A comprehensive numerical algorithm for solving service points location problems

This article introduces a numerical algorithm to solve the generalized max-separable optimization problem Min F(f1, f2, … , fn) under the set of constraints rij(xj) ⩽ 0, where the function F is non-decreasing and continuous in each of its components, and the functions rij(xj) are continuous for each index. This work is motivated from the class of emergency service location problems, which were studied by various authors e.g. [R.A. Cuninghame-Green, The absolute centre of a graph, Disc. Appl. Math. 7 (1984) 275-283; Z. Drezener, On rectangular p-center problem, Naval Research Logisitics 34 (1987) 229-234], is considered. The general version of the considered problem is NP-hard [Z. Drezener, On rectangular p-center problem, Naval Research Logisitics 34 (1987) 229-234; M. Gavalec, O. Hudec, A polynomial algorithm for a balanced location on a graph optimization 35 (1995) 367-372.]. Finally a numerical example is given to illustrate the introduced algorithm.