http://repub.eur.nl/res/aut/704/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/14176/ 2008-02-01T00:00:00Z In this paper, we describe a model and a branch-and-price algorithm to determine an efficient railway rolling stock circulation on a set of interacting train lines. Given the timetable and the passengers’ seat demand, the model determines an allocation of rolling stock to the daily trips. In order to efficiently utilize the train units, they can be added to or removed from the trains at some stations along the lines. These changes in train compositions are subject to several constraints, mainly corresponding to the order of the train units within the trains. A solution is evaluated based on three criteria, i.e. (i) the service to the passengers, (ii) the robustness, and (iii) the cost of the circulation. The developed branch-and-price algorithm was tested on a number of real-life instances of NS Reizigers, the main Dutch operator of passenger trains, thereby outperforming the commercial solver CPLEX 8.0. http://repub.eur.nl/res/pub/14204/ 2007-01-01T00:00:00Z http://repub.eur.nl/res/pub/902/ 2003-09-18T00:00:00Z We describe an algorithmic approach to determine an efficient railway rolling stock circulation on a single line or on a set of interacting lines. Given the timetable and the passengers? seat demand, we develop a branch-and-price algorithm that results in an allocation of rolling stock material to the daily trips. In order to efficiently utilize the train units, they can be added to or removed from the trains at some stations along the line. These changes in train composition are subject to several constraints, for example corresponding to the order of the train units within a train. A solution is evaluated based on three criteria, i.e. the service to passengers, the robustness, and the cost of the circulation. The branch-and-price algorithm that we developed is tested on real-life instances from NS Reizigers, the main Dutch operator of passenger trains. http://repub.eur.nl/res/pub/1098/ 2003-01-01T00:00:00Z Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master problem. In a first approach we apply Lagrangian relaxation directly to this extended formulation, i.e. no simplex method is used. In a second one, we use Lagrangian relaxation to generate new columns, that is Lagrangian relaxation is applied to the compact for-mulation. We will illustrate the ideas behind these algorithms with an application in Lot-sizing. To show the wide applicability of these techniques, we also discuss applications in integrated vehicle and crew scheduling, plant location and cutting stock problems.