@TECHREPORT\{IMM2006-05157,
    author       = "N. J. Rezanova and D. M. Ryan",
    title        = "The Train Driver Recovery Problem - a Set Partitioning Based Model and Solution Method",
    year         = "2006",
    number       = "",
    series       = "IMM-Technical Report-2006-24",
    institution  = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5157-full.html",
    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 Danish 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 therefore 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 problem 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."
}