{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T03:53:21Z","timestamp":1774065201359,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T00:00:00Z","timestamp":1708646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministry of Science and Innovation","award":["PID2019-105824GB-I00"],"award-info":[{"award-number":["PID2019-105824GB-I00"]}]},{"name":"Spanish Ministry of Science and Innovation","award":["PID2021-124981NB-I00"],"award-info":[{"award-number":["PID2021-124981NB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a novel slacks-based interval DEA approach that computes interval targets, slacks, and crisp inefficiency scores. It uses interval arithmetic and requires solving a mixed-integer linear program. The corresponding super-efficiency formulation to discriminate among the efficient units is also presented. We also provide a case study of its application to sustainable tourism in the Mediterranean region, assessing the sustainable tourism efficiency of twelve Mediterranean regions to validate the proposed approach. The inputs and outputs cover the three sustainability dimensions and include GHG emissions as an undesirable output. Three regions were found to be inefficient, and the corresponding inputs and output improvements were computed. A total rank of the regions was also obtained using the super-efficiency model.<\/jats:p>","DOI":"10.3390\/axioms13030144","type":"journal-article","created":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T10:47:30Z","timestamp":1708685250000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel Slacks-Based Interval DEA Model and Application"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0290-6477","authenticated-orcid":false,"given":"Manuel","family":"Arana-Jim\u00e9nez","sequence":"first","affiliation":[{"name":"Department of Statistics and Operational Research, University of Cadiz, 11003 Cadiz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0041-4559","authenticated-orcid":false,"given":"Julio","family":"Lozano-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operational Research, University of Cadiz, 11003 Cadiz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0829-4157","authenticated-orcid":false,"given":"M. Carmen","family":"S\u00e1nchez-Gil","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operational Research, University of Cadiz, 11003 Cadiz, Spain"}]},{"given":"Atefeh","family":"Younesi","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operational Research, University of Cadiz, 11003 Cadiz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0401-3584","authenticated-orcid":false,"given":"Sebasti\u00e1n","family":"Lozano","sequence":"additional","affiliation":[{"name":"Department of Industrial Management, University of Seville, 41004 Sevilla, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhu, J. (2002). Quantitative Models for Performance Evaluation and Benchmarking, Kluwer Academic.","DOI":"10.1007\/978-1-4757-4246-6_7"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cooper, W.W., Seiford, L.M., and Zhu, J. (2004). Handbook on Data Envelopment Analysis, Kluwer Academic.","DOI":"10.1007\/b105307"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/S0377-2217(01)00200-4","article-title":"Data envelopment analysis with imprecise data","volume":"140","author":"Despotis","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S0377-2217(01)00392-7","article-title":"Imprecise data envelopment analysis (IDEA): A review and improvement with an application","volume":"144","author":"Zhu","year":"2003","journal-title":"Eur. J. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1016\/S0305-0548(01)00049-1","article-title":"Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis)","volume":"29","author":"Lee","year":"2002","journal-title":"Comput. Oper. Res."},{"key":"ref_6","first-page":"463","article-title":"Sensitivity and stability analysis in DEA with interval data","volume":"156","author":"Jahanshahloo","year":"2004","journal-title":"Appl. Math. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.cie.2014.10.019","article-title":"Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers","volume":"79","author":"Azizi","year":"2015","journal-title":"Comput. Ind. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.apm.2010.05.019","article-title":"Ranking DMUs by ideal points with interval data in DEA","volume":"35","author":"Jahanshahloo","year":"2011","journal-title":"Appl. Math. Model."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10479-011-0988-y","article-title":"Qualitative and quantitative data envelopment analysis with interval data","volume":"195","author":"Inuiguchi","year":"2011","journal-title":"Ann. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2028","DOI":"10.1016\/j.apm.2013.10.027","article-title":"Interval data without sign restrictions in DEA","volume":"38","author":"Emrouznejad","year":"2014","journal-title":"Appl. Math. Model."},{"key":"ref_11","first-page":"243","article-title":"Evaluating the performance and classifying the interval data in data envelopment analysis","volume":"9","author":"Kordrostami","year":"2014","journal-title":"Int. J. Manag. Sci. Eng. