{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:46:57Z","timestamp":1762508817709,"version":"3.37.3"},"reference-count":46,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:00:00Z","timestamp":1657497600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009038","name":"University of Guilan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2022,7,11]]},"abstract":"<jats:p>The two-stage data envelopment analysis models are among the widely used mathematical programming approaches to evaluate the performance of two-stage structures. In this paper, a two-stage structure with shared inputs and feedback is studied. To reduce undesirable outputs, an additive slack-based measure model is proposed to evaluate the stages and overall efficiencies, while undesirable outputs are weakly disposable. As it does not require determining the weights for combining stages\u2019 efficiencies, all Pareto optimal stages\u2019 efficiencies can be gained. In addition, the proposed approach can identify desirable outputs from undesirable outputs, thereby avoiding the need for weighting. This advantage from the aspect of multiobjective programming helps internal evaluation of the network model to match priorities of managers. The proposed nonlinear model is reformulated as a second-order cone program, which is a convex optimization problem that can be solved to global optimality. This is a computational improvement over the parametric models in the literature. Furthermore, the proposed model is applied for country-wise and area-wise performance evaluations of a real industrial application dataset in mainland China. Results show that the efficiency of the overall system relies between the efficiencies of the two stages and for all DMUs, the first stage\u2019s efficiency scores are always higher than the second stage ones in both evaluations. Also, the Pearson correlation coefficient test results show that the overall efficiency is more correlated with the waste disposal stage. Finally, to show the effect of the decision maker\u2019s preference, a detailed sensitivity analysis is performed.<\/jats:p>","DOI":"10.1155\/2022\/7596736","type":"journal-article","created":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T20:50:08Z","timestamp":1657572608000},"page":"1-14","source":"Crossref","is-referenced-by-count":5,"title":["Additive Slack-Based Measure for a Two-Stage Structure with Shared Inputs and Undesirable Feedback"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0430-3063","authenticated-orcid":true,"given":"M.","family":"Salahi","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran"},{"name":"Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, P.O. 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