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The dock or gate assignment problem with possible delays. (GateAssignWithDelays) A number of vehicles (trucks, airplanes...) arrive over time at an exchange facility. The facility has a number of docks or gates. Each gate can handle at most one vehicle at a time. We would like to assign vehicles to gates so that at most one vehicle is assigned to a specific gate at a specific instance, there is very little delay, the value of the assignments is maximized. Arriving vehicles can be temporarily delayed in the "penalty box" if a gate is not available. Additional realistic features not included: disallowing certain, e.g., large, vehicles to be at adjacent gates;