Linear Time Optimal Approaches for Max-Profit Inverse 1-Median Location Problems

Abstract

This paper is concerned with a new variant of the inverse 1-median location problem in which the aim is to modify the customer weights such that a predetermined facility location becomes a 1-median location and the total profit obtained via the weight improvements is maximized. We develop novel combinatorial approaches with linear time complexities for solving the problem on tree networks and in the plane under the rectilinear and Chebyshev norms.