Optimization Methods for Multistage Freight Train Formation

Abstract

T his 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.

Towards a comprehensive model for track allocation and roll-time scheduling at marshalling yards

“…There are numerous tactics for sorting the wagons using roll-ins and pull-backs (see e.g. Boysen et al (2012) or Gatto et al (2009) for an overview), and this paper considers the practice used in Sweden: multi-stage train formation with mixing tracks (see next section for an introduction, or Bohlin et al (2015) for a more thorough description).…”

“…Their exact methods are faster than CPLEX and the heuristic tabu search yields near optimal solutions. Bohlin et al (2015) presents three integer programming models, D-IP, GC-IP and A-IP, for solving the multi-stage train formation problem with mixing tracks given a wagonto-train allocation, fixed roll-in, pull-back and roll-out times, and no wagon ordering in inbound or outbound trains. The models find the classification bowl track allocation that minimises the work effort required.…”

“…Gestrelius et al (2012) introduces an extension to GC-IP for respecting the wagon ordering in outbound trains. Bohlin et al (2015) evaluates RailLille 2017 -7 th International Conference on Railway Operations Modelling and Analysis GESTRELIUS SARA, ARONSSON MARTIN, JOBORN MARTIN, MARKUS BOHLIN the three different integer programming models using real data from Hallsberg marshalling yard for a five-month period from December 2010 to May 2011. Instances of 2 to 5 days are solved, and a rolling horizon framework is implemented for generating schedules for even longer time periods.…”

“…The aim is to schedule all shunting tasks and also allocate trains to arrival yard tracks and classification bowl tracks. The original multi-stage train formation problem was presented in Bohlin et al (2015).…”

“…The optimisation model E-IP is an extension of the model A-IP previously presented in Bohlin et al (2015). E-IP has three cores: the ordering of events, the allocation of train formation tracks, and the mixing and pull-back scheduling.…”