Solution of minimax location problem in three-dimensional space with rectilinear metric - Krivulin, Nikolai K.; Plotnikov, Pavel V. (Computer Tools in Education, 2018)
A minimax single-facility location problem in three-dimensional space with rectilinear metric (l_1-metric) is examined, and a direct, explicit solution of the problem is obtained using methods of tropical (idempotent) mathematics. In this article the problem is represented in terms of tropical mathematics as a tropical optimization problem. Then a parameter is introduced to represent the minimum value of the objective function, and the problem is reduced to a parameterized system of inequalities. This system is solved for one variable, and the existence conditions of solution are used to obtain optimal values of the second parameter by using an auxiliary optimization problem. Then the auxiliary problem is solved in the same way and the value of the third variable is evaluated. The obtained general solution is transformed into a set of direct solutions written in a compact form for different cases of relationships between the initial parameters of the problem.