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In a conventional method, some essential and uncertain variables, such as return, investment and set up cost, are given by estimation of experts due to lack of historical data. To better solve the problem, uncertainty theory is introduced into this study. A mean-variance model is proposed to help decision makers find an optimal portfolio and its time schedule. Specially, the situation where all the uncertain parameters are normal distribution is discussed. For efficient computation, an equivalent mixed integer linear programming representation is proposed. Another mean-variance model without considering the divisibility is also proposed to see the contrast effect of net present value (NPV). At last, a numerical example under above two scenarios is demonstrated and the effect of risk level to the maximum expected NPV is discussed.<\/jats:p>","DOI":"10.3233\/jifs-169215","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T14:44:09Z","timestamp":1495809849000},"page":"4513-4522","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Uncertain mean-variance model for project portfolio selection problem with divisibility"],"prefix":"10.1177","volume":"32","author":[{"given":"Xingmei","family":"Li","sequence":"first","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiming","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youzhong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaxian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,5,23]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fiae.2015.05.007"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/080734510"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0396-4"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fiae.2015.05.006"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.4236\/am.2010.13023"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.6.1.73"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2016.01.058"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/00137910308965064"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2015.1382"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.04.074"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2007.11.015"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11214-0"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.10.030"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.02.050"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.2307\/1914185"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2014.05.036"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.2014.75"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11518-015-5281-1"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2011.08.025"},{"issue":"1","key":"e_1_3_1_21_2","first-page":"3","article-title":"Why is there a need for uncertainty theory","volume":"6","author":"Liu B.D.","year":"2012","unstructured":"LiuB.D., Why is there a need for uncertainty theory, Journal of Uncertain Systems 6(1) (2012), 3\u201310.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44354-5"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2014.11.005"},{"key":"e_1_3_1_24_2","article-title":"R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach","author":"Mohagheghi V.","year":"2016","unstructured":"MohagheghiV., MousaviS.M., VahdaniB. and ShahriariM.R., R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach, Neural Computing and Applications (2016). 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