12 research outputs found
Optimized shunting with mixed-usage tracks
We consider the planning of railway freight classification at hump yards, where the problem
involves the formation of departing freight train blocks from arriving trains subject to
scheduling and capacity constraints. The hump yard layout considered consists of arrival
tracks of sufficient length at an arrival yard, a hump, classification tracks of non-uniform
and possibly non-sufficient length at a classification yard, and departure tracks of sufficient
length. To increase yard capacity, freight cars arriving early can be stored temporarily
on specific mixed-usage tracks. The entire hump yard planning process is covered in this
paper, and heuristics for arrival and departure track assignment, as well as hump scheduling,
have been included to provide the neccessary input data. However, the central problem
considered is the classification track allocation problem. This problem has previously
been modeled using direct mixed integer programming models, but this approach did not
yield lower bounds of sufficient quality to prove optimality. Later attempts focused on
a column generation approach based on branch-and-price that could solve problem instances
of industrial size. Building upon the column generation approach we introduce
a direct arc-based integer programming model, where the arcs are precedence relations
between blocks on the same classification track. Further, the most promising models
are adapted for rolling-horizon planning. We evaluate the methods on historical data
from the Hallsberg shunting yard in Sweden. The results show that the new arc-based
model performs as well as the column generation approach. It returns an optimal schedule
within the execution time limit for all instances but from one, and executes as fast
as the column generation approach. Further, the short execution times of the column
generation approach and the arc-indexed model make them suitable for rolling-horizon
planning, while the direct mixed integer program proved to be too slow for this.
Extended analysis of the results shows that mixing was only required if the maximum
number of concurrent trains on the classification yard exceeds 29 (there are 32 available
tracks), and that after this point the number of extra car roll-ins increases heavily
Track Allocation in Freight-Train Classification with Mixed Tracks
We consider the process of forming outbound trains from cars of inbound trains at rail-freight
hump yards. Given the arrival and departure times as well as the composition of the trains, we
study the problem of allocating classification tracks to outbound trains such that every outbound
train can be built on a separate classification track. We observe that the core problem can be
formulated as a special list coloring problem in interval graphs, which is known to be NP-complete.
We focus on an extension where individual cars of different trains can temporarily be stored on
a special subset of the tracks. This problem induces several new variants of the list-coloring
problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We
show that in case of uniform and sufficient track lengths, the corresponding coloring problem can
be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off
prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer
program to tackle the problem. As a case study, we consider a real-world problem instance from
the Hallsberg RangerbangÄrd hump yard in Sweden. Planning over horizons of seven days, we
obtain feasible solutions from the integer program in all scenarios, and from the heuristics in
most scenarios
Shunting passenger trains: getting ready for departure
In this paper we consider the problem of shunting train units on a railway station. Train units arrive at and depart from the station according to a given train schedule and in between the units may have to be stored at the station. The assignment of arriving to departing train units (called matching) and the scheduling of the movements to realize this matching is called shunting. The goal is to realize the shunting using a minimal number of shunt movements.\ud
For a restricted version of this problem an ILP approach has been presented in the literature. In this paper, we consider the general shunting problem and derive a greedy heuristic approach and an exact solution method based on dynamic programming. Both methods are flexible in the sense that they allow the incorporation of practical planning rules and may be extended to cover additional requirements from practice
Optimisation of simultaneous train formation and car sorting at marshalling yards
Efficient and correct freight train marshalling is vital for high quality carload freight transportations. During marshalling, it is desirable that cars are sorted according to their individual drop-off locations in the outbound freight trains. Furthermore, practical limitations such as non-uniform and limited track lengths and the arrival and departure times of trains need to be considered. This paper presents a novel optimisation method for freight marshalling scheduling under these circumstances. The method is based on an integer programming formulation that is solved using column generation and branch and price. The approach minimises the number of extra shunting operations that have to be performed, and is evaluated on real-world data from the Hallsberg marshalling yard in Sweden
Hump Yard Track Allocation with Temporary Car Storage
In rail freight operation, freight cars need to be separated and reformed into new trains at
hump yards. The classification procedure is complex and hump yards constitute bottlenecks
in the rail freight network, often causing outbound trains to be delayed. One of the problems
is that planning for the allocation of tracks at hump yards is difficult, given that the planner
has limited resources (tracks, shunting engines, etc.) and needs to foresee the future capacity
requirements when planning for the current inbound trains. In this paper, we consider
the problem of allocating classification tracks in a rail freight hump yard for arriving and
departing trains with predetermined arrival and departure times. The core problem can be
formulated as a special list coloring problem. We focus on an extension where individual
cars can temporarily be stored on a special subset of the tracks. An extension where individual
cars can temporarily be stored on a special subset of the tracks is also considered. We
model the problem using mixed integer programming, and also propose several heuristics
that can quickly give feasible track allocations. As a case study, we consider a real-world
problem instance from the Hallsberg RangerbangÄrd hump yard in Sweden. Planning over
horizons over two to four days, we obtain feasible solutions from both the exact and heuristic
approaches that allow all outgoing trains to leave on time
Online Train Shunting
At the occasion of ATMOS 2012, Tim Nonner and Alexander Souza defined a new train shunting problem that can roughly be described as follows. We are given a train visiting stations in a given order and cars located at some source stations. Each car has a target station. During the trip of the train, the cars are added to the train at their source stations and removed from it at their target stations. An addition or a removal of a car in the strict interior of the train incurs a cost higher than when the operation is performed at the end of the train. The problem consists in minimizing the total cost, and thus, at each source station of a car, the position the car takes in the train must be carefully decided. Among other results, Nonner and Souza showed that this problem is polynomially solvable by reducing the problem to the computation of a minimum independent set in a bipartite graph. They worked in the offline setting, i.e. the sources and the targets of all cars are known before the trip of the train starts. We study the online version of the problem, in which cars become known at their source stations. We derive a 2-competitive algorithm and prove than no better ratios are achievable. Other related questions are also addressed
Advances in Condition Monitoring, Optimization and Control for Complex Industrial Processes
The book documents 25 papers collected from the Special Issue âAdvances in Condition Monitoring, Optimization and Control for Complex Industrial Processesâ, highlighting recent research trends in complex industrial processes. The book aims to stimulate the research field and be of benefit to readers from both academic institutes and industrial sectors