{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T06:10:04Z","timestamp":1774419004430,"version":"3.50.1"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:00:00Z","timestamp":1773014400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:00:00Z","timestamp":1773014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper. Res. Forum"],"DOI":"10.1007\/s43069-026-00617-2","type":"journal-article","created":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T06:32:35Z","timestamp":1773037955000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributionally Robust Chance-Constrained Multicommodity Network Flow Problem in Dynamic Networks: A Column-Generation Approach"],"prefix":"10.1007","volume":"7","author":[{"given":"Salman","family":"Khodayifar","sequence":"first","affiliation":[]},{"given":"Somayeh","family":"Khezri","sequence":"additional","affiliation":[]},{"given":"Panos M.","family":"Pardalos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,9]]},"reference":[{"issue":"1","key":"617_CR1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1287\/ijoc.1100.0380","volume":"23","author":"A Alt\u0131n","year":"2011","unstructured":"Alt\u0131n A, Yaman H, P\u0131nar M\u00c7 (2011) The robust network loading problem under hose demand uncertainty: formulation, polyhedral analysis, and computations. INFORMS J Comput 23(1):75\u201389","journal-title":"INFORMS J Comput"},{"issue":"1","key":"617_CR2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1002\/net.3230080107","volume":"8","author":"AA Assad","year":"1978","unstructured":"Assad AA (1978) Multicommodity network flows\u2014a survey. Networks 8(1):37\u201391","journal-title":"Networks"},{"issue":"5439","key":"617_CR3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","volume":"286","author":"AL Barabasi","year":"1999","unstructured":"Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509\u2013512","journal-title":"Science"},{"key":"617_CR4","doi-asserted-by":"crossref","unstructured":"Barmish BR, Lagoa CM, Tempo R (1997) Radially truncated uniform distributions for probabilistic robustness of control systems. In\u00a0Proceedings of the 1997 American Control Conference (Cat. No. 97CH36041). IEEE 1:853\u2013857","DOI":"10.1109\/ACC.1997.611925"},{"issue":"4","key":"617_CR5","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1287\/moor.23.4.769","volume":"23","author":"A Ben-Tal","year":"1998","unstructured":"Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769\u2013805","journal-title":"Math Oper Res"},{"issue":"1","key":"617_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-6377(99)00016-4","volume":"25","author":"A Ben-Tal","year":"1999","unstructured":"Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25(1):1\u201313","journal-title":"Oper Res Lett"},{"issue":"3","key":"617_CR7","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/PL00011380","volume":"88","author":"A Ben-Tal","year":"2000","unstructured":"Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88(3):411\u2013421","journal-title":"Math Program"},{"issue":"3","key":"617_CR8","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1137\/S1052623401399903","volume":"15","author":"D Bertsimas","year":"2005","unstructured":"Bertsimas D, Popescu I (2005) Optimal inequalities in probability theory: a convex optimization approach. SIAM J Optim 15(3):780\u2013804","journal-title":"SIAM J Optim"},{"issue":"1","key":"617_CR9","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1287\/opre.1030.0065","volume":"52","author":"D Bertsimas","year":"2004","unstructured":"Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35\u201353","journal-title":"Oper Res"},{"key":"617_CR10","doi-asserted-by":"crossref","unstructured":"Bozhenyuk A, Gerasimenko E, Rozenberg I (2017) Method of maximum two-commodity flow search in a fuzzy temporal graph. Advances in Fuzzy Logic and Technology 2017. Springer, Cham, pp 249\u2013260","DOI":"10.1007\/978-3-319-66830-7_23"},{"issue":"1","key":"617_CR11","first-page":"31","volume":"37","author":"RE