The 1-median and 1-highway problem

J. M. Díaz-Báñez, M. Korman, P. Pérez-Lantero, I. Ventura

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we study a facility location problem in the plane in which a single point (median) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L1 or Manhattan metric. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. We represent the highway by a line segment with fixed length and arbitrary orientation. This problem was introduced in [Computers & Operations Research 38(2) (2011) 525-538]. They gave both a characterization of the optimal solutions and an algorithm running in O(n 3logn) time, where n represents the number of clients. In this paper we show that the previous characterization does not work in general. Moreover, we provide a complete characterization of the solutions and give an algorithm solving the problem in O(n3) time.

Original languageEnglish
Pages (from-to)552-557
Number of pages6
JournalEuropean Journal of Operational Research
Volume225
Issue number3
DOIs
Publication statusPublished - 2013 Mar 16
Externally publishedYes

Keywords

  • Geometric optimization
  • Location
  • Time distance
  • Transportation

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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  • Cite this

    Díaz-Báñez, J. M., Korman, M., Pérez-Lantero, P., & Ventura, I. (2013). The 1-median and 1-highway problem. European Journal of Operational Research, 225(3), 552-557. https://doi.org/10.1016/j.ejor.2012.09.028