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1142\/S0219622015500248","article-title":"Modeling Centralized Resources Allocation and Target Setting in Imprecise Data Envelopment Analysis","volume":"14","author":"Beigi","year":"2015","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2991\/ijcis.d.201019.001","article-title":"An Extended Three-Stage DEA Model with Interval Inputs and Outputs","volume":"14","author":"Cheng","year":"2020","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1051\/ro\/2022056","article-title":"A ranking framework based on interval self and cross-efficiencies in a two-stage DEA system","volume":"56","author":"Kremantzis","year":"2022","journal-title":"RAIRO\u2014Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.cor.2014.03.002","article-title":"A new fuzzy DEA model for evaluation of efficiency and effectiveness of suppliers in sustainable supply chain management context","volume":"54","author":"Azadi","year":"2015","journal-title":"Comput. Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.fss.2004.12.011","article-title":"Interval efficiency assessment using data envelopment analysis","volume":"153","author":"Wang","year":"2005","journal-title":"Fuzzy Sets Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3237","DOI":"10.1016\/j.apm.2008.10.030","article-title":"A generalized model for data envelopment analysis with interval data","volume":"33","author":"Jahanshahloo","year":"2009","journal-title":"Appl. Math. Model."},{"key":"ref_18","first-page":"162","article-title":"Productivity of steam power-plants using uncertain DEA-based Malmquist index in the presence of undesirable outputs","volume":"10","year":"2018","journal-title":"Int. J. Inf. Decis. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1287\/mnsc.39.10.1261","article-title":"A Procedure for Ranking Efficient Units in Data Envelopment Analysis","volume":"39","author":"Andersen","year":"1993","journal-title":"Manag. Sci."},{"key":"ref_20","unstructured":"Zhu, J. (2014). International Series in Operations Research & Management Science, Springer International Publishing."},{"key":"ref_21","first-page":"174","article-title":"Infeasibility Of Super-Efficiency Data Envelopment Analysis Models","volume":"37","author":"Seiford","year":"1999","journal-title":"INFOR Inf. Syst. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102728","DOI":"10.1016\/j.ipm.2021.102728","article-title":"Super efficiency SBM-DEA and neural network for performance evaluation","volume":"58","author":"Zhong","year":"2021","journal-title":"Inf. Process. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Li, D., Zhai, Y., Tian, G., and Mendako, R.K. (2022). Tourism Eco-Efficiency and Influence Factors of Chinese Forest Parks under Carbon Peaking and Carbon Neutrality Target. Sustainability, 14.","DOI":"10.3390\/su142113979"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1016\/j.ejor.2022.04.024","article-title":"Random Forests and the measurement of super-efficiency in the context of Free Disposal Hull","volume":"304","author":"Esteve","year":"2023","journal-title":"Eur. J. Oper. Res."},{"key":"ref_25","first-page":"363","article-title":"Continuous models combining slacks-based measures of efficiency and super-efficiency","volume":"31","year":"2022","journal-title":"Cent. Eur. J. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/S0377-2217(01)00324-1","article-title":"A slacks-based measure of super-efficiency in data envelopment analysis","volume":"143","author":"Tone","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1111\/itor.12257","article-title":"Super SBI Dynamic Network DEA approach to measuring efficiency in the provision of public services","volume":"25","author":"Moreno","year":"2016","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.fss.2020.12.011","article-title":"Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model","volume":"422","author":"Younesi","year":"2021","journal-title":"Fuzzy Sets Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1080\/09669580208667183","article-title":"Sustainable Tourism: An Overview of the Concept and its Position in Relation to Conceptualisations of Tourism","volume":"10","author":"Hardy","year":"2002","journal-title":"J. Sustain. Tour."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Guo, Y., Jiang, J., and Li, S. (2019). A Sustainable Tourism Policy Research Review. Sustainability, 11.","DOI":"10.3390\/su11113187"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.tourman.2018.08.025","article-title":"Tourist arrivals, energy consumption and pollutant emissions in a developing economy\u2013implications for sustainable tourism","volume":"72","author":"Nepal","year":"2019","journal-title":"Tour. Manag."},{"key":"ref_32","first-page":"660","article-title":"Efficiency Analysis of Industrial Water Treatment in China Based on Two-stage Undesirable Fixed-sum Output DEA Model","volume":"9","author":"Ma","year":"2021","journal-title":"J. Syst. Sci. Inf."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, Y., Zhu, Z., and Zhuang, L. (2022). Exploring the Ecological Performance of China\u2019s Tourism Industry: A Three-Stage Undesirable SBM-DEA Approach with Carbon Footprint. Int. J. Environ. Res. Public Health, 19.","DOI":"10.3390\/ijerph192215367"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1080\/13683500.2019.1579174","article-title":"An approach to measuring sustainable tourism at the local level in Europe","volume":"23","author":"Navarro","year":"2020","journal-title":"Curr. Issues Tour."},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1287\/mnsc.30.9.1078","article-title":"Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis","volume":"30","author":"Banker","year":"1984","journal-title":"Manag. