Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Ritesh Ojha, Wenbo Chen, Hanyu Zhang, Reem Khir, Alan Erera, Pascal Van Hentenryck

TL;DR

The paper tackles the Outbound Load Planning Problem (OLPP) at parcel terminals, where jointly deciding trailer counts and commodity routing is NP-hard and exhibits symmetries that destabilize planner trust. It introduces the Lexicographic Outbound Load Planning Problem (LOLPP) to break symmetries by prioritizing plan stability (via a reference plan) while minimizing trailer capacity, and proposes optimization proxies that pair a neural network predictor with a repair layer to deliver near-optimal, feasible load plans in seconds. The contributions include a formal LOLPP formulation, an optimization-proxy framework combining ML with feasibility repair, and extensive industrial-scale computational results showing orders-of-magnitude speedups and improved consistency, plus tangible business gains from load consolidation and alternate routing. This work enables real-time, planner-friendly adjustments in large networks by balancing consolidation benefits with stability and operational feasibility. It also lays groundwork for extending the approach to terminal clusters and integrated inbound-outbound planning.

Abstract

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.

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

TL;DR

The paper tackles the Outbound Load Planning Problem (OLPP) at parcel terminals, where jointly deciding trailer counts and commodity routing is NP-hard and exhibits symmetries that destabilize planner trust. It introduces the Lexicographic Outbound Load Planning Problem (LOLPP) to break symmetries by prioritizing plan stability (via a reference plan) while minimizing trailer capacity, and proposes optimization proxies that pair a neural network predictor with a repair layer to deliver near-optimal, feasible load plans in seconds. The contributions include a formal LOLPP formulation, an optimization-proxy framework combining ML with feasibility repair, and extensive industrial-scale computational results showing orders-of-magnitude speedups and improved consistency, plus tangible business gains from load consolidation and alternate routing. This work enables real-time, planner-friendly adjustments in large networks by balancing consolidation benefits with stability and operational feasibility. It also lays groundwork for extending the approach to terminal clusters and integrated inbound-outbound planning.

Abstract

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.
Paper Structure (33 sections, 4 theorems, 20 equations, 12 figures, 6 tables, 1 algorithm)

This paper contains 33 sections, 4 theorems, 20 equations, 12 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. The Outbound Load Planning Problem (OLPP)
  4. High-Level Problem Description
  5. Problem Formulation
  6. Planning Realities in the Field
  7. Primary and Alternate Routing Options
  8. Planners in the Loop
  9. The Lexicographic Outbound Load Planning Problem (LOLPP)
  10. Learning the LOLPP
  11. The Overall Approach
  12. Optimization Proxies
  13. The Machine Learning Model
  14. The Repair Procedure
  15. The Training Data
  16. ...and 18 more sections

Key Result

Theorem 1

(Model Capacity) (arora2016understanding) Let $f: \mathbb{R}^d \rightarrow \mathbb{R}$ be a piecewise linear function with $p$ pieces. If $f$ is represented by a ReLU network with depth $k+1$, then it must have size at least $\frac{1}{2}kp^{\frac{1}{k}}-1$. Conversely, any piecewise linear function

Figures (12)

  • Figure 1: The primary terminal for commodities processed at terminal A and destined for terminal D on day $4$ is denoted by solid green arc and the two alternate terminals are denoted by solid blue and solid brown arcs.
  • Figure 2: An example to highlight the alternate (symmetric) optimal solutions for OLPP (Model \ref{['CreateLoadsModel']}).
  • Figure 3: (color online) Sensitivity analysis of the OLPP, LOLPP, and LOLPP$^{-2}$ on a real-world medium-sized instance from our industry partner.
  • Figure 4: The Overall Pipeline of the Optimization-based Learning Approach: In the offline setting, the dataset is generated and augmented by solving historical instances with the proposed LOLPP model. The ML model is trained in a supervised learning fashion. In the online setting, the optimization proxies take as input a new instance and output a near-optimal feasible load plan and commodity volume allocation plan in seconds.
  • Figure 5: The Machine Learning Model for the LOLPP.
  • ...and 7 more figures

Theorems & Definitions (9)

  • Theorem 1
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Claim 4
  • proof
  • Proposition 5
  • proof