The multiple container loading problem with loading docks

Abstract

This paper introduces a multiple container loading problem with practical constraints and loading situations at several docks. In the real world, items may be stored on several loading docks in the depot. So, to pack items stored on a dock, it may be necessary to move or reload the items loaded into the container at the previous docks. We present a realistic definition of reloading conditions and design a temporary loading pattern for each dock to reduce the reloading effort. We propose a column generation-based heuristic algorithm that uses a tree search to solve the subproblem. The proposed algorithm can solve benchmark instances with one loading dock with only a 1.3% deviation from the literature's best results. It can also solve real-world instances with several loading docks in reasonable running times and reduce the total cost by 21.6%, compared to the case where only one loading dock is considered.