{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T16:00:36Z","timestamp":1742400036917,"version":"3.37.3"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":["11171094","14A110024"],"award-info":[{"award-number":["11171094","14A110024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Key Project of Education Department of Henan Province","award":["11171094","14A110024"],"award-info":[{"award-number":["11171094","14A110024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.<\/jats:p>","DOI":"10.1155\/2014\/490297","type":"journal-article","created":{"date-parts":[[2014,3,26]],"date-time":"2014-03-26T17:06:16Z","timestamp":1395853576000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3695-387X","authenticated-orcid":true,"given":"Hongwei","family":"Jiao","sequence":"first","affiliation":[{"name":"School of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2195-1844","authenticated-orcid":true,"given":"Yongqiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Henan Normal University, Xinxiang 453007, China"},{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"467","volume":"44","year":"1969","journal-title":"Accounting Review"},{"key":"2","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1080\/01621459.1971.10482319","volume":"66","year":"1971","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"3","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":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00120666"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.08.016"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.06.045"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.06.101"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.09.047"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/276245"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-012-0602-8"},{"year":"1990","key":"11"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/490297.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/490297.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/490297.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T19:30:47Z","timestamp":1565292647000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/490297\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":11,"alternative-id":["490297","490297"],"URL":"https:\/\/doi.org\/10.1155\/2014\/490297","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}