{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T16:17:41Z","timestamp":1772641061767,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T00:00:00Z","timestamp":1712534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T00:00:00Z","timestamp":1712534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["Ciencia Frontera 87787"],"award-info":[{"award-number":["Ciencia Frontera 87787"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s10479-024-05937-2","type":"journal-article","created":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T23:10:07Z","timestamp":1712531407000},"page":"589-613","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semi-Markov control models for systems of large populations of interacting objects with possible unbounded costs: a mean field approach"],"prefix":"10.1007","volume":"358","author":[{"given":"M. Elena","family":"Mart\u00ednez-Manzanares","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3453-4508","authenticated-orcid":false,"given":"J. Adolfo","family":"Minj\u00e1rez-Sosa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"issue":"6","key":"5937_CR1","doi-asserted-by":"publisher","first-page":"3666","DOI":"10.1137\/18M1196479","volume":"57","author":"B Acciaio","year":"2019","unstructured":"Acciaio, B., Backhoff-Veraguas, J., & Carmona, R. (2019). Extended mean field control problems: Stochastic maximum principle and transport perspective. SIAM Journal on Control and Optimization, 57(6), 3666\u20133693.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"4","key":"5937_CR2","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1137\/S0363012900371083","volume":"40","author":"MA Rami","year":"2002","unstructured":"Rami, M. A., Moore, J. B., & Zhou, X. Y. (2002). Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM Journal on Control and Optimization, 40(4), 1296\u20131311.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"5937_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-8508-7","volume-title":"Mean field games and mean field type control theory","author":"A Bensoussan","year":"2013","unstructured":"Bensoussan, A., Frehse, J., & Yam, P. (2013). Mean field games and mean field type control theory (Vol. 101). Springer."},{"issue":"11","key":"5937_CR4","doi-asserted-by":"publisher","first-page":"3222","DOI":"10.1016\/j.automatica.2013.08.017","volume":"49","author":"R Elliott","year":"2013","unstructured":"Elliott, R., Li, X., & Ni, Y.-H. (2013). Discrete time mean-field stochastic linear-quadratic optimal control problems. Automatica, 49(11), 3222\u20133233.","journal-title":"Automatica"},{"issue":"1","key":"5937_CR5","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s10626-010-0094-3","volume":"21","author":"N Gast","year":"2011","unstructured":"Gast, N., & Gaujal, B. (2011). A mean field approach for optimization in discrete time. Discrete Event Dynamic Systems, 21(1), 63\u2013101.","journal-title":"Discrete Event Dynamic Systems"},{"issue":"9","key":"5937_CR6","doi-asserted-by":"publisher","first-page":"2266","DOI":"10.1109\/TAC.2012.2186176","volume":"57","author":"N Gast","year":"2012","unstructured":"Gast, N., Gaujal, B., & Le Boudec, J. (2012). Mean field for Markov decision processes: From discrete to continuous optimization. IEEE Transactions on Automatic Control, 57(9), 2266\u20132280.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"4","key":"5937_CR7","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s40304-014-0023-0","volume":"1","author":"M Hafayed","year":"2013","unstructured":"Hafayed, M. (2013). A mean-field necessary and sufficient conditions for optimal singular stochastic control. Communications in Mathematics and Statistics, 1(4), 417\u2013435.","journal-title":"Communications in Mathematics and Statistics"},{"issue":"1","key":"5937_CR8","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s00245-015-9312-6","volume":"74","author":"C Higuera-Chan","year":"2016","unstructured":"Higuera-Chan, C., Jasso-Fuentes, H., & Minj\u00e1rez-Sosa, J. (2016). Discrete-time control for systems of interacting objects with unknown random disturbance distributions: A mean field approach. Applied Mathematics & Optimization, 74(1), 197\u2013227.","journal-title":"Applied Mathematics & Optimization"},{"issue":"1","key":"5937_CR9","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3934\/jdg.2017004","volume":"4","author":"C Higuera-Chan","year":"2017","unstructured":"Higuera-Chan, C., Jasso-Fuentes, H., & Minj\u00e1rez-Sosa, J. (2017). Control systems of interacting objects modeled as a game against nature under a mean field approach. Journal of Dynamics & Games, 4(1), 59.","journal-title":"Journal of Dynamics & Games"},{"key":"5937_CR10","doi-asserted-by":"crossref","unstructured":"Le\u00a0Boudec, J., McDonald, D., & Mundinger, J. (2007). A generic mean field convergence result for systems of interacting objects. In: Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007), pp. 3\u201318. IEEE.","DOI":"10.1109\/QEST.2007.8"},{"key":"5937_CR11","unstructured":"Peyrard, N., & Sabbadin, R. (2006). Mean field approximation of the policy iteration algorithm for graph-based Markov decision processes. In: Proceedings of the 2006 Conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29\u2013September 1, 2006, Riva del Garda, Italy, pp. 595\u2013599."