Abstract
This article provides an overview about the main results and findings developed in the dissertation of the author [8]. In this thesis, we develop methods in mathematical optimization to dimension networks at minimal cost. Given hardware and cost models, the challenge is to provide network topologies and efficient capacity plans that meet the demand for network traffic (data, passengers, freight). We incorporate crucial aspects of practical interest such as the discrete structure of available capacities as well as the uncertainty of demand forecasts. The considered planning problems typically arise in the strategic design of telecommunication or public transport networks and also in logistics. One of the essential aspects studied in this work is the use of cutting planes to enhance solution approaches based on multi-commodity flow formulations. Providing theoretical and computational evidence for the efficacy of inequalities based on network cuts, we extend existing theory and algorithmic work in different directions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Achterberg, T., & Raack, C. (2010). The MCF-separator—detecting and exploiting multi-commodity flows in MIPs. Mathematical Programming C, 2, 125–165.
Andersen, K., Cornuéjols, G., & Li, Y. (2005). Split closure and intersection cuts. Mathematical Programming, 102(3), 457–493.
Dash, S., Günlük, O., & Raack, C. (2011). A note on the MIR closure and basic relaxations of polyhedra. Operations Research Letters, 39(3), 198–199.
Gurobi Optimization. GUROBI, 2012
IBM. IBM ILOG CPLEX Optimizer, 2012
Koster, A. M. C. A., Kutschka, M., & Raack, C. (2011). Robust network design: Formulations, valid inequalities, and computations. Networks, 61(2), 128–149.
Poss, M., & Raack, C. (2012). Affine recourse for the robust network design problem: Between static and dynamic routing. Networks, 61(2), 180–198.
Raack C. (2012). Capacitated network design multi-commodity flow formulations, cutting planes, and demand uncertainty. PhD thesis, TU Berlin.
Raack, C., Koster, A. M. C. A., Orlowski, S., & Wessäly, R. (2011). On cut-based inequalities for capacitated network design polyhedra. Networks, 57(2), 141–156.
Zuse Institute Berlin. SCIP—Solving Constraint Integer Programs, 2012.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Raack, C. (2014). Capacitated Network Design. In: Huisman, D., Louwerse, I., Wagelmans, A. (eds) Operations Research Proceedings 2013. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-07001-8_49
Download citation
DOI: https://doi.org/10.1007/978-3-319-07001-8_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07000-1
Online ISBN: 978-3-319-07001-8
eBook Packages: Business and EconomicsBusiness and Management (R0)