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","article-title":"Generalized Hukuhara differentiability of interval-valued functions and interval differential equations","volume":"71","author":"Stefanini","year":"2009","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1016\/j.fss.2009.06.009","article-title":"A generalization of Hukuhara difference and division for interval and fuzzy arithmetic","volume":"161","author":"Stefanini","year":"2010","journal-title":"Fuzzy Sets Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s10700-009-9061-6","article-title":"The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions","volume":"8","author":"Wu","year":"2009","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2018.04.009","article-title":"Karush\u2013Kuhn\u2013Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability","volume":"362","author":"Stefanini","year":"2019","journal-title":"Fuzzy Sets Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s11123-018-0534-x","article-title":"DEA target setting using lexicographic and endogenous directional distance function approaches","volume":"50","author":"Lozano","year":"2018","journal-title":"J. Product. Anal."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"734962","DOI":"10.1016\/j.aquaculture.2020.734962","article-title":"Efficiency data analysis in EU aquaculture production","volume":"520","author":"Lozano","year":"2020","journal-title":"Aquaculture"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1996","DOI":"10.1080\/01605682.2021.1967211","article-title":"Ranking decision making units based on the multi-directional efficiency measure","volume":"73","author":"Soltani","year":"2021","journal-title":"J. Oper. Res. Soc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1838","DOI":"10.1016\/j.jclepro.2008.02.008","article-title":"Envisioning sustainability three-dimensionally","volume":"16","author":"Lozano","year":"2008","journal-title":"J. Clean. Prod."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.1080\/09669582.2020.1775621","article-title":"A systematic scoping review of sustainable tourism indicators in relation to the sustainable development goals","volume":"31","author":"Rasoolimanesh","year":"2020","journal-title":"J. Sustain. Tour."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Huang, C.W., Ng, E., Fang, W.T., and Lo, L. (2022). Assessing the Effectiveness of Environmental Training for Diving Tourists Using the DEA Model. Sustainability, 14.","DOI":"10.3390\/su14031639"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2022\/5435076","article-title":"Application of Two-Stage Network Super-Efficiency DEA to Efficiency Analysis of Chinese Commercial Banks","volume":"2022","author":"Li","year":"2022","journal-title":"J. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1111\/rsp3.12420","article-title":"Mapping destination competitiveness in Indonesia\u2019s Nusa Tenggara Timur (NTT) province: A Malmquist\u2013data envelopment analysis approach","volume":"13","author":"Bire","year":"2021","journal-title":"Reg. Sci. Policy Pract."},{"key":"ref_49","first-page":"346","article-title":"An approach to the travel and tourism competitiveness index in the Caribbean region","volume":"23","author":"Rubio","year":"2020","journal-title":"Int. J. Tour. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/s12597-022-00619-8","article-title":"Estimating the hospitality efficiency in Mexico using Data Envelopment Analysis","volume":"60","author":"Flegl","year":"2022","journal-title":"OPSEARCH"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ijhm.2018.03.015","article-title":"Analyzing hotel efficiency from a regional perspective: The role of environmental determinants","volume":"75","year":"2018","journal-title":"Int. J. Hosp. Manag."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"259","DOI":"10.5709\/ce.1897-9254.214","article-title":"Two-Stage Data Envelopment Analysis of Spanish Regions: Efficiency Determinants and Stability Analysis","volume":"10","year":"2016","journal-title":"Contemp. Econ."},{"key":"ref_53","first-page":"31","article-title":"Measuring Tourism Efficiency of European Countries by Using Data Envelopment Analysis","volume":"13","year":"2017","journal-title":"Eur. Sci. Journal, ESJ"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"33","DOI":"10.4018\/IJVCSN.2018010103","article-title":"Sustainability Analysis of Tourism in India: Data Envelopment Analysis Approach","volume":"10","author":"Kumar","year":"2018","journal-title":"Int. J. Virtual Communities Soc. Netw."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Radovanov, B., Dudic, B., Gregus, M., Marcikic Horvat, A., and Karovic, V. (2020). Using a Two-Stage DEA Model to Measure Tourism Potentials of EU Countries and Western Balkan Countries: An Approach to Sustainable Development. Sustainability, 12.","DOI":"10.3390\/su12124903"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Wang, R., Xia, B., Dong, S., Li, Y., Li, Z., Ba, D., and Zhang, W. (2020). Research on the Spatial Differentiation and Driving Forces of Eco-Efficiency of Regional Tourism in China. Sustainability, 13.","DOI":"10.3390\/su13010280"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Gao, J., Shao, C., and Chen, S. (2022). Evolution and Driving Factors of the Spatiotemporal Pattern of Tourism Efficiency at the Provincial Level in China Based on SBM\u2013DEA Model. Int. J. Environ. Res. Public Health, 19.","DOI":"10.3390\/ijerph191610118"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:03:55Z","timestamp":1760105035000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,23]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["axioms13030144"],"URL":"https:\/\/doi.org\/10.3390\/axioms13030144","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,23]]}}}