Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks

Abstract

This paper is concerned with the upgrading selective obnoxious p-median location problem on tree networks in which the existing customer points and the candidate facility locations are assumed to be two selective subsets of the vertex set of the underlying tree. The task is to augment the edge lengths within associated bounds and a budget constraint on the overall modification cost so that the optimal selective obnoxious p-median objective value is maximized under the new edge lengths. Exact optimal algorithms with polynomial time complexities are developed for cases $$p=1 $$ and $$p\ge 2$$. Moreover, it is shown that if the bound constraints are dropped, then the problems under investigation can be solved in lower times.