{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T17:17:17Z","timestamp":1779902237898,"version":"3.53.1"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"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>Today, over 80% of global trade is seaborne. In a world of global supply chains and complex industrial development processes, seaports and port operators play an integral role of utmost importance and act as an incentive to the development of the marine economy and particularly, the national economy in general. Most importantly, the supply chain and demand shocks of Covid-19 on container ports and the container shipping industry have intensified competition among terminal operators. Thus, it is imperative that managers evaluate competitiveness by measuring their past and current performance efficiency indexes. In so doing, we present a hybrid data envelopment analysis (DEA) model that combines the DEA Malmquist method and the epsilon-based measure (EBM) for the first time to address the issue of performance evaluation of seaport terminal operators. The applicability of the proposed hybrid approach is illustrated with a case study of the top 14 seaport companies in Vietnam. First, the Malmquist model is used to assess the total productivity growth rates of the companies, and its decomposition into technical efficiency change (catch-up) and technological investment (frontier-shift). Second, the EBM model is used to calculate the efficiency and inefficiency score of each company. Besides indicating the best-performing companies from certain aspects during the research period (2015\u20132020), the results reflect that the gap of applying the EBM method in the field of the maritime industry was successfully addressed, and together with the Malmquist model, the integrated framework can be an effective and equitable evaluation model for any area. Furthermore, the managerial implication provides a useful guideline for practitioners in the maritime sector in improving their operational efficacy and helps customers in selecting the best seaport companies in the outsourcing strategy.<\/jats:p>","DOI":"10.3390\/axioms10020048","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T10:24:33Z","timestamp":1617186273000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Efficiency Assessment of Seaport Terminal Operators Using DEA Malmquist and Epsilon-Based Measure Models"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2374-3830","authenticated-orcid":false,"given":"Chia-Nan","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8982-3254","authenticated-orcid":false,"given":"Ngoc-Ai-Thy","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7185-6557","authenticated-orcid":false,"given":"Hsin-Pin","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Marketing and Distribution Management, National Kaohsiung University of Science and Technology, Kaohsiung 81157, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8874-0836","authenticated-orcid":false,"given":"Hsien-Pin","family":"Hsu","sequence":"additional","affiliation":[{"name":"Department of Supply Chain Management, National Kaohsiung University of Science and Technology, Kaohsiung 81164, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8559-0868","authenticated-orcid":false,"given":"Thanh-Tuan","family":"Dang","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan"},{"name":"Department of Logistics and Supply Chain Management, Hong Bang International University, Ho Chi Minh 723000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"ref_1","unstructured":"UNCTAD (2021, February 20). Review of Maritime Transport 2018. Available online: https:\/\/unctad.org\/webflyer\/review-maritime-transport-2018."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.jtrangeo.2010.03.008","article-title":"Functions and actors of inland ports: European and North American dynamics","volume":"18","author":"Rodrigue","year":"2010","journal-title":"J. Transp. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Nhieu, N.-L., Chung, Y.-C., and Pham, H.-T. (2021). Multi-objective optimization models for sustainable perishable intermodal multi-product networks with delivery time window. Mathematics, 9.","DOI":"10.3390\/math9040379"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Dang, T.-T., Le, T.Q., and Kewcharoenwong, P. (2020). Transportation optimization models for intermodal networks with fuzzy node capacity, detour factor, and vehicle utilization constraints. Mathematics, 8.","DOI":"10.3390\/math8122109"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Karam, A., Eltawil, A., Hegner, B., and Reinau, K. (2020). Energy-efficient and integrated allocation of berths, quay cranes, and internal trucks in container terminals. Sustainability, 12.","DOI":"10.3390\/su12083202"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.ajsl.2016.12.003","article-title":"Service quality evaluation and ranking of container terminal operators","volume":"32","author":"Sayareh","year":"2016","journal-title":"Asian, J. Shipp. Logist."