Load Factor Optimization for the Auto Carrier Loading Problem

The distribution of passenger vehicles is a complex task and a high cost factor for automotive original equipment manufacturers (OEMs). On the way from the production plant to the customer, vehicles travel long distances on different carriers, such as ships, trains, and trucks. To save costs, OEMs and logistics service providers aim to maximize their loading capacities. Modern auto carriers are extremely flexible. Individual platforms can be rotated, extended, or combined to accommodate vehicles of different shapes and weights and to nest them in a way that makes the best use of the available space. In practice, finding feasible combinations is done with the help of simple heuristics or based on personal experience. In research, most papers that deal with auto carrier loading focus on route or cost optimization. Only a rough approximation of the loading subproblem is considered. In this paper, we present two different methodologies to approximate realistic load factors considering the flexibility of modern auto carriers and their height, length, and weight constraints. Based on our industry partner’s process, the vehicle distribution follows a first in, first out principle. For the first approach, we formulate the problem as a mixed integer, quadratically constrained assignment problem. The second approach considers the problem as a two-dimensional nesting problem with irregular shapes. We perform computational experiments using real-world data from a large German automaker to validate and compare both models with each other and with an approximate model adapted from the literature. The simulation results for the first approach show that, on average, for 9.37% of all auto carriers, it is possible to load an additional vehicle compared with the current industry solution. This translates to 1.36% less total costs. The performance of the nesting approach is slightly worse, but as it turns out, it is well-suited to check load combinations for feasibility.