Train Repathing in Emergencies Based on Fuzzy Linear Programming

Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm

Optimising locomotive requirements for a pre-planned train schedule: a dissertation submitted in partial fulfilment of the requirements for the degree of Bachelor of Applied Computing with Honours at Lincoln University

Every rail operator wishes to minimise the size of their locomotive fleet in order to reduce costs. This minimum fleet size problem requires a rail operator to allocate locomotives to the trains in a predefined train schedule so that the total number of locomotives required is minimised. The key to this is deciding how and when to transfer locomotives to where they can be better utilised. The rail operator for this hypothetical problem runs approximately 7,200 trains per week involving movements between 780 locations. An integer programming formulation was developed based on the work by Ahuja, Liu, Orlin, Sharma and Shughart (2002)¹ and a solver applied this formulation to a train schedule to find the optimal solution. As the solution process was highly computationally intensive, the largest partial train schedule that was able to be solved by the integer programming solver was 21% of the size of the full train schedule, taking 2½ hours to converge on the optimal solution. An alternative algorithm, called the work unit levels algorithm, was developed. This algorithm schedules locomotives by identifying all valid ways to transfer locomotives between trains, then allocating the train schedule in an order dependent on the possible interconnections between trains. When this algorithm was applied to the largest partial train schedule that could be solved by the integer programming solver, it arrived at a similar solution in 6 seconds. The algorithm took 13 minutes to solve the full problem

On the Complexity of Train Assignment Problems

We consider a problem faced by train companies: How can trains be assigned to satisfy scheduled routes in a cost efficient way? Currently, many railway companies create solutions by hand, a time-consuming task which is too slow for interaction with the schedule creators. Further, it is difficult to measure how efficient the manual solutions are. We consider several variants of the problem. For some, we give efficient methods to solve them optimally, while for others, we prove hardness results and propose approximation algorithms