The continuous stop location problem in public transportation networks

In: Asia Pacific Journal of Operations Research. Submitted, 2006

Authors

• Anita Schöbel
• Horst W. Hamacher
• Annegret Liebers
• Dorothea Wagner

Abstract

In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network. The positive effect of new stops is given by the better access of the potential customers to their closest station, while the increasement of travel time caused by the additional stopping activities of the trains leads to a negative effect. The goal is to cover all given demand points with a minimal amount of additional traveling time, where covering may be defined with respect to an arbitrary norm (or even a gauge). Unfortunately, this problem is NP-hard, even if only the Euclidean distance is used. In this paper, we give a reduction to a finite candidate set leading to a discrete set covering problem. Moreover, we identify network structures in which the coefficient matrix of the resulting set covering problem is totally unimodular, and use this result to derive efficient solution approaches. Various extensions of the problem are also discussed.

BibTeX

 
@Article{ SchoebelEtAl:ContStopLoc, 
   title = { The continuous stop location problem in public transportation networks }, 
   author = { Anita Schöbel and Horst W. Hamacher and Annegret Liebers and Dorothea Wagner },    
   journal = { Asia Pacific Journal of Operations Research },             
   year = 2006, 
} 

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This publication belongs to the project DeNDeMA.