIT: I hasten to add that I didn't work on the algorithm itself, but more the underlying processes the airlines and ground handlers need to follow with analytics to monitor and measure performance (I just realised my sentence above made my role sound way grander than it really was!)