},{"issue":"2","key":"5937_CR12","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1002\/asjc.2306","volume":"23","author":"T Song","year":"2021","unstructured":"Song, T., & Liu, B. (2021). Discrete-time mean-field stochastic linear-quadratic optimal control problem with finite horizon. Asian Journal of Control, 23(2), 979\u2013989.","journal-title":"Asian Journal of Control"},{"key":"5937_CR13","volume-title":"Advances in probability and mathematical statistics","author":"CG Higuera-Chan","year":"2021","unstructured":"Higuera-Chan, C. G. (2021). Approximation and mean field control of systems of large populations. In D. Hernandez-Hernandez, F. Leonardi, R. H. Mena, & J. C. Pardo Millan (Eds.), Advances in probability and mathematical statistics. Springer."},{"issue":"3","key":"5937_CR14","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10626-021-00339-z","volume":"31","author":"M Mart\u00ednez-Manzanares","year":"2021","unstructured":"Mart\u00ednez-Manzanares, M., & Minj\u00e1rez-Sosa, J. (2021). A mean field absorbing control model for interacting objects systems. Discrete Event Dynamic Systems, 31(3), 349\u2013372.","journal-title":"Discrete Event Dynamic Systems"},{"key":"5937_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6746-2","volume-title":"Controlled Markov processes","author":"E Dynkin","year":"1979","unstructured":"Dynkin, E., & Yushkevich, A. (1979). Controlled Markov processes (Vol. 235). Springer."},{"key":"5937_CR16","volume-title":"Discrete-time Markov control processes: Basic optimality criteria","author":"O Hern\u00e1ndez-Lerma","year":"2012","unstructured":"Hern\u00e1ndez-Lerma, O., & Lasserre, J. B. (2012). Discrete-time Markov control processes: Basic optimality criteria (Vol. 30). Springer."},{"key":"5937_CR17","volume-title":"Adaptive Markov control processes","author":"O Hern\u00e1ndez-Lerma","year":"2012","unstructured":"Hern\u00e1ndez-Lerma, O. (2012). Adaptive Markov control processes (Vol. 79). Springer."},{"issue":"3","key":"5937_CR18","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s001860400406","volume":"61","author":"F Luque-V\u00e1squez","year":"2005","unstructured":"Luque-V\u00e1squez, F., & Minj\u00e1rez-Sosa, J. (2005). Semi-Markov control processes with unknown holding times distribution under a discounted criterion. Mathematical Methods of Operations Research, 61(3), 455\u2013468.","journal-title":"Mathematical Methods of Operations Research"},{"issue":"3","key":"5937_CR19","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10440-011-9605-y","volume":"114","author":"F Luque-V\u00e1squez","year":"2011","unstructured":"Luque-V\u00e1squez, F., Minj\u00e1rez-Sosa, J., & Carmen Rosas-Rosas, L. (2011). Semi-Markov control models with partially known holding times distribution: discounted and average criteria. Acta Applicandae Mathematicae, 114(3), 135\u2013156.","journal-title":"Acta Applicandae Mathematicae"},{"key":"5937_CR20","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.spl.2013.10.015","volume":"84","author":"F Luque-V\u00e1squez","year":"2014","unstructured":"Luque-V\u00e1squez, F., & Minj\u00e1rez-Sosa, J. A. (2014). A note on the $$\\sigma $$-compactness of sets of probability measures on metric spaces. Statistics & Probability Letters, 84, 212\u2013214.","journal-title":"Statistics & Probability Letters"},{"key":"5937_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4832-0022-4.50006-5","volume-title":"Probability measures on metric spaces","author":"K Parthasarathy","year":"1967","unstructured":"Parthasarathy, K. (1967). Probability measures on metric spaces. Academic Press."},{"key":"5937_CR22","volume-title":"Further topics on discrete-time Markov control processes","author":"O Hern\u00e1ndez-Lerma","year":"2012","unstructured":"Hern\u00e1ndez-Lerma, O., & Lasserre, J. B. (2012). Further topics on discrete-time Markov control processes (Vol. 42). Springer."},{"key":"5937_CR23","volume-title":"Markov decision processes: Discrete stochastic dynamic programming","author":"M Puterman","year":"2014","unstructured":"Puterman, M. (2014). Markov decision processes: Discrete stochastic dynamic programming. Wiley."},{"key":"5937_CR24","volume-title":"Probability and real analysis","author":"R Ash","year":"1972","unstructured":"Ash, R. (1972). Probability and real analysis. Wiley."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05937-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-024-05937-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05937-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T11:04:29Z","timestamp":1772622269000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-024-05937-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,8]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["5937"],"URL":"https:\/\/doi.org\/10.1007\/s10479-024-05937-2","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,8]]},"assertion":[{"value":"26 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Author M. Elena Mart\u00ednez-Manzanares declares that she has no Conflict of interest. Author J. Adolfo Minj\u00e1rez-Sosa declares that he has no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}