{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:50:13Z","timestamp":1754157013377,"version":"3.41.2"},"reference-count":10,"publisher":"Emerald","issue":"10","license":[{"start":{"date-parts":[[2009,10,16]],"date-time":"2009-10-16T00:00:00Z","timestamp":1255651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,10,16]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to find the best approximation algorithm for solving the more general case of single\u2010supplier multi\u2010retailer capacitated economic lot\u2010sizing (SM\u2010CELS) problem in deterministic inventory theory, which is the non\u2010deterministic polynomial (NP)\u2010hard problem.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Since few theoretical results have been published on polynomial time approximation algorithms for SM\u2010CELS problems, this paper develops a fully polynomial time approximation scheme (FPTAS) for the problem with monotone production and holding\u2010backlogging cost functions. First the optimal solution of a rounded problem is presented as the approximate solution and its straightforward dynamic\u2010programming (DP) algorithm. Then the straightforward DP algorithm is converted into an FPTAS by exploiting combinatorial properties of the recursive function.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>An FPTAS is designed for the SM\u2010CELS problem with monotone cost functions, which is the strongest polynomial time approximation result.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>The main limitation is that the supplier only manufactures without holding any products when the model is applied.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The paper presents the best result for the SM\u2010CELS problem in deterministic inventory theory.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The LP\u2010rounding technique, an effective approach to design approximation algorithms for NP\u2010hard problems, is successfully applied to the SM\u2010CELS problem in this paper.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910994105","type":"journal-article","created":{"date-parts":[[2009,11,14]],"date-time":"2009-11-14T07:01:03Z","timestamp":1258182063000},"page":"1735-1746","source":"Crossref","is-referenced-by-count":1,"title":["An FPTAS for SM\u2010CELS problem with monotone cost functions"],"prefix":"10.1108","volume":"38","author":[{"given":"Jianteng","family":"Xu","sequence":"first","affiliation":[]},{"given":"Qingpu","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Qingguo","family":"Bai","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022021119431694700_b1","doi-asserted-by":"crossref","unstructured":"Chubanov, S., Kovalyov, M.Y. and Pesch, E. 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(2004), \u201cInventory replenishment model: lot sizing versus just\u2010in\u2010time\u201d, Operation Research Letters, Vol. 32, pp. 581\u201090.","DOI":"10.1016\/j.orl.2003.12.008"},{"key":"key2022021119431694700_frd3","unstructured":"Liu, H.X., Wang, H.W. and Yang, J.B. (2005), \u201cDynamic stability analysis of an inventory control system\u201d, Advances in Systems Science and Applications, Vol. 5 No. 3, pp. 359\u201067."},{"key":"key2022021119431694700_frd4","unstructured":"Pan, J.M., Tang, X.W. and Lu, Y.J. (2004), \u201cSupply chain volume flexibility decision model under utility\u201d, Advances in Systems Science and Applications, Vol. 7 No. 4, pp. 551\u20106."},{"key":"key2022021119431694700_frd5","unstructured":"Zhang, M., Yang, C. and Yang, J. (2006), \u201cLocation models of perishable commodities distribution system based on time constraints\u201d, Advances in Systems Science and Applications, Vol. 6 No. 2, pp. 234\u20109."}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684920910994105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910994105\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910994105\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:26:45Z","timestamp":1753399605000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/38\/10\/1735-1746\/271863"}},"subtitle":[],"editor":[{"given":"Mian\u2010yun","family":"Chen","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,10,16]]},"references-count":10,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2009,10,16]]}},"alternative-id":["10.1108\/03684920910994105"],"URL":"https:\/\/doi.org\/10.1108\/03684920910994105","relation":{},"ISSN":["0368-492X"],"issn-type":[{"type":"print","value":"0368-492X"}],"subject":[],"published":{"date-parts":[[2009,10,16]]}}}