{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T17:48:03Z","timestamp":1784742483311,"version":"3.55.0"},"reference-count":48,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T00:00:00Z","timestamp":1563494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.<\/jats:p>","DOI":"10.3390\/a12070143","type":"journal-article","created":{"date-parts":[[2019,7,22]],"date-time":"2019-07-22T02:55:37Z","timestamp":1563764137000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Bi-Level Multi-Objective Production Planning Problem with Multi-Choice Parameters: A Fuzzy Goal Programming Algorithm"],"prefix":"10.3390","volume":"12","author":[{"given":"Murshid","family":"Kamal","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4158-2866","authenticated-orcid":false,"given":"Srikant","family":"Gupta","sequence":"additional","affiliation":[{"name":"Jaipuria Institute of Management, Jaipur 302022, Rajasthan, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prasenjit","family":"Chatterjee","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, MCKV Institute of Engineering, Howrah-711204, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8522-1942","authenticated-orcid":false,"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[{"name":"Department of logistics, Military academy, University of Defence, Belgrade 11000, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4452-5768","authenticated-orcid":false,"given":"Zeljko","family":"Stevic","sequence":"additional","affiliation":[{"name":"Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Doboj 71000, Bosnia and Herzegovina"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1287\/mnsc.30.8.1004","article-title":"Two-level linear programming","volume":"30","author":"Bialas","year":"1984","journal-title":"Manag. 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