{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:05:08Z","timestamp":1649063108036},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:p> In this paper, we investigate a semi-on-line version for a special case of three machines M<jats:sub>1<\/jats:sub>, M<jats:sub>2<\/jats:sub>, M<jats:sub>3<\/jats:sub> where the processing time of the largest job is known in advance. A speed s<jats:sub>i<\/jats:sub>(s<jats:sub>1<\/jats:sub> = s<jats:sub>2<\/jats:sub> = 1, 1 \u2264 s<jats:sub>3<\/jats:sub> = s) is associated with machine M<jats:sub>i<\/jats:sub>. Our goal is to maximize the C<jats:sub> min <\/jats:sub> \u2014 the minimum workload of three machines. We give a C<jats:sub> min 3<\/jats:sub> algorithm and prove its competitive ratio is [Formula: see text] and the algorithm is the best possible for 1 \u2264 s \u2264 2. We also claim the competitive ratio of algorithm C<jats:sub> min 3<\/jats:sub> is tight. <\/jats:p>","DOI":"10.1142\/s0217595905000558","type":"journal-article","created":{"date-parts":[[2005,6,9]],"date-time":"2005-06-09T07:25:56Z","timestamp":1118301956000},"page":"229-237","source":"Crossref","is-referenced-by-count":1,"title":["SEMI-ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON THREE SPECIAL UNIFORM MACHINES"],"prefix":"10.1142","volume":"22","author":[{"given":"RUN-ZI","family":"LUO","sequence":"first","affiliation":[{"name":"Mathematics Department, Shanghai University, Shanghai 200444, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SHI-JIE","family":"SUN","sequence":"additional","affiliation":[{"name":"Mathematics Department, Shanghai University, Shanghai 200444, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-63397-9_3"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(92)90004-M"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/0603019"},{"key":"rf4","first-page":"39","author":"Epstein L.","journal-title":"Proc. of the 3rd ARACNE"},{"key":"rf5","volume-title":"Computers and Intractability","author":"Garey M. R.","year":"1979"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(00)00070-5"},{"key":"rf7","first-page":"107","volume":"17","author":"He Y.","journal-title":"Acta Mathematica Applicate Sinica"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013855712183"},{"key":"rf9","first-page":"31","volume":"20","author":"He Y.","journal-title":"Asia-Pacific Journal of Operational Research"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s006070050020"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(96)00055-7"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595905000558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:42:58Z","timestamp":1565116978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595905000558"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1142\/S0217595905000558"],"URL":"https:\/\/doi.org\/10.1142\/s0217595905000558","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}