A mixed-integer programming model and a matheuristic algorithm for the multi-block train formation and shipment path optimization problem

Hossein Ebrahimi-Marvast

doi:10.1016/j.jrtpm.2026.100596

A mixed-integer programming model and a matheuristic algorithm for the multi-block train formation and shipment path optimization problem

2026-07-16

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AI

H

Hossein Ebrahimi-Marvast

M

Mohammad Reisi‐Nafchi *

G

Ghasem Moslehi

DOI：10.1016/j.jrtpm.2026.100596

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Abstract

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• MILP model for joint shipment routing and multi-block train formation. • Incorporates yard/link capacities, accumulation, classification, and swapping costs. • Valid inequalities and reduction rules significantly improve MILP solvability. • Matheuristic tailored for large-scale instances yields near-optimal solutions. • Validated on three datasets showing improved cost-efficiency and feasibility.

Keywords:

Multi-block train service

Routing

Train formation

Mixed-integer programming

Matheuristic algorithm

A mixed-integer programming model and a matheuristic algorithm for the multi-block train formation and shipment path optimization problem

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