{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T04:25:30Z","timestamp":1778905530485,"version":"3.51.4"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:00:00Z","timestamp":1652486400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:00:00Z","timestamp":1652486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We discuss a widely used air traffic flow management formulation. We show that this formulation can lead to a solution where air delays are assigned to flights during their take-off which is prohibited in practice. Although air delay is more expensive than ground delay, the model may assign air delay to a few flights during their take-off to save more on not having as much ground delay. We present a modified formulation and verify its functionality in avoiding incorrect solutions.<\/jats:p>","DOI":"10.1007\/s10479-022-04740-1","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T08:03:01Z","timestamp":1652515381000},"page":"267-279","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On the binary formulation of air traffic flow management problems"],"prefix":"10.1007","volume":"321","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5265-0836","authenticated-orcid":false,"given":"Sadeque","family":"Hamdan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9498-165X","authenticated-orcid":false,"given":"Oualid","family":"Jouini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4497-7537","authenticated-orcid":false,"given":"Ali","family":"Cheaitou","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7679-9670","authenticated-orcid":false,"given":"Zied","family":"Jemai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5868-2388","authenticated-orcid":false,"given":"Tobias Andersson","family":"Granberg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"4740_CR1","first-page":"1156","volume":"219","author":"A Agust\u00edn","year":"2012","unstructured":"Agust\u00edn, A., Alonso-Ayuso, A., Escudero, L. F., & Pizarro, C. (2012). On air traffic flow management with rerouting. Part I: deterministic case. European Journal of Operational Research, 219, 1156\u2013166.","journal-title":"European Journal of Operational Research"},{"key":"4740_CR2","first-page":"1167","volume":"219","author":"A Agust\u00edn","year":"2012","unstructured":"Agust\u00edn, A., Alonso-Ayuso, A., Escudero, L. F., & Pizarro, C. (2012). On air traffic flow management with rerouting. Part II: stochastic case. European Journal of Operational Research, 219, 1167\u2013177.","journal-title":"European Journal of Operational Research"},{"key":"4740_CR3","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.cie.2018.05.046","volume":"122","author":"A Akgunduz","year":"2018","unstructured":"Akgunduz, A., & Kazerooni, H. (2018). A non-time segmented modeling for air-traffic flow management problem with speed dependent fuel consumption formulation. Computers & Industrial Engineering, 122, 181\u2013188. https:\/\/doi.org\/10.1016\/j.cie.2018.05.046.","journal-title":"Computers & Industrial Engineering"},{"issue":"1","key":"4740_CR4","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10479-013-1347-y","volume":"222","author":"A Alonso-Ayuso","year":"2014","unstructured":"Alonso-Ayuso, A., Escudero, L. F., & Mart\u00edn-Campo, F. J. (2014). On modeling the air traffic control coordination in the collision avoidance problem by mixed integer linear optimization. Annals of Operations Research, 222(1), 89\u2013105.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"4740_CR5","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0377-2217(98)00381-6","volume":"120","author":"A Alonso","year":"2000","unstructured":"Alonso, A., Escudero, L. F., & Ortu\u00f1o, M. T. (2000). A stochastic 0\u20131 program based approach for the air traffic flow management problem. European Journal of Operational Research, 120(1), 47\u201362.","journal-title":"European Journal of Operational Research"},{"key":"4740_CR6","doi-asserted-by":"publisher","unstructured":"Andreatta, G., Odoni, A. R., & Richetta, O. (1993). Models for the ground holding problem. In: Bianco, L., Odoni, A. R. (eds) Large scale computation and information processing in air traffic control. Transportation analysis (125\u2013168), Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/978-3-642-84980-0_5.","DOI":"10.1007\/978-3-642-84980-0_5"},{"issue":"1","key":"4740_CR7","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1287\/trsc.1060.0163","volume":"41","author":"JA Atkin","year":"2007","unstructured":"Atkin, J. A., Burke, E. K., Greenwood, J. S., & Reeson, D. (2007). Hybrid metaheuristics to aid runway scheduling at london heathrow airport. Transportation Science, 41(1), 90\u2013106.","journal-title":"Transportation Science"},{"issue":"1\u20132","key":"4740_CR8","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s13676-012-0006-9","volume":"1","author":"C Barnhart","year":"2012","unstructured":"Barnhart, C., Fearing, D., Odoni, A., & Vaze, V. (2012). Demand and capacity management in air transportation. EURO Journal on Transportation and Logistics, 1(1\u20132), 135\u2013155.","journal-title":"EURO Journal on Transportation and Logistics"},{"issue":"1","key":"4740_CR9","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1023\/B:ANOR.0000032574.01332.98","volume":"130","author":"N Barnier","year":"2004","unstructured":"Barnier, N., & Brisset, P. (2004). Graph coloring for air traffic flow management. Annals of Operations Research, 130(1), 163\u2013178.