An algebraic approach to multidimensional minimax location problems with Chebyshev distance

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Abstract

Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location problems, and second, to extend the area of application of idempotent algebra. A new algebraic approach based on investigation of extremal properties of eigenvalues for irreducible matrices is developed to solve multidimensional problems that involve minimization of functionals defined on idempotent vector semimodules. Furthermore, an unconstrained location problem is considered and then represented in the idempotent algebra settings. A new algebraic solution is given that reduces the problem to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. Finally, the solution is extended to solve a constrained location problem.
Original languageEnglish
Pages (from-to)191-200
JournalWSEAS Transactions on Mathematics
Volume10
Issue number6
StatePublished - 2011

Keywords

  • single facility location problem
  • Chebyshev distance
  • idempotent semifield
  • eigenvalue
  • eigenvector

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