'Multidimensional' extensions and a nested dual approach for the m-median problem

Pitu B. Mirchandani, Aissa Oudjit, Richard T. Wong

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

A general framework for modeling median type locational decisions, where (i) travel costs and demands may be stochastic, (ii) multiple services or commodities need to be considered, and/or (iii) multiple median type objectives might exist, is presented-using the concept of "multidimensional networks". The classical m-median problem, the stochastic m-median problem, the multicommodity m-median problem and and multiobjective m-median problem are defined within this framework. By an appropriate transformation of variables, the multidimensional m-median problem simplifies to the classical m-median problem but with a K-fold increase in the number of nodes, where K is the number of dimensions of the network. A nested dual approach to solve the resulting classical m-median problem, that uses Erlenkotter's facility location scheme as a subroutine, is presented. Computational results indicate that the procedure may perhaps be the best available one to solve the m-median problem exactly.

Original languageEnglish (US)
Pages (from-to)121-137
Number of pages17
JournalEuropean Journal of Operational Research
Volume21
Issue number1
DOIs
StatePublished - Jul 1985
Externally publishedYes

Keywords

  • Lagrange multipliers
  • Location
  • general transportation
  • integer programming
  • networks

ASJC Scopus subject areas

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

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