{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:40:38Z","timestamp":1777704038670,"version":"3.51.4"},"reference-count":22,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2017,8,24]],"date-time":"2017-08-24T00:00:00Z","timestamp":1503532800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,8,24]]},"abstract":"<jats:p>The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented.<\/jats:p>","DOI":"10.3233\/jifs-17086","type":"journal-article","created":{"date-parts":[[2017,8,25]],"date-time":"2017-08-25T13:30:12Z","timestamp":1503667812000},"page":"1687-1697","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Solution of a class of generalized assignment problem"],"prefix":"10.1177","volume":"33","author":[{"given":"Supriya","family":"Kar","sequence":"first","affiliation":[{"name":"Research Scholar, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur, West Bengal, India"}]},{"given":"Kajla","family":"Basu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur, West Bengal, India"}]},{"given":"Sathi","family":"Mukherjee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gobinda Prasad Mahavidyalaya, Amarkanan, Bankura, West Bengal, India"}]}],"member":"179","published-online":{"date-parts":[[2017,8,24]]},"reference":[{"issue":"1","key":"e_1_3_2_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01584319","article-title":"The alternating basis algorithm for the assignment problem","volume":"13","author":"Barr R.","year":"1977","unstructured":"BarrR., GloverF. and KlingmanD., The alternating basis algorithm for the assignment problem, Mathematical Programming 13(1) (1977), 1\u201313.","journal-title":"Mathematical Programming"},{"issue":"4","key":"e_1_3_2_3_2","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1287\/opre.28.4.969","article-title":"Solving the assignment problem by relaxation","volume":"28","author":"Hung M.S.","year":"1980","unstructured":"HungM.S. and RomW.O., Solving the assignment problem by relaxation, Operations Research 28(4) (1980), 969\u2013982.","journal-title":"Operations Research"},{"issue":"7","key":"e_1_3_2_4_2","first-page":"1717","article-title":"An improved algorithm for the bottleneck assignment problem","volume":"19","author":"Gafinkel R.S.","year":"1971","unstructured":"GafinkelR.S., An improved algorithm for the bottleneck assignment problem, Operations Research 19(7) (1971), 1717\u20131751.","journal-title":"Operations Research"},{"issue":"3","key":"e_1_3_2_5_2","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/0377-2217(93)90198-V","article-title":"A variation of the assignment problem","volume":"68","author":"Geetha S.","year":"1993","unstructured":"GeethaS. and NairK.P.K., A variation of the assignment problem, European Journal of Operational Research 68(3) (1993), 422\u2013426.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"e_1_3_2_6_2","first-page":"150","article-title":"Assignment problem with multiple attributes of crisp, fuzzy and linguistic type data","volume":"2","author":"Mukherjee S.","year":"2010","unstructured":"MukherjeeS. and BasuK., Assignment problem with multiple attributes of crisp, fuzzy and linguistic type data, International Journal of Optimization: Theory, Methods and Applications 2(2) (2010), 150\u2013159.","journal-title":"International Journal of Optimization: Theory, Methods and Applications"},{"key":"e_1_3_2_7_2","first-page":"119","article-title":"On a class of assignment problem","volume":"2","author":"Mukherjee S.","unstructured":"MukherjeeS. and BasuK., On a class of assignment problem, Journal of the Assam Academic of Mathematics 2, 119\u2013135.","journal-title":"Journal of the Assam Academic of Mathematics"},{"issue":"1","key":"e_1_3_2_8_2","first-page":"1","article-title":"Solving intuitionistic fuzzy assignment problem by using similarity measures and score functions","volume":"2","author":"Mukherjee S.","year":"2011","unstructured":"MukherjeeS. and BasuK., Solving intuitionistic fuzzy assignment problem by using similarity measures and score functions, International Journal of Pure and Applied Sciences and Technology 2(1) (2011), 1\u20138. ISSN 2229-6107.","journal-title":"International Journal of Pure and Applied Sciences and Technology"},{"key":"e_1_3_2_9_2","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.knosys.2011.09.007","article-title":"Solution of a class of intuitionistic fuzzy assignment problem by using similarity measures","volume":"27","author":"Mukherjee S.","year":"2012","unstructured":"MukherjeeS. and BasuK., Solution of a class of intuitionistic fuzzy assignment problem by using similarity measures, Knowledge Based Systems, Elsevier 27 (2012), 170\u2013179.","journal-title":"Knowledge Based Systems, Elsevier"},{"key":"e_1_3_2_10_2","first-page":"75","article-title":"Application of neutrosophic set theory in generalized assignment problem","volume":"9","author":"Kar S.","year":"2015","unstructured":"KarS., BasuK. and MukherjeeS., Application of neutrosophic set theory in generalized assignment problem, Neutrosophic Sets and Systems 9 (2015), 75\u201379.","journal-title":"Neutrosophic Sets and Systems"},{"key":"e_1_3_2_11_2","first-page":"31","article-title":"Solution of multi-criteria assignment problem using neutrosophic set theory","volume":"10","author":"Kar S.","year":"2015","unstructured":"KarS., BasuK. and MukherjeeS., Solution of multi-criteria assignment problem using neutrosophic set theory, Neutrosophic Sets and Systems 10 (2015), 31\u201338.","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"e_1_3_2_12_2","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/BF01585178","article-title":"An