One day at the Brunsbüttel lock

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On 23 January 2023, 49 ships arrived at the Brunsbüttel lock on the Kiel Canal. Brunsbüttel is the western end of the canal. Ships come in from the Elbe, or they leave the canal and go out onto the river.

The lock has two large chambers. Each is 330 metres long and 45 metres wide, and both stay open all day. A ship that uses one of them is inside for 45 minutes. The 45 minutes is the time to pass through one large chamber at Brunsbüttel, from the gate on the Elbe side to the gate on the canal side, or in the other direction. It is not the trip along the canal to Kiel-Holtenau, which takes about 8 hours and is not in this model.

Two smaller chambers sit beside the large ones. Each is 125 metres by 22 metres, and a passage through one of them takes 30 minutes. This first version leaves them unused.

The ships

The arrivals come from an archive of AIS tracks on the Kiel Canal, published by Fraunhofer through the mFUND project on Mobilithek. A track is the path of one ship: a series of positions, each with a time. An arrival is the first position within 500 metres of the lock. That gives the 49 ships on this day.

These are records of where the ships sailed. They are not the lock's own log, so they do not say which chamber a ship was sent to.

The schedule

Each ship needs a chamber, one of the two large ones, and a start time. A legal plan starts each ship at or after it arrives, keeps it in that chamber for 45 minutes, and never puts two ships in the same chamber at once. Waiting for a ship is how long it sits before it enters, and the cost is the sum of those waits; for this day that sum is 2430 minutes. CP-SAT, from OR-Tools, tries the legal combinations of chamber and start time, and it does not stop at the first plan that works. It keeps going until it can prove no legal plan has a smaller total wait. The page plays that proven plan, and it does not run the search in the browser.

The animation

You can see the animation of that day. Ships approach, enter a chamber, and leave. The lock and the canal are drawn from OpenStreetMap. The water outside the western mouth is the Elbe. The North Sea and the Baltic are not in this map. The canal line in the data stops well short of Holtenau.