{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T18:57:04Z","timestamp":1770145024971,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,3,23]],"date-time":"2019-03-23T00:00:00Z","timestamp":1553299200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 154 B07"],"award-info":[{"award-number":["TRR 154 B07"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 154 B08"],"award-info":[{"award-number":["TRR 154 B08"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006463","name":"Bayerisches Staatsministerium f\u00fcr Wirtschaft und Medien, Energie und Technologie","doi-asserted-by":"publisher","award":["Energie Campus N\u00fcrnberg"],"award-info":[{"award-number":["Energie Campus N\u00fcrnberg"]}],"id":[{"id":"10.13039\/501100006463","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001656","name":"Helmholtz-Gemeinschaft","doi-asserted-by":"publisher","award":["EnergySystem 2050"],"award-info":[{"award-number":["EnergySystem 2050"]}],"id":[{"id":"10.13039\/501100001656","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s10589-019-00085-x","type":"journal-article","created":{"date-parts":[[2019,3,23]],"date-time":"2019-03-23T15:02:27Z","timestamp":1553353347000},"page":"791-819","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Robust optimal discrete arc sizing for tree-shaped potential networks"],"prefix":"10.1007","volume":"73","author":[{"given":"Martin","family":"Robinius","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3778-262X","authenticated-orcid":false,"given":"Lars","family":"Schewe","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6208-5677","authenticated-orcid":false,"given":"Martin","family":"Schmidt","sequence":"additional","affiliation":[]},{"given":"Detlef","family":"Stolten","sequence":"additional","affiliation":[]},{"given":"Johannes","family":"Th\u00fcrauf","sequence":"additional","affiliation":[]},{"given":"Lara","family":"Welder","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,3,23]]},"reference":[{"issue":"1","key":"85_CR1","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s10589-007-9016-1","volume":"37","author":"MH Afshar","year":"2007","unstructured":"Afshar, M.H., Mari\u00f1o, M.A.: A parameter-free self-adapting boundary genetic search for pipe network optimization. Comput. Optim. Appl. 37(1), 83\u2013102 (2007). https:\/\/doi.org\/10.1007\/s10589-007-9016-1","journal-title":"Comput. Optim. Appl."},{"key":"85_CR2","volume-title":"Network Flows: Theory, Algorithms, and Applications","author":"RK Ahuja","year":"1993","unstructured":"Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall Inc., Upper Saddle River (1993)"},{"issue":"1","key":"85_CR3","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1002\/net.20145","volume":"49","author":"A Alt\u0131n","year":"2007","unstructured":"Alt\u0131n, A., Amaldi, E., Belotti, P., P\u0131nar, M.\u00c7.: Provisioning virtual private networks under traffic uncertainty. Networks 49(1), 100\u2013115 (2007). https:\/\/doi.org\/10.1002\/net.20145","journal-title":"Networks"},{"issue":"3","key":"85_CR4","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1016\/j.ejor.2007.12.045","volume":"197","author":"J Andre","year":"2009","unstructured":"Andre, J., Bonnans, F., Cornibert, L.: Optimization of capacity expansion planning for gas transportation networks. Eur. J. Oper. Res. 197(3), 1019\u20131027 (2009). https:\/\/doi.org\/10.1016\/j.ejor.2007.12.045","journal-title":"Eur. J. Oper. Res."},{"issue":"3","key":"85_CR5","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s11081-005-1741-7","volume":"6","author":"W Ben-Ameur","year":"2005","unstructured":"Ben-Ameur, W., Kerivin, H.: Routing of uncertain traffic demands. Optim. Eng. 6(3), 283\u2013313 (2005). https:\/\/doi.org\/10.1007\/s11081-005-1741-7","journal-title":"Optim. Eng."