I'm not sure that your description of the problem is completely clear. If we have bridges A1,...,A6, what do you mean by "Flights with short turnaround times ( < 50 minutes ) shall use the same bridge, otherwise, be re-assigned just like any other flight."

The way I see it is that an aircraft is assigned to a bridge. This satisfies the inbound arriving passengers who disembark, the aircraft is fueled and serviced, and refilled with passengers, who depart from that gate on the new flight segment. In this case, the bridge/gate is occupied by the assigned aircraft for a time window (i.e. from say some minutes before aircraft arrival until some few minutes after departure). Because it takes time to maneuver aircraft, you cannot instantly swap aircraft in and out. You would also probably want to avoid moving an aircraft from one gate to another after arrival ---- although that could happen.

Suggest you try this on paper with a colored pencil to mark the occupied fractions of the day, and the available portions that are unoccupied. Then decide what would make a good solution better --- in other words what are the ideal preferred outcomes (for example, avoiding unproductive times when the gate is unusable? or maximizing the number of aircraft operations handled?) Build in adequate aircraft movement time. You could get fancy and try to avoid ramp congestion too.

Then, you can try to form that problem with your constraints as an optimization task. There are many variants of this packing problem, but as I said, the best way to start is with an accurate view of your objective.

Thank you Mr Morton for your reply,

When we assign a flight to a bridge/gate, we do take into consideration the steps you mentioned (refuelling, manoeuvring the aircraft ...), that’s what the second constraint stand for:

• · If a bridge is assigned, to be re-assigned again, we must make sure the time elapsed between the assigned flight and the next one is at least 40 minutes.

The same rule applies for flights with turnarounds, if the turnaround time exceeds 50 minutes, we treat the departure flight as any other random flight, which means it won’t keep the same bridge.

I hope the attached picture provides more insight.

There is two ways to go around this problem and i have delt with similar problems in the past:

1. Using linear prohramming techniques with constraints to solve the problem. This can be easily coded in excel

2. Use more intuitive approach like decision tree models. These models helps in easy scaling up. You can use all the constraints to build a model and use live stream of data to make realtime decisisons.