A Lagrangian heuristic for a dock assignment problem with trailer transportation

This paper presents a Lagrangian heuristic that combines Lagrangian relaxation with an enumerative search tree for finding high-quality solutions to a dock assignment problem. Trailers are assigned to gates for loading or unloading activities; the parking lot is used as a buffer zone. Transportation between the parking lot and the gates is performed by additional resources called terminal tractors. After loading or unloading, a trailer cannot be transported to the parking lot by a terminal tractor if all tractors are busy. The trailer remains at the gate until a terminal tractor becomes available, which may prevent other trailers from being loaded or unloaded there. We refer to this phenomenon as blocking. The problem is modeled as a three-stage flexible flow shop.