# Large-scale rail freight flow assignment with the tree-shaped path

## TL;DR

This paper investigates the unique tree-shaped path pattern in rail freight flow assignment, develops a nonlinear programming model, and proposes a simulated annealing algorithm for large-scale problem solving.

## Contribution

It introduces a novel nonlinear binary programming model capturing the tree-shaped path characteristic and provides an effective heuristic algorithm for large-scale instances.

## Key findings

- Revealed the formation mechanism of tree-shaped paths in rail yards.
- Developed a nonlinear binary programming model for RFFA.
- Outlined a simulated annealing algorithm for large-scale problems.

## Abstract

The rail freight flow assignment (RFFA) is a key point of network design and operations management. Unlike a road network, the freight flow assignment pattern in a rail system has unique characteristics, and the most significant one is the tree-shaped path. More specifically, when two or more shipments arrive at a rail yard, those intended for the same destination will be treated as a single freight flow and be shipped through the same path during the remainder of the trip, regardless of their origins. This paper reveals the forming mechanism of the tree-shaped path from the perspective of rail yard operations, and develops a nonlinear programming model for the RFFA problem. Considering the notably large number of quadratic terms generated from the tree-shaped constraints, the model is difficult to solve even for small-size instances. We thus introduce binary decision variables and modify the model into a nonlinear binary programming problem. In order to solve large-scale RFFA problems, we outline a simulated annealing algorithm.

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Source: https://tomesphere.com/paper/1812.03013