Reducing Complexity for Quantum Approaches in Train Load Optimization

TL;DR

This paper introduces a compact mathematical formulation for train load optimization that implicitly models rehandle costs, reducing model complexity and improving scalability in logistics planning.

Contribution

A novel formulation for train load optimization that eliminates explicit rehandle variables, significantly reducing model size and computational complexity.

Findings

The new model reduces the number of variables and constraints compared to conventional formulations.

The simulated annealing heuristic effectively finds high-quality loading plans using the new model.

Results demonstrate improved scalability and practical effectiveness in rail logistics planning.

Abstract

Efficiently planning container loads onto trains is a computationally challenging combinatorial optimization problem, central to logistics and supply chain management. A primary source of this complexity arises from the need to model and reduce rehandle operations-unproductive crane moves required to access blocked containers. Conventional mathematical formulations address this by introducing explicit binary variables and a web of logical constraints for each potential rehandle, resulting in large-scale models that are difficult to solve. This paper presents a fundamental departure from this paradigm. We introduce an innovative and compact mathematical formulation for the Train Load Optimization (TLO) problem where the rehandle cost is calculated implicitly within the objective function. This novel approach helps prevent the need for dedicated rehandle variables and their associated constraints, leading to a dramatic reduction in model size. We provide a formal comparison against a conventional model to analytically demonstrate the significant reduction in the number of variables and constraints. The efficacy of our compact formulation is assessed through a simulated annealing metaheuristic, which finds high-quality loading plans for various problem instances. The results confirm that our model is not only more parsimonious but also practically effective, offering a scalable and powerful tool for modern rail logistics.