In the design of telecommunication networks, decisions concerning capacity installation and routing of commodities have to be taken simultaneously. Network loading problems formalize these decisions in mathematical optimization models. Several variants of the problem exist: bifurcated or non-bifurcated routing, bidirected or unidirected capacity installation, and symmetric versus non-symmetric routing restrictions. Moreover, different concepts of reliability can be considered. In this paper, we study the polyhedral structure of two basic problems for non-bifurcated routing: network loading with bidirected and unidirected capacity installation.we show that strong valid inequalities for the substructure restricted to a single edge, are also strong valid inequalities for the overall models. In a computational study, several classes of inequalities, both for the substructure and the overall problem, are compared on real-life instances for both variants of network loading.
van Hoesel, C. P. M., Koster, A. M. C. A., van de Leensel, R. L. J. M., & Savelsbergh, M. W. P. (2003). Bidirected and unidirected capacity installation in telecommunication networks. Discrete Applied Mathematics, 133(1-3), 103-121. https://doi.org/10.1016/S0166-218X(03)00436-0