The Two Level Network Design Problem with Secondary Hop Constraints

Abstract

The Two Level Network Design problem asks for a cost-minimal Steiner subtree of a given graph G = (V,E) that connects all primary customers using a primary technology only, and all secondary customers using either the primary or the secondary technology. Thereby, the secondary technology is cheaper but less reliable and hence, hop constraints on the length of each secondary path are imposed. In addition, in some applications facility opening costs need to be paid for transition nodes, i.e., for nodes where the change of technology takes place. We consider various MIP models for this new problem and derive a new class of strong inequalities that we call generalized cut-jump constraints. We also show that these inequalities can be obtained by projecting the cut-set formulation obtained on a graph in which we split the potential facility locations and introduce layers for installing the secondary technology.