},{"key":"85_CR6","unstructured":"Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press, Princeton. http:\/\/press.princeton.edu\/titles\/9099.html (2009). Accessed 8 Mar 2019"},{"key":"85_CR7","unstructured":"Bragalli, C., D\u2019Ambrosio, C., Lee, J., Lodi, A., Toth, P.: Water Network Design by MINLP. Technical Report (2008). IBM Research Division, RC24495 (W0802-056)"},{"issue":"2","key":"85_CR8","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s11081-011-9141-7","volume":"13","author":"C Bragalli","year":"2012","unstructured":"Bragalli, C., D\u2019Ambrosio, C., Lee, J., Lodi, A., Toth, P.: On the optimal design of water distribution networks: a practical MINLP approach. Optim. Eng. 13(2), 219\u2013246 (2012). https:\/\/doi.org\/10.1007\/s11081-011-9141-7","journal-title":"Optim. Eng."},{"key":"85_CR9","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1007\/11841036_62","volume-title":"Algorithms - ESA 2006, Lecture Notes in Computer Science","author":"C Bragalli","year":"2006","unstructured":"Bragalli, C., D\u2019Ambrosio, C., Lee, J., Lodi, A., Toth, P.: An MINLP solution method for a water network problem. In: Azar, Y., Erlebach, T. (eds.) Algorithms - ESA 2006, Lecture Notes in Computer Science, vol. 4168, pp. 696\u2013707. Springer, Berlin (2006). https:\/\/doi.org\/10.1007\/11841036_62"},{"key":"85_CR10","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s10107-016-0991-9","volume":"157","author":"V Cacchiani","year":"2016","unstructured":"Cacchiani, V., J\u00fcnger, M., Liers, F., Lodi, A., Schmidt, D.R.: Single-commodity robust network design with finite and Hose demand sets. Math. Program. 157, 297\u2013342 (2016). https:\/\/doi.org\/10.1007\/s10107-016-0991-9","journal-title":"Math. Program."},{"issue":"7","key":"85_CR11","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1287\/mnsc.24.7.747","volume":"24","author":"M Collins","year":"1978","unstructured":"Collins, M., Cooper, L., Helgason, R., Kennington, J., LeBlanc, L.: Solving the pipe network analysis problem using optimization techniques. Manag. Sci. 24(7), 747\u2013760 (1978). https:\/\/doi.org\/10.1287\/mnsc.24.7.747","journal-title":"Manag. Sci."},{"issue":"4","key":"85_CR12","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1145\/316194.316209","volume":"29","author":"NG Duffield","year":"1999","unstructured":"Duffield, N.G., Goyal, P., Greenberg, A., Mishra, P., Ramakrishnan, K.K., van der Merive, J.E.: A flexible model for resource management in virtual private networks. SIGCOMM Comput. Commun. Rev. 29(4), 95\u2013108 (1999). https:\/\/doi.org\/10.1145\/316194.316209","journal-title":"SIGCOMM Comput. Commun. Rev."},{"key":"85_CR13","doi-asserted-by":"publisher","unstructured":"Erlebach, T., Ruegg, M.: Optimal bandwidth reservation in hose-model VPNs with multi-path routing. In: 23rd Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 2004, vol. 4, pp. 2275\u20132282. IEEE (2004). https:\/\/doi.org\/10.1109\/INFCOM.2004.1354650","DOI":"10.1109\/INFCOM.2004.1354650"},{"issue":"2","key":"85_CR14","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1006\/jagm.1997.0866","volume":"24","author":"J Fingerhut","year":"1997","unstructured":"Fingerhut, J., Suri, S., Turner, J.S.: Designing least-cost nonblocking broadband networks. J. Algorithms 24(2), 287\u2013309 (1997). https:\/\/doi.org\/10.1006\/jagm.1997.0866","journal-title":"J. Algorithms"},{"key":"85_CR15","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1137\/1.9781611973693.ch2","volume-title":"Chapter 2: physical and Technical Fundamentals of Gas Networks","author":"A F\u00fcgenschuh","year":"2015","unstructured":"F\u00fcgenschuh, A., Gei\u00dfler, B., Gollmer, R., Morsi, A., R\u00f6vekamp, J., Schmidt, M., Spreckelsen, K., Steinbach, M.C.: Chapter 2: physical and Technical Fundamentals of Gas Networks, pp. 17\u201343. Society for Industrial and Applied Mathematics, Philadelphia (2015). https:\/\/doi.org\/10.1137\/1.9781611973693.ch2"},{"key":"85_CR16","doi-asserted-by":"crossref","unstructured":"Gro\u00df, M., Pfetsch, M.E., Schewe, L., Schmidt, M., Skutella, M.: Algorithmic results for potential-based flows: easy and hard cases. Networks 73(3), 306\u2013324 (2018). https:\/\/doi.org\/10.1002\/net.21865","DOI":"10.1002\/net.21865"},{"key":"85_CR17","unstructured":"Gurobi Optimization, Inc.: Gurobi optimizer reference manual. http:\/\/www.gurobi.com (2017). Accessed 8 Mar 2019"},{"issue":"1","key":"85_CR18","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/BF01582879","volume":"52","author":"CT Hansen","year":"1991","unstructured":"Hansen, C.T., Madsen, K., Nielsen, H.B.: Optimization of pipe networks. Math. Program. 