{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T02:32:32Z","timestamp":1768530752338,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,2,1]],"date-time":"2012-02-01T00:00:00Z","timestamp":1328054400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Autom. Comput."],"published-print":{"date-parts":[[2012,2]]},"DOI":"10.1007\/s11633-012-0620-x","type":"journal-article","created":{"date-parts":[[2012,2,21]],"date-time":"2012-02-21T09:52:32Z","timestamp":1329817952000},"page":"87-97","source":"Crossref","is-referenced-by-count":4,"title":["An efficient frontier for sum deviation JIT sequencing problem in mixed-model systems via apportionment"],"prefix":"10.1007","volume":"9","author":[{"given":"Tanka Nath","family":"Dhamala","sequence":"first","affiliation":[]},{"given":"Gyan Bahadur","family":"Thapa","sequence":"additional","affiliation":[]},{"given":"Hong-Nian","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,22]]},"reference":[{"key":"620_CR1","volume-title":"Toyota Production Systems: Practical Approach to Production Management","author":"Y. Monden","year":"1983","unstructured":"Y. Monden. Toyota Production Systems: Practical Approach to Production Management, Norcross, USA: Industrial Engineering and Management Press, 1983."},{"issue":"2","key":"620_CR2","first-page":"38","volume":"2","author":"T. N. Dhamala","year":"2005","unstructured":"T. N. Dhamala, W. Kubiak. A brief survey of just-in-time sequencing for mixed-model systems. International Journal of Operations Research, vol. 2, no. 2, pp. 38\u201347, 2005.","journal-title":"International Journal of Operations Research"},{"issue":"1\u20132","key":"620_CR3","first-page":"29","volume":"29","author":"G. B. Thapa","year":"2009","unstructured":"G. B. Thapa, T. N. Dhamala. Just-in-time sequencing in mixed-model production systems relating with fair representation in apportionment theory. The Nepali Mathematical Sciences Report, vol. 29, no. 1\u20132, pp. 29\u201368, 2009.","journal-title":"The Nepali Mathematical Sciences Report"},{"issue":"2","key":"620_CR4","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1287\/mnsc.35.2.192","volume":"35","author":"J. Miltenburg","year":"1989","unstructured":"J. Miltenburg. Level schedules for mixed-model assembly lines in just-in-time production systems. Management Science, vol. 35, no. 2, pp. 192\u2013207, 1989.","journal-title":"Management Science"},{"issue":"3","key":"620_CR5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0377-2217(93)90215-9","volume":"66","author":"W. Kubiak","year":"1993","unstructured":"W. Kubiak. Minimizing variation of production rates in just-in-time systems: A survey. European Journal of Operational Research, vol. 66, no. 3, pp. 259\u2013271, 1993.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"620_CR6","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF01328809","volume":"6","author":"W. Kubiak","year":"1994","unstructured":"W. Kubiak, S. P. Sethi. Optimal just-in-time schedules for flexible transfer lines. International Journal of Flexible Manufacturing Systems, vol. 6, no. 2, pp. 137\u2013154, 1994.","journal-title":"International Journal of Flexible Manufacturing Systems"},{"issue":"7","key":"620_CR7","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1287\/mnsc.37.7.901","volume":"37","author":"R. Inman","year":"1991","unstructured":"R. Inman, L. Bulfin. Sequencing just-in-time mixed-model assembly lines. Management Science, vol. 37, no. 7, pp. 901\u2013904, 1991.","journal-title":"Management Science"},{"issue":"4\u20135","key":"620_CR8","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/S0167-6377(98)00008-X","volume":"22","author":"M. Balinski","year":"1998","unstructured":"M. Balinski, N. Shahidi. A simple approach to the product rate variation problem via axiomatics. Operations Research Letters, vol. 22, no. 4\u20135, pp. 129\u2013135, 1998.","journal-title":"Operations Research Letters"},{"issue":"2","key":"620_CR9","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.ejor.2007.09.013","volume":"192","author":"N. Boysen","year":"2009","unstructured":"N. Boysen, M. Flieder, A. Scholl. Sequencing mixed-model assembly lines: Survey, classification and model critique. European Journal of Operational Research, vol. 192, no. 2, pp. 349\u2013373, 2009.