You are required to read and agree to the below before accessing a full-text version of an article in the IDE article repository.

The full-text document you are about to access is subject to national and international copyright laws. In most cases (but not necessarily all) the consequence is that personal use is allowed given that the copyright owner is duly acknowledged and respected. All other use (typically) require an explicit permission (often in writing) by the copyright owner.

For the reports in this repository we specifically note that

  • the use of articles under IEEE copyright is governed by the IEEE copyright policy (available at
  • the use of articles under ACM copyright is governed by the ACM copyright policy (available at
  • technical reports and other articles issued by M‰lardalen University is free for personal use. For other use, the explicit consent of the authors is required
  • in other cases, please contact the copyright owner for detailed information

By accepting I agree to acknowledge and respect the rights of the copyright owner of the document I am about to access.

If you are in doubt, feel free to contact

Optimization Methods for Multistage Freight Train Formation


Markus Bohlin, Sara Gestrelius, Florian Dahms, Matúš Mihalák , Holger Flier

Publication Type:

Journal article


Transportation Science



This paper considers mathematical optimization for the multistage train formation problem, which at the core is the allocation of classification yard formation tracks to outbound freight trains, subject to realistic constraints on train scheduling, arrival and departure timeliness, and track capacity. The problem formulation allows the temporary storage of freight cars on a dedicated mixed-usage track. This real-world practice increases the capacity of the yard, measured in the number of simultaneous trains that can be successfully handled. Two optimization models are proposed and evaluated for the multistage train formation problem. The first one is a column-based integer programming model, which is solved using branch and price. The second model is a simplified reformulation of the first model as an arc-indexed integer linear program, which has the same linear programming relaxation as the first model. Both models are adapted for rolling horizon planning and evaluated on a five-month historical data set from the largest freight yard in Scandinavia. From this data set, 784 instances of different types and lengths, spanning from two to five days, were created. In contrast to earlier approaches, all instances could be solved to optimality using the two models. In the experiments, the arc-indexed model proved optimality on average twice as fast as the column-based model for the independent instances, and three times faster for the rolling horizon instances. For the arc-indexed model, the average solution time for a reasonably sized planning horizon of three days was 16 seconds. Regardless of size, no instance took longer than eight minutes to be solved. The results indicate that optimization approaches are suitable alternatives for scheduling and track allocation at classification yards.


author = {Markus Bohlin and Sara Gestrelius and Florian Dahms and Mat{\'u}š Mihal{\'a}k and Holger Flier},
title = {Optimization Methods for Multistage Freight Train Formation },
month = {February},
year = {2015},
journal = {Transportation Science},
url = {}