Practical solutions for a dock assignment problem with trailer transportation

We study a distribution warehouse in which trailers need to be assigned to docks for loading or unloading. A parking lot is used as a buffer zone and transportation between the parking lot and the docks is performed by auxiliary resources called terminal tractors. Each incoming trailer has a known arrival time and each outgoing trailer a desired departure time. The primary objective is to produce a docking schedule such that the weighted sum of the number of late outgoing trailers and the tardiness of these trailers is minimized; the secondary objective is to minimize the weighted completion time of all trailers, both incoming and outgoing. The purpose of this paper is to produce high-quality solutions to large instances that are comparable to a real-life case. This will oblige us to abandon the guarantee of always finding an optimal solution, and we will instead look into a number of sub-optimal procedures. We implement four different methods: a mathematical formulation that can be solved using an IP solver, a branch-and-bound algorithm, a beam search procedure and a tabu search method. Lagrangian relaxation is embedded in the algorithms for computing lower bounds. The different solution frameworks are compared via extensive computational experiments.