An algebraic approach to multidimensional minimax location problems with Chebyshev distance

Understand

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.