  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.