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"4740_CR10","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10479-012-1268-1","volume":"204","author":"JA Bennell","year":"2013","unstructured":"Bennell, J. A., Mesgarpour, M., & Potts, C. N. (2013). Airport runway scheduling. Annals of Operations Research, 204(1), 249\u2013270.","journal-title":"Annals of Operations Research"},{"key":"4740_CR11","doi-asserted-by":"crossref","unstructured":"Bertsimas, D., Lulli, G., & Odoni, A. (2008). The air traffic flow management problem: An integer optimization approach. In International Conference on Integer Programming and Combinatorial Optimization (34\u201346).","DOI":"10.1007\/978-3-540-68891-4_3"},{"issue":"12","key":"4740_CR12","doi-asserted-by":"publisher","first-page":"2234","DOI":"10.1287\/mnsc.1120.1549","volume":"58","author":"D Bertsimas","year":"2012","unstructured":"Bertsimas, D., Farias, V. F., & Trichakis, N. (2012). On the efficiency-fairness trade-off. Management Science, 58(12), 2234\u20132250.","journal-title":"Management Science"},{"issue":"1","key":"4740_CR13","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1287\/trsc.2014.0567","volume":"50","author":"D Bertsimas","year":"2016","unstructured":"Bertsimas, D., & Gupta, S. (2016). Fairness and collaboration in network air traffic flow management: an optimization approach. Transportation Science, 50(1), 57\u201376.","journal-title":"Transportation Science"},{"issue":"1","key":"4740_CR14","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1287\/opre.1100.0899","volume":"59","author":"D Bertsimas","year":"2011","unstructured":"Bertsimas, D., Lulli, G., & Odoni, A. (2011). An integer optimization approach to large-scale air traffic flow management. Operations Research, 59(1), 211\u2013227.","journal-title":"Operations Research"},{"issue":"3","key":"4740_CR15","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1287\/opre.46.3.406","volume":"46","author":"D Bertsimas","year":"1994","unstructured":"Bertsimas, D., & Patterson, S. S. (1994). The air traffic flow management problem with enroute capacities. Operations Research, 46(3), 406\u2013422.","journal-title":"Operations Research"},{"key":"4740_CR16","first-page":"4280","volume":"191","author":"RA Bihr","year":"1990","unstructured":"Bihr, R. A. (1990). A conceptual solution to the aircraft gate assignment problem using 0, 1 linear programming. Computers & Industrial Engineering, 191, 4280\u2013284.","journal-title":"Computers & Industrial Engineering"},{"key":"4740_CR17","doi-asserted-by":"crossref","unstructured":"Boujarif, A., Hamdan, S., & Jouini, O. (2021). Impact of aircraft model and delay duration on the air traffic flow management. In Proceedings of the International Conference on Industrial Engineering and Operations Management, rome 2021 pp. 1153\u20131163.","DOI":"10.1109\/ICMAE52228.2021.9522473"},{"key":"4740_CR18","doi-asserted-by":"crossref","unstructured":"Boujarif, A., Hamdan, S., & Jouini, O. (2021). Impact of airport capacity optimization on the air traffic flow management. In 2021 12th International Conference on Mechanical and Aerospace Engineering (icmae) pp. 429\u2013434.","DOI":"10.1109\/ICMAE52228.2021.9522473"},{"key":"4740_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1023\/A:1018909224543","volume":"81","author":"L Brunetta","year":"1998","unstructured":"Brunetta, L., Guastalla, G., & Navazio, L. (1998). Solving the multi-airport ground holding problem. Annals of Operations Research, 81, 271\u2013288.","journal-title":"Annals of Operations Research"},{"key":"4740_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10479-020-03589-6","volume":"310","author":"L Chen","year":"2020","unstructured":"Chen, L., Han, S., Du, C., & Luo, Z. (2020). A real-time integrated optimization of the aircraft holding time and rerouting under risk area. Annals of Operations Research, 310, 1\u201320.","journal-title":"Annals of Operations Research"},{"issue":"6","key":"4740_CR21","doi-asserted-by":"publisher","first-page":"12430","DOI":"10.1016\/j.eswa.2012.04.071","volume":"391","author":"C-H Cheng","year":"2012","unstructured":"Cheng, C.-H., Ho, S. C., & Kwan, C.