The inverse 1-median location problem on uncertain tree networks with tail value at risk criterion

Abstract

In an inverse 1-median location problem on a tree network, the goal is to modify the vertex weights of the underlying tree network at the minimum total cost such that a predetermined vertex becomes the 1-median. This paper investigates the case that the vertex weights and modification costs are considered as uncertain variables. We first obtain a necessary and sufficient condition for the α-1-median on uncertain trees. Based on this condition, we transform the problem into a linear programming model with deterministic constraints. Finally, we consider the proposed model with tail value at risk objective under the weighted l1 norm and present a solution algorithm for the problem with time complexity of O(nlog n).