Optimizing Railcar Movements to Create Outbound Trains in a Freight Railyard

TL;DR

This paper introduces a mixed-integer programming model and a heuristic algorithm for optimizing railcar movements in freight yards, significantly improving solution speed and quality for train assembly problems.

Contribution

It presents a novel large-scale mixed-integer programming model and an adaptive heuristic for efficient railcar grouping and movement optimization in freight yards.

Findings

ARG-DP algorithm is 355 times faster than MIP solver on simulated yards.

Achieves 60% optimal solutions with 6.65% average gap in simulations.

In real yard tests, solutions are 229 times faster with 50% optimality rate.

Abstract

A typical freight railyard at a manufacturing facility contains multiple tracks used for storage, classification, and outbound train assembly. Individual railcar storage locations on classification tracks are often determined before knowledge of their destination locations is known, giving rise to railcar shunting or switching problems, which require retrieving subsets of cars distributed throughout the yard to assemble outbound trains. To address this combinatorially challenging problem class, we propose a large-scale mixed-integer programming model that tracks railcar movements and corresponding costs over a finite planning horizon. The model permits simultaneous movement of multiple car groups via a locomotive and seeks to minimize repositioning costs. We also provide a dynamic programming formulation of the problem, demonstrate the NP-hardness of the corresponding optimization problem, and present an adaptive railcar grouping dynamic programming (ARG-DP) heuristic, which groups railcars with common destinations for efficient moves. Average results from a series of numerical experiments demonstrate the efficiency and quality of the ARG-DP algorithm in both simulated yards and a real yard. On average, across 60 test cases of simulated yards, the ARG-DP algorithm obtains solutions 355 times faster than solving the mixed-integer programming model using a commercial solver, while finding an optimal solution in 60% of the instances and maintaining an average optimality gap of 6.65%. In 10 cases based on the Gaia railyard in Portugal, the ARG-DP algorithm achieves solutions 229 times faster on average, finding an optimal solution in 50% of the instances with an average optimality gap of 6.90%.