MILP-based approaches for a bin-packing problem with a fixed-plus-linear charge scheme

In this paper, we consider a truck loading problem with a fixed-plus-linear charge scheme, which is thought to be more suitable for short-distance freight transportation than fixed charge schemes. Here, we study a mixed-integer linear program (MILP) formulation of this problem and develop two methods for solving it. We discuss the property of optimal solutions and tighten the formulation. Based on the polyhedral knowledge of orbit opes, we also provide a symmetry-breaking heuristic for this problem. We conduct a series of numerical experiments to indicate that the computational performance of the MILP formulation can be significantly improved by applying our method.