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The resource is used to reduce the processing time that is inversely proportional to the resource consumption amount. Furthermore, there exist the lower and upper bounds on the amount of the resources consumed by each job. The objective is to minimize the makespan plus the total resource consumption cost. We show that the problem can be solved in strongly polynomial time. <\/jats:p>","DOI":"10.1142\/s0217595923500185","type":"journal-article","created":{"date-parts":[[2023,5,13]],"date-time":"2023-05-13T02:01:17Z","timestamp":1683943277000},"source":"Crossref","is-referenced-by-count":5,"title":["A Resource Allocation Problem with Convex Resource-Dependent Processing Times Under A Two-Machine Flow Shop Environment"],"prefix":"10.1142","volume":"41","author":[{"given":"Byung-Cheon","family":"Choi","sequence":"first","affiliation":[{"name":"School of Business, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea"}]},{"given":"Jun-Ho","family":"Lee","sequence":"additional","affiliation":[{"name":"School of Business, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea"}]}],"member":"219","published-online":{"date-parts":[[2023,6,5]]},"reference":[{"key":"S0217595923500185BIB001","first-page":"17","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables","author":"Abramowitz M","year":"1972","edition":"9"},{"key":"S0217595923500185BIB002","doi-asserted-by":"publisher","DOI":"10.1145\/77600.77615"},{"key":"S0217595923500185BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018943300630"},{"key":"S0217595923500185BIB004","doi-asserted-by":"publisher","DOI":"10.7737\/JKORMS.2021.46.2.001"},{"key":"S0217595923500185BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-022-01934-1"},{"key":"S0217595923500185BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2011.11.001"},{"key":"S0217595923500185BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-014-1531-8"},{"key":"S0217595923500185BIB008","doi-asserted-by":"publisher","DOI":"10.7494\/dmms.2007.1.2.59"},{"key":"S0217595923500185BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(03)00103-5"},{"key":"S0217595923500185BIB010","doi-asserted-by":"publisher","DOI":"10.1080\/01605682.2021.1886616"},{"key":"S0217595923500185BIB011","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010918518726"},{"key":"S0217595923500185BIB012","doi-asserted-by":"publisher","DOI":"10.1287\/moor.15.4.736"},{"key":"S0217595923500185BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s42452-020-1946-6"},{"key":"S0217595923500185BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2015.12.014"},{"key":"S0217595923500185BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68619-6_11"},{"key":"S0217595923500185BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(03)00081-9"},{"key":"S0217595923500185BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(03)00187-4"},{"key":"S0217595923500185BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2004.12.008"},{"key":"S0217595923500185BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.02.003"},{"key":"S0217595923500185BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2006.04.002"},{"key":"S0217595923500185BIB021","doi-asserted-by":"publisher","DOI":"10.1080\/07408170601181674"},{"key":"S0217595923500185BIB022","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1520-6750(199810)45:7<705::AID-NAV4>3.0.CO;2-F"},{"key":"S0217595923500185BIB023","doi-asserted-by":"publisher","DOI":"10.1287\/opre.28.5.1155"},{"key":"S0217595923500185BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-010-0746-6"},{"key":"S0217595923500185BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2009.11.012"},{"key":"S0217595923500185BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/s10951-007-0044-6"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595923500185","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T03:43:21Z","timestamp":1712547801000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.worldscientific.com\/doi\/10.1142\/S0217595923500185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,5]]},"references-count":26,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["10.1142\/S0217595923500185"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1142\/s0217595923500185","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,5]]},"article-number":"2350018"}}