Integrated Learning and Optimization for Joint Routing and Loading Decisions in Preowned Automobile Shipping

We study highway-based shipping of preowned automobiles by auto carriers, an important although overlooked problem in the automobile shipping literature. The special structure associated with auto carriers implies many different ways of loading a set of automobiles to an auto carrier with different loading costs. Thus, in addition to vehicle routing decisions, loading decisions are essential in automobile shipping optimization. The objective of our problem is to maximize the total revenue minus the total routing and loading cost subject to time windows and loading constraints among others. Most existing automobile shipping studies treat loading and routing separately; some studies partially address the loading aspect in routing optimization but only check the loading feasibility without evaluating the quality of loading decisions. We, thus, contribute to the literature by fully integrating loading decisions into routing decision making. An integrated machine learning (ML) and optimization approach is proposed to solve the problem. The overall approach follows a column generation–based solution framework, in which an insertion heuristic is proposed to find new routes based on existing routes, and ML is employed to predict the loading feasibility and estimate the minimum loading cost of a given route without solving the complex loading optimization problem. The integration of the ML approach and the insertion heuristic enables us to find high-quality new routes quickly in each column generation iteration. Two variants of this integrated approach are evaluated against a benchmark sequential approach in which routing and loading are tackled separately and another benchmark approach in which routing and loading are optimized jointly without using ML. Computational experiments demonstrate that the proposed integrated ML and optimization approach generates significantly better solutions than the sequential benchmark approach with only slightly more computation time and similar solutions to the joint optimization benchmark approach but with significantly less computation time. The proposed solution approach can be adopted by automobile shipping companies. It can also be adapted for other joint optimization problems, such as those in aircraft load planning. Funding: Y. Sun is partially supported by the National Science Foundation [Grants 2332161, 2100745, and 2055347]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0712 .