Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance

We consider a constrained minimax single-facility location problem with addends on the plane with rectilinear distance. The problem is first formulated in a standard form, and then represented in terms of tropical mathematics as a constrained optimization problem. We apply methods and results of tropical optimization to obtain direct, explicit solutions to the optimization problem. The results obtained are used to derive solutions of the location problem, and of its special cases with reduced sets of constraints, in a closed form, ready for immediate computation. Numerical solutions of example problems are given, and graphical illustrations are presented. Key-Words: minimax location problem, rectilinear distance, idempotent semifield, tropical optimization, explicit solution. MSC (2010): 65K10, 15A80, 90B85, 65K05, 90C48