Tree network 1-median location with interval data: a parameter space-based approach

We consider a family of 1-median location problems on a tree network where the vertex weights are ranges rather than point values. We define a new framework for making sound decisions under uncertainty which is primarily based on the interplay between the points in the tree and the data that induce the family of problems. An important feature of this framework is that it provides a novel understanding of the problem under uncertainty by collectively handling all possible realizations of the weights. The key element is the notion of a region of a optimality. Based on the regions of optimality, we define three optimality criteria and give low-order polynomial methods to compute the associated solution sets.