-L. (2012). The use of meta-heuristics for airport gate assignment. Expert Systems with Applications, 391(6), 12430\u201312437.","journal-title":"Expert Systems with Applications"},{"key":"4740_CR22","unstructured":"Churchill, A., Lovell, D., Ball, M., & Smith, R. (2009). Evaluating a new formulation for large-scale traffic flow management. In Europe Air Traffic Management Research and Development Seminar pp. 1\u201310."},{"key":"4740_CR23","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1016\/j.trb.2018.09.009","volume":"117","author":"V Dal Sasso","year":"2018","unstructured":"Dal Sasso, V., Djeumou Fomeni, F., Lulli, G., & Zografos, K. G. (2018). Incorporating stakeholders\u2019 priorities and preferences in 4d trajectory optimization. Transportation Research Part B: Methodological, 117, 594\u2013609.","journal-title":"Transportation Research Part B: Methodological"},{"issue":"2","key":"4740_CR24","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1016\/j.ejor.2019.01.039","volume":"276","author":"V Dal Sasso","year":"2019","unstructured":"Dal Sasso, V., Djeumou Fomeni, F., Lulli, G., & Zografos, K. G. (2019). Planning efficient 4d trajectories in air traffic flow management. European Journal of Operational Research, 276(2), 676\u2013687.","journal-title":"European Journal of Operational Research"},{"key":"4740_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.tre.2017.12.002","volume":"110","author":"X Diao","year":"2018","unstructured":"Diao, X., & Chen, C.-H. (2018). A sequence model for air traffic flow management rerouting problem. Transportation Research Part E: Logistics and Transportation Review, 110, 15\u201330.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"7","key":"4740_CR26","doi-asserted-by":"publisher","first-page":"1867","DOI":"10.1016\/j.cor.2003.12.003","volume":"32","author":"H Ding","year":"2005","unstructured":"Ding, H., Lim, A., Rodrigues, B., & Zhu, Y. (2005). The over-constrained airport gate assignment problem. Computers & Operations Research, 32(7), 1867\u20131880.","journal-title":"Computers & Operations Research"},{"key":"4740_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2019.104768","author":"D Garc\u0107a-Heredia","year":"2019","unstructured":"Garc\u0107a-Heredia, D., Alonso-Ayuso, A., & Molina, E. (2019). A combinatorial model to optimize air traffic flow management problems. Computers & Operations Research. https:\/\/doi.org\/10.1016\/j.cor.2019.104768.","journal-title":"Computers & Operations Research"},{"key":"4740_CR28","doi-asserted-by":"crossref","unstructured":"Hamdan, S., Cheaitou, A., Jouini, O., Jemai, Z., Alsyouf, I., & Bettayeb, M. (2018). On fairness in the network air traffic flow management with rerouting. In 2018 9th International Conference on Mechanical and Aaerospace Engineering (icmae) pp. 100\u2013105.","DOI":"10.1109\/ICMAE.2018.8467624"},{"key":"4740_CR29","doi-asserted-by":"crossref","unstructured":"Hamdan, S., Cheaitou, A., Jouini, O., Jemai, Z., Alsyouf, I., & Bettayeb, M. (2019). An environmental air traffic flow management model. In 2019 8th International Conference on Modeling Simulation and Applied Optimization (icmsao) pp. 1\u20135.","DOI":"10.1109\/ICMSAO.2019.8880331"},{"key":"4740_CR30","doi-asserted-by":"crossref","unstructured":"Hamdan, S., Jouini, O., Cheaitou, A., Jemai, Z., Alsyouf, I., & Bettayeb, M. (2020). Optimal air traffic flow management with carbon emissions considerations. In H. A. Le Thi, H. M. Le, & T. Pham Dinh (Eds.), Optimization of complex systems: Theory models algorithms and applications (pp. 1078\u20131088). Cham: Springer International Publishing.","DOI":"10.1007\/978-3-030-21803-4_106"},{"issue":"2","key":"4740_CR31","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1287\/trsc.2021.1087","volume":"56","author":"S Hamdan","year":"2021","unstructured":"Hamdan, S., Cheaitou, A., Jouini, O., Granberg, T. A., Jemai, Z., Alsyouf, I., & Josefsson, B. (2021). Central authority-controlled air traffic flow management: An optimization approach. Transportation Science, 56(2), 299\u2013321. https:\/\/doi.org\/10.1287\/trsc.2021.1087.","journal-title":"Transportation Science"},{"key":"4740_CR32","doi-asserted-by":"publisher","first-page":"105336","DOI":"10.1016\/j.cor.2021.105336","volume":"132","author":"S Ikli","year":"2021","unstructured":"Ikli, S., Mancel, C., Mongeau, M., Olive, X., & Rachelson, E. (2021). The aircraft runway scheduling problem: A survey. Computers & Operations Research, 132, 105336.","journal-title":"Computers & Operations Research"},{"issue":"3","key":"4740_CR33","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1017\/S0269888912000240","volume":"27","author":"U Junker","year":"2012","unstructured":"Junker, U. (2012). Air traffic flow management with heuristic repair. The Knowledge Engineering Review, 27(3), 333\u2013342. https:\/\/doi.org\/10.1017\/S0269888912000240.","journal-title":"The Knowledge Engineering Review"},{"key":"4740_CR34","doi-asserted-by":"crossref","unstructured":"Liu, F., & Hu, M. (2009). Airspace