Burkard","year":"1993","unstructured":"Burkard RE, Dlaska K, Klinz B (1993) The quickest flow problem. Z Oper Res 37(1):31\u201358","journal-title":"Z Oper Res"},{"issue":"1","key":"617_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10957-006-9084-x","volume":"130","author":"GC Calafiore","year":"2006","unstructured":"Calafiore GC, El Ghaoui L (2006) On distributionally robust chance-constrained linear programs. J Optim Theory Appl 130(1):1\u201322","journal-title":"J Optim Theory Appl"},{"issue":"3","key":"617_CR13","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0305-0548(02)00197-1","volume":"31","author":"HI Calvete","year":"2004","unstructured":"Calvete HI (2004) The quickest path problem with interval lead times. Comput Oper Res 31(3):383\u2013395","journal-title":"Comput Oper Res"},{"key":"617_CR14","doi-asserted-by":"crossref","unstructured":"Charikar M, Naamad Y, Rexford J, Zou XK (2018) Multicommodity flow with in-network processing. In\u00a0International Symposium on Algorithmic Aspects of Cloud Computing\u00a0(pp 73\u2013101). Springer, Cham","DOI":"10.1007\/978-3-030-19759-9_6"},{"key":"617_CR15","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cor.2016.06.010","volume":"76","author":"M El Khadiri","year":"2016","unstructured":"El Khadiri M, Yeh WC (2016) An efficient alternative to the exact evaluation of the quickest path flow network reliability problem. Computers & Operations Research 76:22\u201332","journal-title":"Computers & Operations Research"},{"issue":"7-8","key":"617_CR16","doi-asserted-by":"crossref","first-page":"2151","DOI":"10.1016\/j.apm.2013.10.032","volume":"38","author":"A Fakhri","year":"2014","unstructured":"Fakhri A, Ghatee M (2014) Fractional multicommodity flow problem: duality and optimality conditions. Appl Math Model 38(7\u20138):2151\u20132162","journal-title":"Appl Math Model"},{"key":"617_CR17","doi-asserted-by":"crossref","unstructured":"Fleischer L, Skutella M (2002) The quickest multicommodity flow problem. In\u00a0International Conference on Integer Programming and Combinatorial Optimization\u00a0(pp 36\u201353). Springer, Berlin, Heidelberg","DOI":"10.1007\/3-540-47867-1_4"},{"issue":"1","key":"617_CR18","first-page":"97","volume":"5","author":"LR Ford Jr","year":"1958","unstructured":"Ford LR Jr, Fulkerson DR (1958) A suggested computation for maximal multicommodity network flows. Manage Sci 5(1):97\u2013101","journal-title":"Manage Sci"},{"issue":"3","key":"617_CR19","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1287\/opre.6.3.419","volume":"6","author":"LR Ford Jr","year":"1958","unstructured":"Ford LR Jr, Fulkerson DR (1958) Constructing maximal dynamic flows from static flows. Oper Res 6(3):419\u2013433","journal-title":"Oper Res"},{"key":"617_CR20","unstructured":"Fragkos I, Cordeau JF, Jans R (2017) The multi-period multicommodity network design problem. CIRRELT, Centre interuniversitaire de recherche sur les r\u00e9seaux d'entreprise, la logistique et le transport= interuniversity research centre on enterprise networks, logistics and transportation"},{"key":"617_CR21","first-page":"105","volume":"350","author":"P Ghasemi","year":"2019","unstructured":"Ghasemi P, Khalili-Damghani K, Hafezalkotob A, Raissi S (2019) Uncertain multi-objective multicommodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning. Appl Math Comput 350:105\u2013132","journal-title":"Appl Math Comput"},{"issue":"5\u20136","key":"617_CR22","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1016\/j.mcm.2008.08.009","volume":"49","author":"M Ghatee","year":"2009","unstructured":"Ghatee M, Hashemi SM (2009) Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design. Math Comput Model 49(5\u20136):1030\u20131043","journal-title":"Math Comput Model"},{"issue":"3","key":"617_CR23","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1023\/A:1011233219223","volume":"18","author":"GD Glockner","year":"2001","unstructured":"Glockner GD, Nemhauser GL, Tovey CA (2001) Dynamic network flow with