Abstract
Traditional network location theory is concerned with the optimal location of facilities which can be considered as single points (emergency medical service stations, switching centers in communication networks, bus stops, mail boxes, etc.) However, in many real problems the facility to be located is too large to be modeled as a point. Examples of such problems include the location of pipelines and high speed train lines, the design of emergency routes, newspaper delivery routes, subway lines, etc. We will refer to this kind of facilities as extensive facilities or structures, and they may have the shape of a path, a tree, a cycle or a more general subgraph.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Balas, E. and A. Ho. (1980). Set Covering Algorithms using Cutting Planes, Heuristics and Subgradient Optimization: A Computational Study. Mathematical Programming, 12:37–60.
Church, R. and J. Current. (1993). Maximal Covering Tree Problems. Naval Research Logistics, 40:129–142.
Current, J. (1988). The Design of a Hierarchical Transportation Network with Transshipment Facilities. Transportation Science, 22:270–277.
Current, J., J.L. Cohon and C.S. ReVelle. (1984). The Shortest Covering Path Problem: An Application of Locational Constraints to Network Design. Journal of Regional Science, 24:161–183.
Current, J., H. Pirkul and E. Rolland. (1994). Efficient Algorithms for Solving the Shortest Covering Path Problem. Transportation Science, 28:317–327.
Current, J., C.S. ReVelle and J.L. Cohon. (1985). The Maximum Covering/Shortest Path Problem: A Multiobjective Network Design and Routing Formulation. European Journal of Operational Research, 21:189–199.
Current, J., C.S. ReVelle and J.L. Cohon. (1987). The Median Shortest Path Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in the Design of Transportation Networks. Transportation Science, 21:188–197.
Current, J. and D.A. Schilling. (1989). The Covering Salesman Problem. Transportation Science, 23:208–213.
Current, J. and D.A. Schilling. (1994b). The Median Tour and Maximal Covering Tour Problems: Formulation and Heuristics. European Journal of Operational Research, 73:114–126.
Ehrgott, M., J. Fretag, H.W. Hamacher and F. Maffioli. (1995). Heuristics for the K-Cardinality Tree Subgraph Problems. Working paper.
Fischetti, M., J.J. Salazar Gonzalez and P. Toth. (1995). The Symmetric Generalized Travelling Salesman Polytope. Networks, 26:113–123.
Fischetti, M., J.J. Salazar Gonzalez and P. Toth. (1997). A Branch-and-Cut Algorithm for the Symmetric Generalized Travelling Salesman Problem. Operations Research, 45:378–394.
Gendreau, M., A. Hertz and G. Laporte. (1992). New Insertion and Postoptimization Procedures for the Traveling Salesman Problem. Operations Research, 40:1086–1094.
Gendreau, M., G. Laporte and F. Semet. (1997). The Covering Tour Problem. Operations Research, 45:568–576.
Goldman, A.J. (1971). Optimal Center Location in Simple Networks. Transportation Science, 5:406–409.
Hakimi, S.L., E.F. Schmeichel and M. Labbe. (1993). On Locating Path-or Tree-Shaped Facilities on Networks. Networks, 23:543–555.
Hutson, V.A. and C.S. ReVelle. (1989). Maximal Direct Covering Tree Problems. Transportation Science, 23:188–299.
Hutson, V.A. and C. ReVelle. (1993). Indirect Covering Tree Problems on Spanning Tree Networks. European Journal of Operational Research, 65:20–32.
Kim, T.U., T.J. Lowe, A. Tamir and J.E. Ward. (1996). On the Location of a Tree-Shaped Facility. Networks, 28:167–175.
Kim, T.U., T.J. Lowe and J.E. Ward. (1991). Locating a Median Subtree on a Network. INFOR, 29:153–166.
Kim, T.U., T.J. Lowe, J.E. Ward and R.L. Francis. (1989). A Minimum Length Covering Subgraph of a Network. Annals of Operations Research, 18:245–260.
Kim, T.U., T.J. Lowe, J.E. Ward and R.L. Francis. (1990). A minimum-Length covering Subtree of a Tree. Naval Research Logistics, 37:309–326.
Maffioli, F. (1991). Finding the Best Subtree of a Tree. Politecnico di Milano. Technical report 91.041.
Mesa, J.A. and T.B. Boffey. (1996). A Review of Extensive Facility Location in Networks. European Journal of Operational Research, 95:592–603.
Minieka, E. (1985). The Optimal Location of a Path or Tree in a Tree Network. Networks, 15:309–321.
Minieka, E. and N.H. Patel. (1983). On Finding the Core of a Tree with a Specified Length. Journal of Algorithms, 4:345–352.
Richey, M.B. (1990). Optimal Location of a Path or Tree on a Network with Cycles. Networks, 20:391–407.
Sahni, S. (1977). General Techniques for Combinatorial Approximations. Operations Research, 25:920–936.
Steuer, R.E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. Wiley series in probability and mathematical statistics-applied. Wiley.
Tamir, A. (1992). On the Complexity of Some Classes of Location Problems. Transportation Science, 26:352–354.
Tamir, A. (1993). Fully Polynomial Approximation Schemes for Locating a Tree-Shaped Facility: A Generalization of the Knapsack Problem. Working paper. Tel-Aviv University.
Toregas, C. and C. ReVelle. (1972). Optimal Location under Time or Distance Constraints. Papers of the Regional Science Association, 28:133–143.
Toregas, C. and C. ReVelle. (1973). Binary Logic Solutions to a Class of Location Problems. Geographical Analysis, 5:145–155.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Labbé, M., Laporte, G., Rodríguez-Martín, I. (1998). Path, Tree and Cycle Location. In: Crainic, T.G., Laporte, G. (eds) Fleet Management and Logistics. Centre for Research on Transportation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5755-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5755-5_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7637-8
Online ISBN: 978-1-4615-5755-5
eBook Packages: Springer Book Archive