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"620_CR10","first-page":"266","volume":"1","author":"T. N. Dhamala","year":"2009","unstructured":"T. N. Dhamala, S. R. Khadka. A review on sequencing approaches for mixed-model just-in-time production system. Iranian Journal of Optimization, vol. 1, no. 3, pp. 266\u2013290, 2009.","journal-title":"Iranian Journal of Optimization"},{"key":"620_CR11","volume-title":"Paradoxes in Politics: An Introduction to the Nonobvious in Political Science","author":"S. J. Brams","year":"1976","unstructured":"S. J. Brams. Paradoxes in Politics: An Introduction to the Nonobvious in Political Science, New York, USA: Free Press, 1976."},{"key":"620_CR12","volume-title":"Fair Representation: Meeting the Ideal of One Man, One Vote","author":"M. Balinski","year":"2001","unstructured":"M. Balinski, H. P. Young. Fair Representation: Meeting the Ideal of One Man, One Vote, 2ed ed., Washington D. C., USA: Brookings Institution Press, 2001.","edition":"2ed ed."},{"issue":"3","key":"620_CR13","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/S0377-2217(00)00110-7","volume":"131","author":"J. Baustista","year":"2001","unstructured":"J. Baustista, R. Companys, A. Corominas. Solving the generalized apportionment problem through the optimization of discrepancy functions. European Journal of Operational Research, vol. 131, no. 3, pp. 676\u2013684, 2001.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"620_CR14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.2307\/2691355","volume":"65","author":"B. A. Bradberry","year":"1992","unstructured":"B. A. Bradberry. A geometric view of some apportionment paradoxes. Mathematics Magazine, vol. 65, no. 1, pp. 3\u201317, 1992.","journal-title":"Mathematics Magazine"},{"key":"620_CR15","unstructured":"G. B. Thapa, T. N. Dhamala. A synthetic study to minimize the inequality measures in just-in-time sequencing problem via optimization methods. In Proceedings of the 5th Asian Mathematical Conference, Malaysia, pp. 462\u2013470, 2009."},{"issue":"3","key":"620_CR16","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1080\/03155986.2001.11732444","volume":"39","author":"M. Y. Kovalyov","year":"2001","unstructured":"M. Y. Kovalyov, W. Kubiak, J. S. Yeomans. A computational analysis of balanced JIT optimization algorithms. Information Processing and Operational Research, vol. 39, no. 3, pp. 299\u2013316, 2001.","journal-title":"Information Processing and Operational Research"},{"key":"620_CR17","doi-asserted-by":"crossref","first-page":"701","DOI":"10.2307\/2318729","volume":"82","author":"M. Balinski","year":"1975","unstructured":"M. Balinski, H. P. Young. The quota method of apportionment. American Mathematical Monthly, vol. 82, pp. 701\u2013729, 1975.","journal-title":"American Mathematical Monthly"},{"key":"620_CR18","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"C. H. Papadimitrou","year":"2003","unstructured":"C. H. Papadimitrou, K. Steiglitz. Combinatorial Optimization: Algorithms and Complexity, Portugal: Prentice Hall of India, 2003."},{"issue":"4","key":"620_CR19","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1145\/115234.115349","volume":"38","author":"E. Balas","year":"1991","unstructured":"E. Balas, D. Miller, J. Pekny, P. Toth. A parallel shortest augmenting path algorithm for the assignment problem. Journal of the ACM, vol. 38, no. 4, pp. 985\u20131004, 1991.","journal-title":"Journal of the ACM"},{"issue":"2\u20133","key":"620_CR20","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1023\/A:1024847308982","volume":"27","author":"W. Kubiak","year":"2003","unstructured":"W. Kubiak. Cyclic just-in-time sequences are optimal. Journal of Global Optimization, vol. 27, no. 2\u20133, pp. 333\u2013347, 2003.","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"620_CR21","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1090\/S0002-9947-1928-1501423-0","volume":"30","author":"E. V. Huntington","year":"1928","unstructured":"E. V. Huntington. The apportionment of representatives in congress. Transactions of the American Mathematical Society, vol. 30, no. 1, pp. 85\u2013110, 1928.","journal-title":"Transactions of the American Mathematical Society"},{"issue":"4","key":"620_CR22","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1137\/0133043","volume":"33","author":"M. L. Balinski","year":"1977","unstructured":"M. L. Balinski, H. P. Young. On huntington methods of apportionment. SIAM Journal on Applied Mathematics, vol. 33, no. 4, pp. 607\u2013618, 1977.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"620_CR23","unstructured":"G. A. Bliss, E. Brown, L. Eisenhart, R. Pearl. Report to the president of national academy of sciences. In 70th congressional record, pp. 4966\u20134967, 1929."},{"key":"620_CR24","unstructured":"Morse, Marton, J. V. Newmann, L. P. Eisenhart. Report to the President of the National Academy of Sciences, USA, 1948."