{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:40:50Z","timestamp":1768725650528,"version":"3.49.0"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11161001"],"award-info":[{"award-number":["11161001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2013XYZ025"],"award-info":[{"award-number":["2013XYZ025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005323","name":"Beifang University of Nationalities","doi-asserted-by":"publisher","award":["11161001"],"award-info":[{"award-number":["11161001"]}],"id":[{"id":"10.13039\/501100005323","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005323","name":"Beifang University of Nationalities","doi-asserted-by":"publisher","award":["2013XYZ025"],"award-info":[{"award-number":["2013XYZ025"]}],"id":[{"id":"10.13039\/501100005323","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.1155\/2013\/276245","type":"journal-article","created":{"date-parts":[[2013,6,11]],"date-time":"2013-06-11T17:01:12Z","timestamp":1370970072000},"page":"1-7","source":"Crossref","is-referenced-by-count":21,"title":["A Global Optimization Algorithm for Sum of Linear Ratios Problem"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yuelin","family":"Gao","sequence":"first","affiliation":[{"name":"Institute of Information & System Science, Beifang University of Nationalities, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siqiao","family":"Jin","sequence":"additional","affiliation":[{"name":"Institute of Information & System Science, Beifang University of Nationalities, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"3","key":"1","doi-asserted-by":"crossref","first-page":"295","DOI":"10.15807\/jorsj.39.295","volume":"39","year":"1996","journal-title":"Journal of the Operations Research Society of Japan"},{"key":"2","series-title":"Princeton Series in Computer Science","first-page":"221","volume-title":"Optimizing the sum of linear fractional functions","year":"1992"},{"key":"3","series-title":"Nonconvex Optimization and Its Applications","first-page":"xiv+353","volume":"48","year":"2000"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00120666"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008376731013"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.09.047"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.08.016"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9199-8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/646205"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.06.045"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/276245.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/276245.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/276245.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T01:47:34Z","timestamp":1563155254000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/276245\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":10,"alternative-id":["276245","276245"],"URL":"https:\/\/doi.org\/10.1155\/2013\/276245","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}