uncertain arc capacities: decomposition algorithm and computational results. Comput Optim Appl 18(3):233\u2013250","journal-title":"Comput Optim Appl"},{"key":"617_CR24","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.endm.2018.01.014","volume":"64","author":"E Grande","year":"2018","unstructured":"Grande E, Nicosia G, Pacifici A, Roselli V (2018) An exact algorithm for a multicommodity min-cost flow overtime problem. Electronic Notes in Discrete Mathematics 64:125\u2013134","journal-title":"Electronic Notes in Discrete Mathematics"},{"key":"617_CR25","doi-asserted-by":"crossref","unstructured":"Grob M, Skutella M (2012) Maximum multicommodity flows over time without intermediate storage. In\u00a0European Symposium on Algorithms\u00a0(pp 539\u2013550). Springer, Berlin, Heidelberg","DOI":"10.1007\/978-3-642-33090-2_47"},{"issue":"3","key":"617_CR26","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ipl.2005.10.004","volume":"97","author":"J Guo","year":"2006","unstructured":"Guo J, Niedermeier R (2006) A fixed-parameter tractability result for multicommodity demand flow in trees. Inf Process Lett 97(3):109\u2013114","journal-title":"Inf Process Lett"},{"issue":"3","key":"617_CR27","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.tcs.2007.02.046","volume":"379","author":"A Hall","year":"2007","unstructured":"Hall A, Hippler S, Skutella M (2007) Multicommodity flows over time: efficient algorithms and complexity. Theoret Comput Sci 379(3):387\u2013404","journal-title":"Theoret Comput Sci"},{"key":"617_CR28","doi-asserted-by":"crossref","unstructured":"Hoeffding W (1994) Probability inequalities for sums of bounded random variables. The Collected Works of Wassily Hoeffding. Springer, New York, NY, pp 409\u2013426","DOI":"10.1007\/978-1-4612-0865-5_26"},{"issue":"3","key":"617_CR29","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1287\/opre.11.3.344","volume":"11","author":"TC Hu","year":"1963","unstructured":"Hu TC (1963) Multicommodity network flows. Oper Res 11(3):344\u2013360","journal-title":"Oper Res"},{"issue":"1","key":"617_CR30","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s11235-015-0067-9","volume":"62","author":"O Kabadurmus","year":"2016","unstructured":"Kabadurmus O, Smith AE (2016) Multicommodity k-splittable survivable network design problems with relays. Telecommun Syst 62(1):123\u2013133","journal-title":"Telecommun Syst"},{"key":"617_CR31","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.tre.2015.01.005","volume":"76","author":"CV Karsten","year":"2015","unstructured":"Karsten CV, Pisinger D, Ropke S, Brouer BD (2015) The time constrained multicommodity network flow problem and its application to liner shipping network design. Transportation Research Part E: Logistics and Transportation Review 76:122\u2013138","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"2","key":"617_CR32","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1287\/opre.26.2.209","volume":"26","author":"JL Kennington","year":"1978","unstructured":"Kennington JL (1978) A survey of linear cost multicommodity network flows. Oper Res 26(2):209\u2013236","journal-title":"Oper Res"},{"key":"617_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-022-01873-x","author":"R Khanjani-Shiraz","year":"2022","unstructured":"Khanjani-Shiraz R, Babapour-Azar A, Hosseini-Nodeh Z, Pardalos PM (2022) Distributionally robust joint chance-constrained support vector machines. Optim Lett. https:\/\/doi.org\/10.1007\/s11590-022-01873-x","journal-title":"Optim Lett"},{"key":"617_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2023.106260","author":"S Khezri","year":"2023","unstructured":"Khezri S, Khodayifar S (2023) Joint chance-constrained multi-objective multi-commodity minimum cost network flow problem with copula theory. Comput Oper Res. https:\/\/doi.org\/10.1016\/j.cor.2023.106260","journal-title":"Comput Oper Res"},{"issue":"3","key":"617_CR35","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1007\/s11590-019-01519-5","volume":"15","author":"S