Outbound Load Planning in Parcel Delivery Service Networks Using Machine Learning and Optimization

The load planning problem is a critical challenge in service network design for parcel carriers: it decides how many trailers (or loads), perhaps of different types, to assign for dispatch over time between pairs of terminals. Another key challenge is to determine a flow plan that specifies how parcel volumes are assigned to planned loads. This paper considers the Outbound Load Planning Problem (OLPP) that considers flow and load planning challenges jointly to adjust loads and flows as demand forecast changes over time before the day of terminal operations. The paper develops a decision support tool to inform planners making these decisions at terminals across the network. It formulates the OLPP as a mixed-integer programming (MIP) model and shows that it admits a large number of symmetries in a network where each commodity can be routed through primary and alternate terminals. As a result, an optimization solver may return fundamentally different solutions to closely related problems (i.e., OLPPs with slightly different inputs), confusing planners and reducing trust in optimization. To remedy this limitation, the first contribution of the paper is to propose a lexicographical optimization approach that eliminates those symmetries by generating optimal solutions while staying close to a reference plan. The second contribution of the paper is the design of an optimization proxy that addresses the computational challenges of the optimization model. The optimization proxy combines a machine learning model and an MIP-based repair procedure to find near-optimal solutions that satisfy real-time constraints imposed by planners in the loop. An extensive computational study on industrial instances shows that the optimization proxy is around 10 times faster than the commercial solver in obtaining solutions of similar quality; the optimization proxy is also orders of magnitude faster for generating solutions that are consistent with each other. The proposed approach also demonstrates the benefits of the OLPP for load consolidation and the significant savings obtained from combining machine learning and optimization.

Funding: This work was supported by the NSF AI Institute for Advances in Optimization [Grant Award 2112533].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0672.