The Train Driver Recovery Problem – a Set Partitioning Based Model and Solution Method Natalia J. Rezanova Informatics and Mathematical Modelling, Technical University of Denmark Richard Petersens Plads 1, Building 305, DK-2800 Kgs. Lyngby, Denmark e-mail:
[email protected] David M. Ryan The Department of Engineering Science, Faculty of Engineering The University of Auckland Private Bag 92019, Auckland Mail Centre, Auckland 1142, New Zealand e-mail:
[email protected] IMM-TECHNICAL REPORT-2006-24 Abstract The need to recover a train driver schedule occurs during major disruptions in the daily railway operations. Using data from the train driver schedule of the Dan- ish passenger railway operator DSB S-tog A/S, a solution method to the Train Driver Recovery Problem (TDRP) is developed. The TDRP is formulated as a set partitioning problem. The LP relaxation of the set partitioning formulation of the TDRP possesses strong integer properties. The proposed model is there- fore solved via the LP relaxation and Branch & Price. Starting with a small set of drivers and train tasks assigned to the drivers within a certain time period, the LP relaxation of the set partitioning model is solved with column generation. If a feasible solution is not found, further drivers are gradually added to the prob- lem or the optimization time period is increased. Fractions are resolved with a constraint branching strategy using the depth-first search of the Branch & Bound tree. Preliminarily results are encouraging, showing that nearly all tested real-life instances produce integer solutions to the LP relaxation and solutions are found within a few seconds.