approximation algorithm for generalized assignment problem","volume":"62","author":"Shymos D.B.","year":"1993","unstructured":"ShymosD.B. and TardosE., An approximation algorithm for generalized assignment problem, Mathematical Programming 62(1-3) (1993), 461\u2013474, North Holland.","journal-title":"Mathematical Programming"},{"issue":"3","key":"e_1_3_2_13_2","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.orl.2005.05.006","article-title":"Approximation algorithm for generalized assignment problem by Israel beniaminy","volume":"34","author":"Nutov D.Z.","year":"2006","unstructured":"NutovD.Z., Approximation algorithm for generalized assignment problem by Israel beniaminy, Journal Oparations Research Letters Archive 34(3) (2006), 283\u2013288, Elsevier Science Publishers, B.V. Amsterdam, The Netherlands.","journal-title":"Journal Oparations Research Letters Archive"},{"key":"e_1_3_2_14_2","doi-asserted-by":"crossref","unstructured":"KarS. BasuK. and MukherjeeS. Generalized Fuzzy Assignment Problem with restriction on the cost of job under hesitant fuzzy environment Springer India Opsearch Vol. 52 pp. 401\u2013411. Print ISSN 0030-3887 Online ISSN 0975-0320.","DOI":"10.1007\/s12597-014-0192-3"},{"key":"e_1_3_2_15_2","first-page":"123","article-title":"A new approach to study the multiobjective assignment problem","volume":"53","author":"Bao C.-P.","year":"2007","unstructured":"BaoC.-P., TsaiM.-C. and TsaiM.-I., A new approach to study the multiobjective assignment problem, An Interdisciplinary Journal 53 (2007), 123\u2013132.","journal-title":"An Interdisciplinary Journal"},{"issue":"34","key":"e_1_3_2_16_2","first-page":"1651","article-title":"An algorithm to solve multi objective assignment problem using Interactive Fuzzy Goal Programming approach","volume":"6","author":"De P.K.","year":"2011","unstructured":"DeP.K. and YadavB., An algorithm to solve multi objective assignment problem using Interactive Fuzzy Goal Programming approach, International Journal contemp. Math, Sciences 6(34) (2011), 1651\u20131662.","journal-title":"International Journal contemp. Math, Sciences"},{"key":"e_1_3_2_17_2","volume-title":"Learning and Intelligent Optimization. LION 2007. Lecture Notes in Computer Science","author":"Garrett D.","year":"2008","unstructured":"GarrettD., GuptaD.D., Multi objective landscape analysis and the Generalized Assignment Problem In: ManiezzoV., BattitiR. & WatsonJ.P. (eds): Learning and Intelligent Optimization. LION 2007. Lecture Notes in Computer Science, 2008, Vol 5313. Springer, Berlin, Heidelberg."},{"key":"e_1_3_2_18_2","unstructured":"SubtilR.F. CarranoE.G. TakahashiR.H.C. SouzaM.J.F. and de SouzaS.R. Improved Genetic Operators for the multi objective generalized assignment problem Laborat\u00f3rio de Banco de Dados- Researchgate 2010."},{"key":"e_1_3_2_19_2","unstructured":"PramanikS. and BiswasP. Multi objective assignment problem with generalized trapezoidal fuzzy numbers International Journal of Applied Information Systems 2(6) 13\u201320. ISSN 2249-0868 Foundation of Computer Science New York USA."},{"issue":"3","key":"e_1_3_2_20_2","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1016\/j.eswa.2012.05.045","article-title":"Solving fuzzy multi objective generalized assignment problem directly via bees algorithm and fuzzy ranking","volume":"40","author":"Tapkan P.","year":"2013","unstructured":"TapkanP., OzbakirL. and BaykasogluA., Solving fuzzy multi objective generalized assignment problem directly via bees algorithm and fuzzy ranking, Expert Systems with Applications 40(3) (2013), 892\u2013898.","journal-title":"Expert Systems with Applications"},{"issue":"2","key":"e_1_3_2_21_2","first-page":"91","article-title":"Pareto Optimal Solutions for multi objective generalized assignment problem","volume":"21","author":"Prakash S.","year":"2010","unstructured":"PrakashS., Pareto Optimal Solutions for multi objective generalized assignment problem, Sajie Journals 21(2) (2010), 91\u2013100.","journal-title":"Sajie Journals"},{"issue":"1","key":"e_1_3_2_22_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF01299390","article-title":"Multi-dimensional assignment formulation of data association problems arising from multi-target and multi-sensor tracking","volume":"3","author":"Poore A.B.","year":"1994","unstructured":"PooreA.B., Multi-dimensional assignment formulation of data association problems arising from multi-target and multi-sensor tracking, Computational Optimization and Applications, Springer 3(1) (1994), 27\u201357.","journal-title":"Computational Optimization and Applications, Springer"},{"key":"e_1_3_2_23_2","first-page":"1","volume-title":"of the series Combinatorial Optimization","author":"Spieksma F.C.R.","year":"2000","unstructured":"SpieksmaF.C.R., Multi-Index Assignment Problems: Complexity, Approximation and Applications, Vol. 7 of the series Combinatorial Optimization, 2000, pp. 1\u201312."}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-17086","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-17086","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-17086","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:14Z","timestamp":1777455614000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-17086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,24]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,8,24]]}},"alternative-id":["10.3233\/JIFS-17086"],"URL":"https:\/\/doi.org\/10.3233\/jifs-17086","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,24]]}}}