52(1), 45\u201358 (1991). https:\/\/doi.org\/10.1007\/BF01582879","journal-title":"Math. Program."},{"key":"85_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-3226-5","volume-title":"Pyomo-Optimization Modeling in Python","author":"WE Hart","year":"2012","unstructured":"Hart, W.E., Laird, C., Watson, J.P., Woodruff, D.L.: Pyomo-Optimization Modeling in Python, vol. 67. Springer, Boston, MA (2012). https:\/\/doi.org\/10.1007\/978-1-4614-3226-5"},{"key":"85_CR20","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s12532-011-0026-8","volume":"3","author":"WE Hart","year":"2011","unstructured":"Hart, W.E., Watson, J.P., Woodruff, D.L.: Pyomo: modeling and solving mathematical programs in python. Math. Program. Comput. 3, 219\u2013260 (2011). https:\/\/doi.org\/10.1007\/s12532-011-0026-8","journal-title":"Math. Program. Comput."},{"issue":"3","key":"85_CR21","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10589-015-9756-2","volume":"62","author":"J Humpola","year":"2015","unstructured":"Humpola, J., F\u00fcgenschuh, A.: Convex reformulations for solving a nonlinear network design problem. Comput. Optim. Appl. 62(3), 717\u2013759 (2015). https:\/\/doi.org\/10.1007\/s10589-015-9756-2","journal-title":"Comput. Optim. Appl."},{"key":"85_CR22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973693","volume-title":"Evaluating Gas Network Capacities","year":"2015","unstructured":"Koch, T., Hiller, B., Pfetsch, M., Schewe, L. (eds.): Evaluating Gas Network Capacities. Society for Industrial and Applied Mathematics, Philadelphia (2015). https:\/\/doi.org\/10.1137\/1.9781611973693"},{"key":"85_CR23","unstructured":"Mischner, J., Fasold, H., Kadner, K.: gas2energy.net: Systemplanung in der Gasversorgung; gaswirtschaftliche Grundlagen. Edition gwf, Gas, Erdgas. Oldenbourg Industrieverl. (2011)"},{"issue":"1","key":"85_CR24","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1137\/110827387","volume":"23","author":"AU Raghunathan","year":"2013","unstructured":"Raghunathan, A.U.: Global optimization of nonlinear network design. SIAM J. Optim. 23(1), 268\u2013295 (2013). https:\/\/doi.org\/10.1137\/110827387","journal-title":"SIAM J. Optim."},{"key":"85_CR25","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.apenergy.2017.05.050","volume":"200","author":"M Reuss","year":"2017","unstructured":"Reuss, M., Grube, T., Robinius, M., Preuster, P., Wasserscheid, P., Stolten, D.: Seasonal storage and alternative carriers: a flexible hydrogen supply chain architecture model. Appl. Energy 200, 290\u2013302 (2017). https:\/\/doi.org\/10.1016\/j.apenergy.2017.05.050","journal-title":"Appl. Energy"},{"issue":"1","key":"85_CR26","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1023\/A:1021529709006","volume":"117","author":"RZ R\u00edos-Mercado","year":"2002","unstructured":"R\u00edos-Mercado, R.Z., Wu, S., Scott, L.R., Boyd, E.A.: A reduction technique for natural gas transmission network optimization problems. Ann. Oper. Res. 117(1), 217\u2013234 (2002). https:\/\/doi.org\/10.1023\/A:1021529709006","journal-title":"Ann. Oper. Res."