Khodayifar","year":"2019","unstructured":"Khodayifar S (2019) Minimum cost multicommodity network flow problem in time-varying networks: by decomposition principle. Optim Lett 15(3):1009\u20131026","journal-title":"Optim Lett"},{"issue":"4","key":"617_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10878-025-01370-8","volume":"50","author":"S Khodayifar","year":"2025","unstructured":"Khodayifar S, Farjaie M (2025) Distributionally robust joint chance-constrained approach for the stochastic survivable capacitated network design problem. J Comb Optim 50(4):1\u201328","journal-title":"J Comb Optim"},{"issue":"5","key":"617_CR37","doi-asserted-by":"crossref","first-page":"2993","DOI":"10.1051\/ro\/2025096","volume":"59","author":"S Khodayifar","year":"2025","unstructured":"Khodayifar S, Farjaie M (2025) Joint chance-constrained survivable capacitated multi-commodity network design problem with demand uncertainty. RAIRO-Operations Research 59(5):2993\u20133014","journal-title":"RAIRO-Operations Research"},{"issue":"1\u20132","key":"617_CR38","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10479-017-2450-2","volume":"272","author":"S Khodayifar","year":"2019","unstructured":"Khodayifar S, Raayatpanah MA, Pardalos PM (2019) A polynomial time algorithm for the minimum flow problem in time-varying networks. Ann Oper Res 272(1\u20132):29\u201339","journal-title":"Ann Oper Res"},{"issue":"3","key":"617_CR39","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/net.10112","volume":"43","author":"B Klinz","year":"2004","unstructured":"Klinz B, Woeginger GJ (2004) Minimum\u2010cost dynamic flows: the series\u2010parallel case. Networks: An International Journal 43(3):153\u2013162","journal-title":"Networks: An International Journal"},{"key":"617_CR40","doi-asserted-by":"crossref","unstructured":"Kureichik VM, Evgeniya G (2017) Multicommodity maximum flow determining in a fuzzy graph with vitality degrees. In 2017 IEEE 11th International Conference on Application of Information and Communication Technologies (AICT) IEEE: 1\u20134","DOI":"10.1109\/ICAICT.2017.8687212"},{"issue":"1","key":"617_CR41","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.tre.2008.08.002","volume":"45","author":"DH Lee","year":"2009","unstructured":"Lee DH, Dong M (2009) Dynamic network design for reverse logistics operations under uncertainty. Transportation Research Part E: Logistics and Transportation Review 45(1):61\u201371","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"3","key":"617_CR42","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.dam.2009.09.022","volume":"158","author":"K Lee","year":"2010","unstructured":"Lee K (2010) Integral polyhedra related to integer multicommodity flows on a cycle. Discrete Appl Math 158(3):235\u2013238","journal-title":"Discrete Appl Math"},{"issue":"3","key":"617_CR43","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1016\/j.ejor.2015.02.028","volume":"244","author":"AN Letchford","year":"2015","unstructured":"Letchford AN, Salazar-Gonz\u00e1lez JJ (2015) Stronger multicommodity flow formulations of the capacitated vehicle routing problem. Eur J Oper Res 244(3):730\u2013738","journal-title":"Eur J Oper Res"},{"issue":"1","key":"617_CR44","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0305-0548(99)00007-6","volume":"27","author":"L Li","year":"2000","unstructured":"Li L, Lai KK (2000) A fuzzy approach to the multiobjective transportation problem. Comput Oper Res 27(1):43\u201357","journal-title":"Comput Oper Res"},{"key":"617_CR45","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.adhoc.2017.01.006","volume":"59","author":"H Li","year":"2017","unstructured":"Li H, Zhang T, Zhang Y, Wang K, Li J (2017) A maximum flow algorithm based on storage time aggregated graph for delay-tolerant networks. Ad Hoc Netw 59:63\u201370","journal-title":"Ad Hoc Netw"},{"issue":"9","key":"617_CR46","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1057\/jors.2009.86","volume":"61","author":"XY