{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T18:57:00Z","timestamp":1788375420832,"version":"build-2803163510"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,12,11]],"date-time":"2019-12-11T00:00:00Z","timestamp":1576022400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,12,11]],"date-time":"2019-12-11T00:00:00Z","timestamp":1576022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10479-019-03499-2","type":"journal-article","created":{"date-parts":[[2019,12,11]],"date-time":"2019-12-11T13:05:46Z","timestamp":1576069546000},"page":"1455-1476","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal scale sizes in input\u2013output allocative data envelopment analysis models"],"prefix":"10.1007","volume":"315","author":[{"given":"Hajar","family":"Haghighatpisheh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sohrab","family":"Kordrostami","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4160-8509","authenticated-orcid":false,"given":"Alireza","family":"Amirteimoori","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Farhad Hosseinzadeh","family":"Lotfi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,12,11]]},"reference":[{"key":"3499_CR1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1051\/ro\/2011103","volume":"45","author":"A Amirteimoori","year":"2011","unstructured":"Amirteimoori, A., & Emrouznejad, A. (2011). Flexible measures in production process: A DEA-based approach. RAIRO Operations Research, 45, 63\u201374.","journal-title":"RAIRO Operations Research"},{"key":"3499_CR2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.cie.2016.10.010","volume":"103","author":"Q An","year":"2017","unstructured":"An, Q., Yang, M., Chu, J., Jie, Wu, & Zhu, Q. (2017). Efficiency evaluation of an interactive system by data envelopment analysis approach. Computers & Industrial Engineering, 103, 17\u201325.","journal-title":"Computers & Industrial Engineering"},{"key":"3499_CR3","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.cie.2018.04.043","volume":"120","author":"S Assani","year":"2018","unstructured":"Assani, S., Jiang, J., Cao, R., & Yang, F. (2018). Most productive scale size decomposition for multi-stage systems in data envelopment analysis. Computers & Industrial Engineering, 120, 279\u2013287.","journal-title":"Computers & Industrial Engineering"},{"key":"3499_CR4","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0377-2217(84)90006-7","volume":"17","author":"RD Banker","year":"1984","unstructured":"Banker, R. D. (1984). Estimating most productive scale size using data envelopment analysis. European Journal of Operational Research, 17, 35\u201344.","journal-title":"European Journal of Operational Research"},{"key":"3499_CR5","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1287\/mnsc.30.9.1078","volume":"30","author":"RD Banker","year":"1984","unstructured":"Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078\u20131092.","journal-title":"Management Science"},{"key":"3499_CR6","first-page":"809","volume":"67","author":"WJ Baumol","year":"1977","unstructured":"Baumol, W. J. (1977). On the proper cost tests for natural monopoly in a multiproduct industry. American Economic Review, 67, 809\u2013822.","journal-title":"American Economic Review"},{"key":"3499_CR7","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.ejor.2014.09.062","volume":"242","author":"G Cesaroni","year":"2015","unstructured":"Cesaroni, G., & Giovannola, D. (2015). Average\u2013cost efficiency and optimal scale sizes in non-parametric analysis. European Journal of Operational Research, 242, 121\u2013133.","journal-title":"European Journal of Operational Research"},{"key":"3499_CR8","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1002\/nav.3800090303","volume":"9","author":"A Charnes","year":"1962","unstructured":"Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functions. Naval Research Logistics Quarterly, 9, 181\u2013186.","journal-title":"Naval Research Logistics Quarterly"},{"key":"3499_CR9","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/0377-2217(78)90138-8","volume":"2","author":"A Charnes","year":"1978","unstructured":"Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429\u2013444.","journal-title":"European Journal of Operational Research"},{"key":"3499_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/b105307","volume-title":"Handbook of data envelopment analysis","author":"WW Cooper","year":"2004","unstructured":"Cooper, W. W., Seiford, L. M., & Zhu, J. (2004). Handbook of data envelopment analysis. Norwell, MA: Kluwer Academic Publishers."},{"key":"3499_CR11","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.seps.2017.01.008","volume":"61","author":"A Emrouznejad","year":"2018","unstructured":"Emrouznejad, A., & Yang, G. (2018). A survey and analysis of the first 40\u00a0years of scholarly literature in DEA: 1978\u20132016. Socio-Economic Planning Sciences, 61, 4\u20138.","journal-title":"Socio-Economic Planning Sciences"},{"issue":"2","key":"3499_CR12","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/j.omega.2006.01.003","volume":"36","author":"F Erbetta","year":"2008","unstructured":"Erbetta, F., & Rappuoli, L. (2008). Optimal scale in the Italian gas distribution industry using data envelopment analysis. Omega, 36(2), 325\u2013336.","journal-title":"Omega"},{"issue":"3","key":"3499_CR13","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1016\/j.ejor.2015.07.061","volume":"248","author":"CY Lee","year":"2016","unstructured":"Lee, C. Y. (2016). Most productive scale size versus demand fulfillment: A solution to the capacity dilemma. European Journal of Operational Research, 248(3), 954\u2013962.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"3499_CR14","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/j.ejor.2012.01.048","volume":"220","author":"P Ouellette","year":"2012","unstructured":"Ouellette, P., Quesnel, J. P., & Vigeant, S. (2012). Measuring returns to scale in DEA models when the firm is regulated. European Journal of Operational Research, 220(2), 571\u2013576.","journal-title":"European Journal of Operational Research"},{"key":"3499_CR15","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1016\/j.ejor.2016.09.029","volume":"258","author":"VV Podinovski","year":"2017","unstructured":"Podinovski, V. V. (2017). Returns to scale in convex production technologies. European Journal of Operational Research, 258, 970\u2013982.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"3499_CR16","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/j.ejor.2016.05.065","volume":"255","author":"BK Sahoo","year":"2016","unstructured":"Sahoo, B. K., Khoveyni, M., Eslami, R., & Chaudhury, P. (2016). Returns to scale and most productive scale size in DEA with negative data. European Journal of Operational Research, 255(2), 545\u2013558.","journal-title":"European Journal of Operational Research"},{"key":"3499_CR17","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.cor.2017.06.017","volume":"98","author":"Q Zhu","year":"2018","unstructured":"Zhu, Q., Wu, J., & Song, M. (2018). Efficiency evaluation based on data envelopment analysis in the big data context. Computers & Operations Research, 98, 291\u2013300.","journal-title":"Computers & Operations Research"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-019-03499-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-019-03499-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-019-03499-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T11:17:41Z","timestamp":1660303061000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-019-03499-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,11]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["3499"],"URL":"https:\/\/doi.org\/10.1007\/s10479-019-03499-2","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,11]]},"assertion":[{"value":"11 December 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}