},{"key":"85_CR27","unstructured":"Robinius, M.: Strom- und Gasmarktdesign zur Versorgung des deutschen Stra\u00dfenverkehrs mit Wasserstoff. Ph. D. Thesis, RWTH Aachen University (2015)"},{"key":"85_CR28","doi-asserted-by":"publisher","DOI":"10.3390\/en10070957","author":"M Robinius","year":"2017","unstructured":"Robinius, M., Otto, A., Syranidis, K., Ryberg, D., Heuser, P., Welder, L., Grube, T., Markewitz, P., Tietze, V., Stolten, D.: Linking the power and transport sectors\u2013part 2: modelling a sector coupling scenario for germany. Energies (2017). https:\/\/doi.org\/10.3390\/en10070957","journal-title":"Energies"},{"key":"85_CR29","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1016\/j.apenergy.2015.03.017","volume":"147","author":"RZ R\u00edos-Mercado","year":"2015","unstructured":"R\u00edos-Mercado, R.Z., Borraz-S\u00e1nchez, C.: Optimization problems in natural gas transportation systems: a state-of-the-art review. Appl. Energy 147, 536\u2013555 (2015). https:\/\/doi.org\/10.1016\/j.apenergy.2015.03.017","journal-title":"Appl. Energy"},{"key":"85_CR30","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1016\/j.ejor.2016.01.008","volume":"252","author":"N Shiono","year":"2016","unstructured":"Shiono, N., Suzuki, H.: Optimal pipe-sizing problem of tree-shaped gas distribution networks. Eur. J. Oper. Res. 252, 550\u2013560 (2016). https:\/\/doi.org\/10.1016\/j.ejor.2016.01.008","journal-title":"Eur. J. Oper. Res."},{"key":"85_CR31","doi-asserted-by":"publisher","first-page":"3452","DOI":"10.1016\/j.rser.2017.10.110","volume":"82","author":"K Syranidis","year":"2018","unstructured":"Syranidis, K., Robinius, M., Stolten, D.: Control techniques and the modeling of electrical power flow across transmission networks. Renew. Sustain. Energy Rev. 82, 3452\u20133467 (2018). https:\/\/doi.org\/10.1016\/j.rser.2017.10.110","journal-title":"Renew. Sustain. Energy Rev."},{"key":"85_CR32","unstructured":"Szab\u00f3, J.: The set of solutions to nomination validation in passive gas transportation networks with a generalized flow formula. Technical Report, pp. 11\u201344, ZIB, Takustr.7, 14195 Berlin (2012). www.nbn-resolving.de\/urn:nbn:de:0297-zib-15151"},{"key":"85_CR33","doi-asserted-by":"publisher","unstructured":"Vuffray, M., Misra, S., Chertkov, M.: Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: general analysis and application to natural gas flows. In: 2015 54th IEEE Conference on Decision and Control (CDC), pp. 4571\u20134578 (2015). https:\/\/doi.org\/10.1109\/CDC.2015.7402933","DOI":"10.1109\/CDC.2015.7402933"},{"key":"85_CR34","doi-asserted-by":"crossref","unstructured":"Welder, L., Ryberg, D.S., Kotzur, L., Grube, T., Robinius, M., Stolten, D.: Spatio-temporal optimization of a future energy system for power-to-hydrogen applications in Germany. Energy 158, 1130\u20131149 (2018). https:\/\/doi.org\/10.1016\/j.energy.2018.05.059","DOI":"10.1016\/j.energy.2018.05.059"},{"issue":"1349","key":"85_CR35","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1115\/1.4059982","volume":"34","author":"TR Weymouth","year":"1912","unstructured":"Weymouth, T.R.: Problems in natural gas engineering. Trans. Am. Soc. Mech. Eng. 34(1349), 185\u2013231 (1912)","journal-title":"Trans. Am. Soc. Mech. Eng."},{"issue":"2","key":"85_CR36","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/03052158408960635","volume":"7","author":"D Yates","year":"1984","unstructured":"Yates, D., Templeman, A., Boffey, T.: The computational complexity of the problem of determining least capital cost designs for water supply networks. Eng. Optimiz. 7(2), 143\u2013155 (1984). https:\/\/doi.org\/10.1080\/03052158408960635","journal-title":"Eng. Optimiz."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-019-00085-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-019-00085-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-019-00085-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T02:41:18Z","timestamp":1721097678000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-019-00085-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,23]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["85"],"URL":"https:\/\/doi.org\/10.1007\/s10589-019-00085-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,23]]},"assertion":[{"value":"1 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}