Abstract: We consider the Railway TravelingSalesmanProblem. We
show that this problem can be reduced to a variant of the generalizedtravelingsalesmanproblem, defined on an undirected graph G = (V,E)
with the nodes partitioned into clusters, which consists in finding a mini-
mum cost cycle spanning a subset of nodes with the property that exactly
two nodes are chosen from each cluster. We describe an exact exponen-
tial time algorithm for the problem, as well we present two mixed integer
programming models of the problem. Based on one of this models pro-
posed, we present an efficient solution procedure based on a cutting plane
algorithm. Extensive computational results for instances taken from the
railroad company of the Netherlands Nederlandse Spoorwegen and involv-
ing graphs with up to 2182 nodes and 38650 edges are reported.
Abstract: We consider the Railway TravelingSalesmanProblem (RTSP) in which a salesman using the railway network wishes to visit a certain number of cities to carry out his/her business, starting and ending at the same city, and having as goal to minimize the overall time of the journey. RTSP is an $\mathcal{NP}$ -hard problem. Although it is related to the Generalized Asymmetric TravelingSalesmanProblem, in this paper we follow a direct approach and present a modelling of RTSP as an integer linear program based on the directed graph resulted from the timetable information. Since this graph can be very large, we also show how to reduce its size without sacrificing correctness. Finally, we conduct an experimental study with real-world and synthetic data that demonstrates the superiority of the size reduction approach.