},{"issue":"2","key":"620_CR25","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0165-4896(98)00027-4","volume":"37","author":"M. Balinski","year":"1999","unstructured":"M. Balinski, V. Ramirez. Parametric methods of apportionment, rounding and production. Mathematical Social Sciences, vol. 37, no. 2, pp. 107\u2013122, 1999.","journal-title":"Mathematical Social Sciences"},{"issue":"11","key":"620_CR26","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1057\/jors.1996.177","volume":"47","author":"J. Baustista","year":"1996","unstructured":"J. Baustista, R. Companys, A. Corominas. A note on the relation between the product rate variation problem and the apportionment problem. The Journal of the Operational Research Society, vol. 47, no. 11, pp. 1410\u20131414, 1996.","journal-title":"The Journal of the Operational Research Society"},{"key":"620_CR27","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/0-387-33815-2_10","volume":"94","author":"J. Jozefowska","year":"2006","unstructured":"J. Jozefowska, L. Jozefowski, W. Kubiak. Characterization of just-in-time sequencing via apportionment. International Series in Operations Research & Management Science, vol. 94, pp. 175\u2013200, 2006.","journal-title":"International Series in Operations Research & Management Science"},{"issue":"4","key":"620_CR28","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1080\/03155986.2003.11732685","volume":"41","author":"A. Corominas","year":"2003","unstructured":"A. Corominas, N. Moreno. On the relations between optimal solutions for different types of min-sum balanced justin-time optimization problems. Information Systems and Operations Research, vol. 41, no. 4, pp. 333\u2013339, 2003.","journal-title":"Information Systems and Operations Research"},{"issue":"2","key":"620_CR29","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1287\/mnsc.1090.1118","volume":"56","author":"S. Maier","year":"2010","unstructured":"S. Maier, P. Zachariassen, M. Zachariassen. Divisor-based biproportional apportionment in electoral systems: A reallife benchmark study. Management Science, vol. 56, no. 2, pp. 373\u2013387, 2010.","journal-title":"Management Science"},{"issue":"2","key":"620_CR30","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s11633-011-0571-7","volume":"8","author":"A. T. Yang","year":"2011","unstructured":"A. T. Yang, L. D. Zhao. Supply chain network equilibrium with revenue sharing contract under demand disruptions. International Journal of Automation and Computing, vol.8, no. 2, pp. 177\u2013184, 2011.","journal-title":"International Journal of Automation and Computing"},{"issue":"4","key":"620_CR31","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1007\/s11633-010-0545-1","volume":"7","author":"Z. Q. Sheng","year":"2010","unstructured":"Z. Q. Sheng, C. P. Tang, C. X. Lv. Modeling of agile intelligent manufacturing-oriented production scheduling system. International Journal of Automation and Computing, vol.7, no. 4, pp. 596\u2013602, 2010.","journal-title":"International Journal of Automation and Computing"},{"issue":"3","key":"620_CR32","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.dam.2009.09.013","volume":"158","author":"M. Fliedner","year":"2010","unstructured":"M. Fliedner, N. Boysen, A. Scholl. Solving symmetric mixed-model multilevel just-in-time scheduling problems. Discrete Applied Mathematics, vol. 158, no. 3, pp. 222\u2013231, 2010.","journal-title":"Discrete Applied Mathematics"},{"issue":"1\u20132","key":"620_CR33","first-page":"24","volume":"30","author":"G. B. Thapa","year":"2010","unstructured":"G. B. Thapa, T. N. Dhamala, H. Yu. Mathematical model of cross-docking operation in supply chain logistics under multi-level just-in-time production environment. The Nepali Mathematical Sciences Report, vol. 30, no. 1\u20132, pp. 24\u201335, 2010.","journal-title":"The Nepali Mathematical Sciences Report"}],"container-title":["International Journal of Automation and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-012-0620-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11633-012-0620-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-012-0620-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T14:46:41Z","timestamp":1559400401000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11633-012-0620-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["620"],"URL":"https:\/\/doi.org\/10.1007\/s11633-012-0620-x","relation":{},"ISSN":["1476-8186","1751-8520"],"issn-type":[{"value":"1476-8186","type":"print"},{"value":"1751-8520","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2]]}}}