{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:55Z","timestamp":1760144575998,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T00:00:00Z","timestamp":1714521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We present a two-country model (North and South) that describes the phenomenon of offshoring and reshoring. The model is a continuous time-controlled Markov chain with binary states. The main trade-off involves production costs and transaction costs between one country and another. In the first part of this paper, we identify the key parameters of the model: the difference in unit production costs between the two countries considered, the marginal cost of transitioning between countries, and the incentive paid by the North country to all companies that have not relocated at the end of the planning interval. The final goal of our paper is to understand how national tax incentives can influence this process.<\/jats:p>","DOI":"10.3390\/axioms13050300","type":"journal-article","created":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T08:59:39Z","timestamp":1714553979000},"page":"300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Binary-State Continuous-Time Markov Chain Model for Offshoring and Reshoring"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8610-9749","authenticated-orcid":false,"given":"Chiara","family":"Brambilla","sequence":"first","affiliation":[{"name":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, 35121 Padova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4227-2330","authenticated-orcid":false,"given":"Luca","family":"Grosset","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, 35121 Padova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5678-9379","authenticated-orcid":false,"given":"Elena","family":"Sartori","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padova, 35121 Padova, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s10290-012-0139-9","article-title":"Offshoring, domestic outsourcing and productivity: Evidence for a number of European countries","volume":"149","year":"2013","journal-title":"Rev. World Econ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jom.2007.02.012","article-title":"History of offshoring knowledge services","volume":"26","author":"Metters","year":"2008","journal-title":"J. Oper. Manag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10479-023-05346-x","article-title":"Offshoring or reshoring: The impact of tax regulations on operations strategies","volume":"326","author":"Wang","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.pursup.2014.01.004","article-title":"When manufacturing moves back: Concepts and questions","volume":"20","author":"Fratocchi","year":"2014","journal-title":"J. Purch. Supply Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"050250","DOI":"10.1051\/e3sconf\/202447105020","article-title":"The new era of American manufacturing: Evaluating the risks and rewards of reshoring","volume":"471","author":"Kudrenko","year":"2024","journal-title":"E3S Web Conf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s12063-016-0116-x","article-title":"Reshoring: A strategic renewal of luxury clothing supply chains","volume":"9","author":"Robinson","year":"2016","journal-title":"Oper. Manag. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/00396338.2024.2309078","article-title":"The Green Transition and European Industry","volume":"66","author":"Crawford","year":"2024","journal-title":"Survival"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/rode.12382","article-title":"A North-South model of outsourcing and growth","volume":"22","author":"Saito","year":"2018","journal-title":"Rev. Dev. Econ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"20130405","DOI":"10.1098\/rsta.2013.0405","article-title":"Socio-economic applications of finite state mean field games","volume":"372","author":"Gomes","year":"2014","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s00245-013-9202-8","article-title":"Continuous Time Finite State Mean Field Games","volume":"68","author":"Gomes","year":"2013","journal-title":"Appl. Math. Optim."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"139","DOI":"10.37394\/23206.2023.22.17","article-title":"Continuous-Time Markov Decision Problems with Binary State","volume":"22","author":"Brambilla","year":"2023","journal-title":"WSEAS Trans. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1137\/18M1222454","article-title":"On the Convergence Problem in Mean Field Games: A Two State Model without Uniqueness","volume":"57","author":"Cecchin","year":"2019","journal-title":"SIAM J. Control Optim."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Huang, J.J., and Chen, C.Y. (2024). Integrating the Coupled Markov Chain and Fuzzy Analytic Hierarchy Process Model for Dynamic Decision Making. Axioms, 13.","DOI":"10.3390\/axioms13020095"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1007\/s13235-019-00299-y","article-title":"Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions","volume":"9","author":"Sartori","year":"2019","journal-title":"Dyn. Games Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, Y., Xu, X., and Zhang, J. (2022). Optimal Investment Strategy for DC Pension Plan with Deposit Loan Spread under the CEV Model. Axioms, 11.","DOI":"10.3390\/axioms11080382"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Br\u00e9maud, P. (2020). Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues, Springer Nature.","DOI":"10.1007\/978-3-030-45982-6"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1287\/msom.2016.0604","article-title":"Is Reshoring Better Than Offshoring? The Effect of Offshore Supply Dependence","volume":"19","author":"Chen","year":"2017","journal-title":"Manuf. Serv. Oper. Manag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102500","DOI":"10.1016\/j.omega.2021.102500","article-title":"Impact of tariffs and production cost on a multinational firm\u2019s incentive for backshoring under competition","volume":"105","author":"Yang","year":"2021","journal-title":"Omega"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.bushor.2013.08.007","article-title":"Why domestic outsourcing is leading America\u2019s reemergence in global manufacturing","volume":"57","author":"Pearce","year":"2014","journal-title":"Bus. Horiz."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Miao, L., Li, S., Wu, X., and Liu, B. (2024). Mean-Field Stackelberg Game-Based Security Defense and Resource Optimization in Edge Computing. Appl. Sci., 14.","DOI":"10.3390\/app14093538"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/5\/300\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:38:12Z","timestamp":1760107092000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/5\/300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,1]]},"references-count":20,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["axioms13050300"],"URL":"https:\/\/doi.org\/10.3390\/axioms13050300","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,5,1]]}}}