Optimal Algorithms for Train Shunting and Relaxed List Update Problems

This paper considers a Train Shunting problem which occurs in cargo train organizations: We have a locomotive travelling along a track segment and a collection of n cars, where each car has a source and a target. Whenever the train passes the source of a car, it needs to be added to the train, and on the target, the respective car needs to be removed. Any such operation at the end of the train incurs low shunting cost, but adding or removing truly in the interior requires a more complex shunting operation and thus yields high cost. The objective is to schedule the adding and removal of cars as to minimize the total cost. This problem can also be seen as a relaxed version of the well-known List Update problem, which may be of independent interest. We derive polynomial time algorithms for Train Shunting by reducing this problem to finding independent sets in bipartite graphs. This allows us to treat several variants of the problem in a generic way. Specifically, we obtain an algorithm with running time O(n^{5/2}) for the uniform case, where all low costs and all high costs are identical, respectively. Furthermore, for the non-uniform case we have running time of O(n^3). Both versions translate to a symmetric variant, where it is also allowed to add and remove cars at the front of the train at low cost. In addition, we formulate a dynamic program with running time O(n^4), which exploits the special structure of the graph. Although the running time is worse, it allows us to solve many extensions, e.g., prize-collection, economies of scale, and dependencies between consecutive stations

Personnel Scheduling on Railway Yards

In this paper we consider the integration of the personnel scheduling into planning railway yards. This involves an extension of the Train Unit Shunting Problem, in which a conflict-free schedule of all activities at the yard has to be constructed. As the yards often consist of several kilometers of railway track, the main challenge in finding efficient staff schedules arises from the potentially large walking distances between activities. We present two efficient heuristics for staff assignment. These methods are integrated into a local search framework to find feasible solutions to the Train Unit Shunting Problem with staff requirements. To the best of our knowledge, this is the first algorithm to solve the complete version of this problem. Additionally, we propose a dynamic programming method to assign staff members as passengers to train movements to reduce their walking time. Furthermore, we describe several ILP-based approaches to find a feasible solution of the staff assignment problem with maximum robustness, which solution we use to evaluate the quality of the solutions produced by the heuristics. On a set of 300 instances of the train unit shunting problem with staff scheduling on a real-world railway yard, the best-performing heuristic integrated into the local search approach solves 97% of the instances within three minutes on average

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

Integrated Scheduling of Vessels, Cranes and Trains to Minimize Delays in a Seaport Container Terminal

The multiple processes taking place on a daily basis at an intermodal container terminal are often considered individually, given the complexity of their joint consideration. Nevertheless, the integrated planning and scheduling of operations in an intermodal terminal, including the arrivals and departures of trains and vessels, is a very relevant topic for terminal managers, which can benefit from the application of Operations Research (OR) techniques to obtain near-optimal solutions without excessive computational cost. Applying the functional integration technique, we present here a mathematical model for this terminal planning process, and solve it using heuristic procedures, given its complexity and size. Details on the benchmark comparison of a genetic algorithm, a simulated annealing routine and a tabu search are provided for different problem instances

Practice Oriented Algorithmic Disruption Management in Passenger Railways

How to deal with a disruption is a question railway companies face on a daily basis. This thesis focusses on the subject how to handle a disruption such that the passenger service is upheld as much as possible. The current mathematical models for disruption management can not yet be applied in practice, because several important practical considerations are not taken into account. In this thesis several models are presented which take important practical details into account: (1) Creating a macroscopic global feasible solution for all three resource schedules, instead of focussing on one individual resource schedule. (2) Scheduled maintenance appointments required