Locating service centers with precedence constraints

Isotonic regression models have been used extensively with various objective functions. In this paper we consider the isotonic regression model with the minmax criterion. The model is presented and interpreted as a multi-center location problem on the real line, with precedence constraints on the locations of the centers. Viewed as a location problem, this model generalizes the classical (weighted) 1-center problem on the line. We obtain an explicit expression for the optimal objective value, and use it to develop an efficient subquadratic algorithm for solving the problem. Finally we present and discuss a generalization which unifies the above model and other location problems with distance constraints.