Li","year":"2010","unstructured":"Li XY, Aneja YP, Baki F (2010) An ant colony optimization metaheuristic for single-path multicommodity network flow problems. J Oper Res Soc 61(9):1340\u20131355","journal-title":"J Oper Res Soc"},{"key":"617_CR47","doi-asserted-by":"crossref","unstructured":"Lin M, Jaillet P (2014) On the quickest flow problem in dynamic networks\u2013a parametric min-cost flow approach. In Proceedings of the twenty-sixth annual ACM-SIAM symposium on discrete algorithms. Society for industrial and applied mathematics 1343\u20131356","DOI":"10.1137\/1.9781611973730.89"},{"key":"617_CR48","doi-asserted-by":"crossref","first-page":"27532","DOI":"10.1109\/ACCESS.2020.2971027","volume":"8","author":"Y Lu","year":"2020","unstructured":"Lu Y, Lang M, Sun Y, Li S (2020) A fuzzy intercontinental road-rail multi-modal routing model with time and train capacity uncertainty and fuzzy programming approaches. IEEE Access 8:27532\u201327548","journal-title":"IEEE Access"},{"issue":"2","key":"617_CR49","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.orl.2006.02.005","volume":"35","author":"P Mahey","year":"2007","unstructured":"Mahey P, de Souza MC (2007) Local optimality conditions for multicommodity flow problems with separable piecewise convex costs. Oper Res Lett 35(2):221\u2013226","journal-title":"Oper Res Lett"},{"issue":"3","key":"617_CR50","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s10589-012-9500-0","volume":"54","author":"S Mattia","year":"2013","unstructured":"Mattia S (2013) The robust network loading problem with dynamic routing. Comput Optim Appl 54(3):619\u2013643","journal-title":"Comput Optim Appl"},{"issue":"2","key":"617_CR51","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1287\/inte.28.2.32","volume":"28","author":"RD McBride","year":"1998","unstructured":"McBride RD (1998) Advances in solving the multicommodity-flow problem. Interfaces 28(2):32\u201341","journal-title":"Interfaces"},{"key":"617_CR52","doi-asserted-by":"publisher","DOI":"10.1080\/0305215x.2019.1603299","author":"I Mejri","year":"2019","unstructured":"Mejri I, Layeb SB, Haouari M, Mansour FZ (2019) A simulation-optimization approach for the stochastic discrete cost multicommodity flow problem. Eng Optim. https:\/\/doi.org\/10.1080\/0305215x.2019.1603299","journal-title":"Eng Optim"},{"issue":"1","key":"617_CR53","first-page":"1","volume":"310","author":"S Mishra","year":"2020","unstructured":"Mishra S, Singh SP (2020) Designing dynamic reverse logistics network for post-sale service. Ann Oper Res 310(1):1\u201330","journal-title":"Ann Oper Res"},{"issue":"3","key":"617_CR54","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.ejor.2016.07.054","volume":"257","author":"M Mohammadi","year":"2017","unstructured":"Mohammadi M, Jula P, Tavakkoli-Moghaddam R (2017) Design of a reliable multi-modal multicommodity model for hazardous materials transportation under uncertainty. Eur J Oper Res 257(3):792\u2013809","journal-title":"Eur J Oper Res"},{"key":"617_CR55","unstructured":"Mudchanatongsuk S, Ord\u00f3\u00f1ez F, Liu J (2005) Robust solutions for network design under transportation cost and demand uncertainty. USC ISE Working paper 2005\u201305"},{"issue":"1-2","key":"617_CR56","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0166-218X(90)90134-X","volume":"27","author":"H Nagamochi","year":"1990","unstructured":"Nagamochi H, Ibaraki T (1990) Multicommodity flows in certain planar directed networks. Discrete Appl Math 27(1\u20132):125\u2013145","journal-title":"Discrete Appl Math"},{"issue":"1","key":"617_CR57","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1287\/mnsc.46.1.126.15132","volume":"46","author":"A Ouorou","year":"2000","unstructured":"Ouorou A, Mahey P, Vial JP (2000) A survey of algorithms for convex multicommodity flow problems. Manage Sci 46(1):126\u2013147","journal-title":"Manage Sci"},{"issue":"1","key":"617_CR58","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s10589-021-00292-5","volume":"80","author":"S