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

This article focuses on the Outbound Load Planning Problem (OLPP) in parcel delivery service networks, which jointly determines the number and types of trailers to dispatch from a terminal and how to allocate commodity volumes to these trailers while minimizing operational costs. The OLPP’s standard mixed-integer programming (MIP) formulation suffers from solution instability due to symmetries, causing inconsistent load plans that reduce planner trust. To address this, the authors propose the Lexicographic Outbound Load Planning Problem (LOLPP), a biobjective lexicographic model that first minimizes trailer costs and then minimizes deviations from a reference plan to produce stable, consistent solutions. Recognizing the computational challenges of LOLPP for real-time use, the paper introduces an optimization proxy combining a machine learning model that predicts trailer dispatch decisions with a repair procedure that ensures feasibility and volume allocation, enabling fast, high-quality, and consistent load plans. Extensive computational experiments on industrial-scale instances demonstrate that the optimization proxy achieves similar or better solution quality than commercial solvers in a fraction of the time, improves plan stability, and highlights operational benefits such as load consolidation through volume splitting and alternate routing options. The study concludes with suggestions for extending the approach to multi-terminal settings, robust optimization under uncertainty, and alternative learning paradigms.