capacity management based on control workload and coupling constraints between airspaces. In 2009 International Conference on Computer Modeling and Simulation pp. 329\u2013334.","DOI":"10.1109\/ICCMS.2009.46"},{"issue":"2","key":"4740_CR35","doi-asserted-by":"publisher","first-page":"202","DOI":"10.2514\/2.4384","volume":"22","author":"PK Menon","year":"1999","unstructured":"Menon, P. K., Sweriduk, G. D., & Sridhar, B. (1999). Optimal strategies for free-flight air traffic conflict resolution. Journal of Guidance, Control, and Dynamics, 22(2), 202\u2013211.","journal-title":"Journal of Guidance, Control, and Dynamics"},{"issue":"4","key":"4740_CR36","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1287\/trsc.1070.0210","volume":"41","author":"A Mukherjee","year":"2007","unstructured":"Mukherjee, A., & Hansen, M. (2007). A dynamic stochastic model for the single airport ground holding problem. Transportation Science, 41(4), 444\u2013456.","journal-title":"Transportation Science"},{"key":"4740_CR37","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1109\/6979.994791","volume":"3","author":"L Pallottino","year":"2002","unstructured":"Pallottino, L., Feron, E. M., & Bicchi, A. (2002). Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Transactions on Intelligent Transportation Systems, 3, 3\u201311.","journal-title":"IEEE Transactions on Intelligent Transportation Systems"},{"issue":"2","key":"4740_CR38","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/j.ejor.2014.08.045","volume":"241","author":"C Peyronne","year":"2015","unstructured":"Peyronne, C., Conn, A. R., Mongeau, M., & Delahaye, D. (2015). Solving air traffic conflict problems via local continuous optimization. European Journal of Operational Research, 241(2), 502\u2013512.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4740_CR39","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10479-011-0837-z","volume":"203","author":"HD Sherali","year":"2013","unstructured":"Sherali, H. D., & Hill, J. M. (2013). Configuration of airspace sectors for balancing air traffic controller workload. Annals of Operations Research, 203(1), 3\u201331.","journal-title":"Annals of Operations Research"},{"key":"4740_CR40","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.trc.2014.02.021","volume":"45","author":"G S\u00f6lveling","year":"2014","unstructured":"S\u00f6lveling, G., & Clarke, J.-P. (2014). Scheduling of airport runway operations using stochastic branch and bound methods. Transportation Research Part C: Emerging Technologies, 45, 119\u2013137.","journal-title":"Transportation Research Part C: Emerging Technologies"},{"key":"4740_CR41","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/978-1-4614-1608-1_7","volume-title":"Quantitative problem solving methods in the airline industry: A modeling methodology handbook","author":"TWM Vossen","year":"2012","unstructured":"Vossen, T. W. M., Hoffman, R., & Mukherjee, A. (2012). Air traffic flow management. In C. Barnhart & B. Smith (Eds.), Quantitative problem solving methods in the airline industry: A modeling methodology handbook (pp. 385\u2013453). US: Springer."},{"key":"4740_CR42","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/J.DSS.2017.02.005","volume":"96","author":"X Zhang","year":"2017","unstructured":"Zhang, X., & Mahadevan, S. (2017). Aircraft re-routing optimization and performance assessment under uncertainty. Decision Support Systems, 96, 67\u201382. https:\/\/doi.org\/10.1016\/J.DSS.2017.02.005.","journal-title":"Decision Support Systems"},{"issue":"9","key":"4740_CR43","doi-asserted-by":"publisher","first-page":"3421","DOI":"10.1109\/TITS.2018.2874235","volume":"20","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y., Su, R., Sandamali, G. G. N., Zhang, Y., Cassandras, C. G., & Xie, L. (2018). A hierarchical heuristic approach for solving air traffic scheduling and routing problem with a novel air traffic model. IEEE Transactions on Intelligent Transportation Systems, 20(9), 3421\u20133434.","journal-title":"IEEE Transactions on Intelligent Transportation Systems"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04740-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04740-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04740-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T19:08:32Z","timestamp":1674673712000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04740-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,14]]},"references-count":43,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["4740"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04740-1","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,14]]},"assertion":[{"value":"14 April 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No potential competing interest was reported by the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}