Peng","year":"2021","unstructured":"Peng S, Jiang J (2021) Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches. Comput Optim Appl 80(1):153\u2013184","journal-title":"Comput Optim Appl"},{"issue":"1","key":"617_CR59","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s10479-018-2960-6","volume":"283","author":"D Rahmani","year":"2019","unstructured":"Rahmani D (2019) Designing a robust and dynamic network for the emergency blood supply chain with the risk of disruptions. Ann Oper Res 283(1):613\u2013641","journal-title":"Ann Oper Res"},{"issue":"1","key":"617_CR60","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1137\/17M1128204","volume":"28","author":"R Rahmaniani","year":"2018","unstructured":"Rahmaniani R, Crainic TG, Gendreau M, Rei W (2018) Accelerating the Benders decomposition method: application to stochastic network design problems. SIAM J Optim 28(1):875\u2013903","journal-title":"SIAM J Optim"},{"issue":"2","key":"617_CR61","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1016\/j.ejor.2014.04.028","volume":"238","author":"A Sede\u00f1o-Noda","year":"2014","unstructured":"Sede\u00f1o-Noda A, Gonz\u00e1lez-Barrera JD (2014) Fast and fine quickest path algorithm. Eur J Oper Res 238(2):596\u2013606","journal-title":"Eur J Oper Res"},{"issue":"3","key":"617_CR62","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s10589-021-00320-4","volume":"80","author":"T Silva","year":"2021","unstructured":"Silva T, Vallad\u00e3o D, Homem-de-Mello T (2021) A data-driven approach for a class of stochastic dynamic optimization problems. Comput Optim Appl 80(3):687\u2013729","journal-title":"Comput Optim Appl"},{"issue":"1","key":"617_CR63","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1287\/ijoc.1040.0079","volume":"18","author":"H Topaloglu","year":"2006","unstructured":"Topaloglu H, Powell WB (2006) Dynamic-programming approximations for stochastic time-staged integer multicommodity-flow problems. INFORMS J Comput 18(1):31\u201342","journal-title":"INFORMS J Comput"},{"key":"617_CR64","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.cor.2016.08.002","volume":"77","author":"W Van Ackooij","year":"2017","unstructured":"Van Ackooij W, Berge V, de Oliveira W, Sagastiz\u00e1bal C (2017) Probabilistic optimization via approximate p-efficient points and bundle methods. Comput Oper Res 77:177\u2013193","journal-title":"Comput Oper Res"},{"key":"617_CR65","doi-asserted-by":"crossref","unstructured":"Yeh WC, Chang WW, Chiu CW (2009) A simple method for the multi-state quickest path flow network reliability problem. In 2009 8th International conference on reliability, maintainability and safety. IEEE 108\u2013110","DOI":"10.1109\/ICRMS.2009.5270229"},{"issue":"12","key":"617_CR66","doi-asserted-by":"crossref","first-page":"7879","DOI":"10.1109\/TWC.2018.2872551","volume":"17","author":"T Zhang","year":"2018","unstructured":"Zhang T, Li H, Li J, Zhang S, Shen H (2018) A dynamic combined flow algorithm for the two-commodity max-flow problem over delay-tolerant networks. IEEE Trans Wireless Commun 17(12):7879\u20137893","journal-title":"IEEE Trans Wireless Commun"}],"container-title":["Operations Research Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-026-00617-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s43069-026-00617-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-026-00617-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T05:18:50Z","timestamp":1774415930000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s43069-026-00617-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,9]]},"references-count":66,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["617"],"URL":"https:\/\/doi.org\/10.1007\/s43069-026-00617-2","relation":{},"ISSN":["2662-2556"],"issn-type":[{"value":"2662-2556","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,9]]},"assertion":[{"value":"3 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"The authors declare no competing interests.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"32"}}