A new algebraic solution to multidimensional minimax location problems with Chebyshev distance

Understand

Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance.

• A new solution approach is proposed within the framework of idempotent algebra to reduce the problems to solving linear vector equations and minimizing functionals defined on some idempotent semimodule.
• The approach offers a solution in a closed form that actually involves performing matrix-vector multiplications in terms of idempotent algebra for appropriate matrices and vectors.
• To illustrate the solution procedures, numerical and graphical examples of two-dimensional problems are given.