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.ajsl.2018.06.010","article-title":"Service quality evaluation and ranking of container terminal operators through hybrid multi-criteria decision making methods","volume":"34","author":"Hemalatha","year":"2018","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pham, T.Y., and Yeo, G.T. (2019). Evaluation of transshipment container terminals\u2019 service quality in Vietnam: From the shipping com-panies\u2019 perspective. Sustainability, 11.","DOI":"10.3390\/su11051503"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1057\/mel.2013.14","article-title":"Key factors of seaport competitiveness based on the stakeholder perspective: An Analytic Hierarchy Process (AHP) model","volume":"15","author":"Ferreira","year":"2013","journal-title":"Marit. Econ. Logist."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.ajsl.2015.09.003","article-title":"Participation of private investors in container terminal operation: Influence of global terminal operators","volume":"31","author":"Heejung","year":"2015","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.ajsl.2016.01.002","article-title":"An analysis of port service quality and customer satisfaction: The case of Korean container ports","volume":"31","author":"Yeo","year":"2015","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12544-015-0187-z","article-title":"Evaluating Iberian seaport competitiveness using an alternative DEA approach","volume":"8","year":"2016","journal-title":"Eur. Transp. Res. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1057\/s41278-017-0069-5","article-title":"An integrated terminal operating system for enhancing the efficiency of seaport terminal operators","volume":"19","author":"Min","year":"2017","journal-title":"Marit. Econ. Logist."},{"key":"ref_14","unstructured":"Statista (2021, February 20). Maritime Industry in Vietnam. Available online: https:\/\/www.statista.com\/topics\/5936\/maritime-industry-in-vietnam\/."},{"key":"ref_15","unstructured":"Statista (2021, February 20). Leading Sea Ports in Vietnam in 2018. Available online: https:\/\/www.statista.com\/statistics\/1045072\/vietnam-leading-sea-ports-by-throughput\/#:~:text=Vietnam%20has%20320%20ports%20of,in%20Ho%20Chi%20Minh%20City."},{"key":"ref_16","unstructured":"Tan Cang Logistics, and Stevedoring JSC (2021, February 20). TCL\u2014Sustainable Development. Available online: http:\/\/tancanglogistics.com\/en\/introduction\/Pages\/tcl-sustainable-development-140420170403.aspx."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1016\/j.ejor.2010.07.014","article-title":"An epsilon-based measure of efficiency in DEA\u2014A third pole of technical efficiency","volume":"207","author":"Tone","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s41072-018-0027-0","article-title":"The impacts of port infrastructure and logistics performance on economic growth: The mediating role of seaborne trade","volume":"3","author":"Munim","year":"2018","journal-title":"J. Shipp. Trade"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Dong, G., Zhu, J., Li, J., Wang, H., and Gajpal, Y. (2019). Evaluating the environmental performance and operational efficiency of container ports: An application to the maritime silk road. Int. J. Environ. Res. Public Health, 16.","DOI":"10.3390\/ijerph16122226"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sa\u0142abun, W., W\u0105tr\u00f3bski, J., and Shekhovtsov, A. (2020). Are MCDA methods benchmarkable? A comparative study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II methods. Symmetry, 12.","DOI":"10.3390\/sym12091549"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3730","DOI":"10.1016\/j.procs.2020.09.014","article-title":"A comparative case study of the VIKOR and TOPSIS rankings similarity","volume":"176","author":"Shekhovtsov","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kizielewicz, B., W\u0105tr\u00f3bski, J., and Sa\u0142abun, W. (2020). Identification of relevant criteria set in the MCDA process\u2014Wind farm location case study. Energies, 13.","DOI":"10.3390\/en13246548"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Shekhovtsov, A., Kozlov, V., Nosov, V., and Sa\u0142abun, W. (2020). Efficiency of methods for determining the relevance of criteria in sus-tainable transport problems: A comparative case study. Sustainability, 12.","DOI":"10.3390\/su12197915"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/0377-2217(78)90138-8","article-title":"Measuring the efficiency of decision making units","volume":"2","author":"Charnes","year":"1978","journal-title":"Eur. J. Oper. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1057\/palgrave.mel.9100163","article-title":"A Benchmark analysis of Italian seaports using data envelopment analysis","volume":"8","author":"Barros","year":"2006","journal-title":"Marit. Econ. Logist."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.ajsl.2015.06.004","article-title":"The relative efficiency of container terminals in small and medium-sized ports in China","volume":"31","author":"Ding","year":"2015","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.cstp.2020.01.002","article-title":"Port performance in Brazil: A case study using data envelopment analysis","volume":"8","year":"2020","journal-title":"Case Stud. Transp. Policy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"120979","DOI":"10.1016\/j.jclepro.2020.120979","article-title":"Examining eco-efficiency in the port sector via non-radial data envelopment analysis and the response based procedure for detecting unit segments","volume":"259","author":"Quintano","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1108\/09600030810875373","article-title":"Evaluating the comparative efficiency of Chinese third-party logistics providers using data envelopment analysis","volume":"38","author":"Zhou","year":"2008","journal-title":"Int. J. Phys. Distrib. Logist. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4822","DOI":"10.1080\/00207543.2012.657969","article-title":"A logistics provider evaluation and selection methodology based on AHP, DEA and linear programming integration","volume":"50","author":"Falsini","year":"2012","journal-title":"Int. J. Prod. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.ajsl.2016.01.005","article-title":"The efficiency and productivity analysis of large logistics providers services in Korea","volume":"31","author":"Park","year":"2015","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ijpe.2007.05.019","article-title":"Evaluating the efficiency of 3PL logistics operations","volume":"113","author":"Hamdan","year":"2008","journal-title":"Int. J. Prod. Econ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.marpol.2018.10.028","article-title":"Measuring marine environmental efficiency of a cruise shipping company considering corporate social responsibility","volume":"99","author":"Wang","year":"2019","journal-title":"Mar. Policy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2307\/3440861","article-title":"The Malmquist Total Factor Productivity Index","volume":"98","author":"Bjurek","year":"1996","journal-title":"Scand. J. Econ."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Dang, T.-T., Tibo, H., and Duong, D.-H. (2021). Assessing renewable energy production capabilities using DEA window and fuzzy TOPSIS model. Symmetry, 13.","DOI":"10.3390\/sym13020334"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Dang, T.-T., Nguyen, N.-A.-T., and Le, T.-T.-H. (2020). Supporting better decision-making: A combined grey model and data envelopment analysis for efficiency evaluation in e-commerce marketplaces. Sustainability, 12.","DOI":"10.3390\/su122410385"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/S0377-2217(99)00407-5","article-title":"A slacks-based measure of efficiency in data envelopment analysis","volume":"130","author":"Tone","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Nguyen, T.-L., and Dang, T.-T. (2021). Analyzing operational efficiency in real estate companies: An application of GM (1,1) and DEA malmquist model. Mathematics, 9.","DOI":"10.3390\/math9030202"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.cie.2013.07.016","article-title":"A new network epsilon-based DEA model for supply chain performance evaluation","volume":"66","author":"Tavana","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"119354","DOI":"10.1016\/j.energy.2020.119354","article-title":"Airline energy efficiency measures based on an epsilon-based Range-Adjusted Measure model","volume":"217","author":"Cui","year":"2021","journal-title":"Energy"},{"key":"ref_41","unstructured":"IET Stock (2021, February 20). Vietstock Market. Available online: https:\/\/finance.vietstock.vn\/VNM\/tai-chinh.htm."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Barykin, S., Kapustina, I., Kirillova, T., Yadykin, V., and Konnikov, Y. (2020). Economics of digital ecosystems. J. Open Innov. Technol. Mark. Complex., 6.","DOI":"10.3390\/joitmc6040124"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Barykin, S.Y., Kapustina, I.V., Sergeev, S.M., and Yadykin, V.K. (2020). Algorithmic foundations of economic and mathematical modeling of network logistics processes. J. Open Innov. Technol. Mark. Complex., 6.","DOI":"10.3390\/joitmc6040189"},{"key":"ref_44","unstructured":"(2021, March 22). Logistics Vietnam in 2021. Available online: https:\/\/www.bsc.com.vn\/tin-tuc\/tin-chi-tiet\/747986-ssi-research-trien-vong-nganh-cang-bien-va-logistics-nam-2021-ky-vong-phuc-hoi-toan-cau."},{"key":"ref_45","unstructured":"Raconteur (2021, March 22). How Technology Is Creating the Digital Ports of the Future. Available online: https:\/\/www.raconteur.net\/technology\/technology-digital-port\/."},{"key":"ref_46","unstructured":"WorkBoat (2021, February 20). Maritime Industry Plays Key Role in Covid-19 Response. Available online: https:\/\/www.workboat.com\/coastal-inland-waterways\/maritime-industry-plays-key-role-in-covid-19-response."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Wang, C.-N., Dang, T.-T., and Nguyen, N.-A.-T. (2021). Outsourcing reverse logistics for e-commerce retailers: A two-stage fuzzy optimization approach. Axioms, 10.","DOI":"10.3390\/axioms10010034"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Krzhizhanovskaya, V.V., Z\u00e1vodszky, G., Lees, M.H., Dongarra, J.J., Sloot, P.M.A., Brissos, S., and Teixeira, J. (2020). A new coefficient of rankings similarity in decision-making problems. Computational Science\u2014ICCS 2020, Proceedings of the 20th International Conference, Amsterdam, The Netherlands, 3\u20135 June 2020, Springer International Publishing.","DOI":"10.1007\/978-3-030-50436-6"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:55:50Z","timestamp":1760363750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,31]]},"references-count":48,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020048"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020048","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,31]]}}}