鄒昊
摘要:線性規(guī)劃模型及其應(yīng)用學(xué)者們常常用模糊集理論或概率論來處理這種不確定信息。為了尋求一種簡單而準(zhǔn)確地刻畫方式,本文考慮用區(qū)間數(shù)描述這些系統(tǒng)的影響指標(biāo),建立基于區(qū)間數(shù)的線性規(guī)劃模型。針對運輸系統(tǒng)優(yōu)化決策問題,本文將系統(tǒng)運費、供給量、需求量和預(yù)算費用描述為區(qū)間數(shù),建立基于區(qū)間數(shù)的運輸優(yōu)化多目標(biāo)線性規(guī)劃模型,給出算法步驟,通過實例分析來驗證該模型的可行性和準(zhǔn)確性。
Abstract: Linear programming model and its application scholars often use fuzzy set theory or probability theory to deal with such uncertain information. In order to find a simple and accurate way of depicting, this paper considers the use of interval numbers to describe the impact indicators of these systems and establish a linear programming model based on interval numbers. For the transportation system optimization decision problem, this paper describes the system freight, supply amount, demand amount and budget expenses as interval numbers, establishes a multi-objective linear programming model based on interval number for transportation optimization, gives the algorithm steps, and verifies the feasibility and accuracy of model through case analysis.
關(guān)鍵詞:區(qū)間數(shù);線性規(guī)劃模型;運輸系統(tǒng)
Key words: interval number;linear programming model;transportation system
中圖分類號:O221.1 文獻(xiàn)標(biāo)識碼:A 文章編號:1006-4311(2018)30-0182-03
參考文獻(xiàn):
[1]周芳.基于模糊集理論的知識知識融合方法的研究[D].北京:北京理工大學(xué),2013:19-20.
[2]高慶獅.概率論基本部分與模糊集合的統(tǒng)一定義[J].大連理工學(xué)報,2006,46:8-26.
[3]劉東慶.幾種運輸問題的研討[J].蘇州大學(xué)學(xué)報,2006(02):10-13.
[4]高淑萍.運輸問題的模糊優(yōu)化算法和理論[D].中國博士學(xué)位論文全文數(shù)據(jù)庫,2010(02):2-16.
[5]胡啟洲.區(qū)間數(shù)理論的研究及其應(yīng)用[M].北京:科學(xué)出版社,2010(06):18-19.
[6]房勇,汪壽陽.模糊投資組合優(yōu)化:理論與方法[M].北京:高等教育出版社,2005:46-48.
[7]Changkong, V, and Haimes, Y, Multiabjective Decision Making Theory andMethpdlody, Amsterdam; North-Halled, 1983(03): 1-4.
[8]張先軍.不確定運輸問題的模型及算法[D].中國優(yōu)秀碩士學(xué)位論文全文數(shù)據(jù)庫,2006(08):2-6.
[9]趙志理.區(qū)間線性規(guī)劃的優(yōu)化條件與區(qū)間矩陣的分解[J].運籌學(xué)與控制論,2013(02):6-8.
[10]曾霽.運輸問題的區(qū)間規(guī)劃模型[J].四川理工學(xué)院學(xué)報,2008(04):2-6.
[11]S. Florentin, C. Adrian and F. Massimiliano, PORTFOLIO OPTIMIZATIONUSING INTERVAL ANALYSIS, ECONOMIC COMPUTATIONAND ECONOMIC CYBERNETICS STUDIES AND RESEARCH,vol. 49, Issue 1, 2015.
[12]K. K. Lai, S. Y. Wang, J. P. Xu, S. S. Zhu, and Y. Fang, A Class ofLinear Interval Programming Problems and Its Application to PortfolioSelection, IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol. 10, no.6, 2002.
[13]R.E. Moore, R.B. Kearfott and M.J.Cloud, Introduction to IntervalAnalysis, SIAM Press, Philadelphia, PA. 2009.
[14]Y. F. Sun, G. Aw, K. Lay Teo and G. L. Zhou, PORTFOLIOOPTIMIZATION USING A NEW PROBABILISTIC RISK MEASURE,JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,vol. 11, No. 4, 1275-1283, 2015.