Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks

The load planning problem is a critical challenge in service network design for parcel carriers: it decides how many trailers to assign for dispatch over time between pairs of terminals. Another key challenge is to determine a flow plan, which 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 in order to adjust loads and flows as the demand forecast changes over time before the day of operations in a terminal. The paper aims at developing a decision-support tool to inform planners making these decisions at terminals across the network. The paper formulates the OLPP as a mixed-integer programming 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, confusing planners and reducing trust in optimization. To remedy this limitation, this paper proposes a lexicographical optimization approach that eliminates those symmetries by generating optimal solutions staying close to a reference plan. Moreover, this paper designs an optimization proxy that addresses the computational challenges of the optimization model. The optimization proxy combines a machine-learning model and a 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 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.