Upgrading selective obnoxious p-median location problems on tree networks

In this paper, we investigate the upgrading selective obnoxious p-median location problem on tree networks in which the set of existing customer points and the set of candidate facility locations are assumed to be two selective subsets of the vertices of the underlying tree. The aim 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. Novel combinatorial solution algorithms with polynomial time complexities are developed for cases and .