基于乐观值和悲观值的不确定机会约束规划模型及应用
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摘要
为了克服随机规划、模糊规划以及不确定规划期望值模型在实际应用中的局限性,基于乐观值和悲观值,提出了新的不确定机会约束规划模型。首先,根据目标函数的分类,分别定义了收益函数和成本函数的乐观值与悲观值,并在此基础上建立了不确定机会约束规划Maximax、Maximin、Minimin和Minimax模型;其次,给出了不确定机会约束规划模型的等价转化方法,将无法直接求解的不确定模型转化为可直接求解的等价确定模型,并分析了乐观值和悲观值随信度水平变化的规律;最后,以西安市某快递营业网点出行时间计划问题为例,对本文提出的模型、方法以及信度水平的影响进行了分析,指出信度水平实际上反映了决策者的风险偏好程度,实例结果表明本文提出的模型及方法具有可行性、有效性和实用性。
To overcome the application limitations of stochastic programming,fuzzy programming and uncertain programming expected value model,a uncertain chance-constrained programming model is proposed based on optimistic and pessimistic values.Firstly,the optimistic and pessimistic values of the revenue function and cost function are defined based on the classification of objective functions.On this basis,the Maximax,Maximin,Minimin,and Minimax models of uncertain chance-constrained programming are established.Secondly,the equivalent transformation methods are proposed,making it possible to solve the uncertain chance-constrained programming models directly.The influences of belief degree on the models are also studied.Finally,the proposed models,methods and the influences of belief degree are analyzed by an example of the travel time planning problem of an express delivery network in Xi'an.And it is also pointed out that the belief degree can reflect the risk preference of the decision makers in this case.The results prove the feasibility,validity and practicability of the proposed models and methods.
To overcome the application limitations of stochastic programming,fuzzy programming and uncertain programming expected value model,a uncertain chance-constrained programming model is proposed based on optimistic and pessimistic values.Firstly,the optimistic and pessimistic values of the revenue function and cost function are defined based on the classification of objective functions.On this basis,the Maximax,Maximin,Minimin,and Minimax models of uncertain chance-constrained programming are established.Secondly,the equivalent transformation methods are proposed,making it possible to solve the uncertain chance-constrained programming models directly.The influences of belief degree on the models are also studied.Finally,the proposed models,methods and the influences of belief degree are analyzed by an example of the travel time planning problem of an express delivery network in Xi'an.And it is also pointed out that the belief degree can reflect the risk preference of the decision makers in this case.The results prove the feasibility,validity and practicability of the proposed models and methods.
引文
[1]CHARNES A,COOPER W W.Management models and industrial applications of linear programming[M].New York:Wiley,1961:1-467.
[2]LIU B.Dependent-chance programming:a class of stochastic optimization[J].Computers&Mathematics with Applications,1997,34(12):89-104.
[3]KAHNEMAN D,TVERSKY A.Prospect theory:an analysis of decisions under risk[J].Econometrica,1979,47(2):263-291.
[4]KAHNEMAN D,TVERSKY A.Rational choice and the framing of decisions[J].Journal of Business,1986,59(4):S251-S278.
[5]ZADEH L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[6]ZADEH L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets&Systems,1978,1(1):3-28.
[7]LIU B,LIU Y K.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Trans.on Fuzzy Systems,2002,10(4):445-450.
[8]LIU B,IWAMURA K.Chance constrained programming with fuzzy parameters[J].Fuzzy Sets&Systems,1998,94(2):227-237.
[9]LIU B,IWAMURA K.A note on chance constrained programming with fuzzy coefficients[J].Fuzzy Sets&Systems,1998,100(1/3):229-233.
[10]LIU B.Minimax chance constrained programming models for fuzzy decision systems[J].Information Sciences,1998,112(1/4):25-38.
[11]LIU B.Dependent-chance programming in fuzzy environments[J].Fuzzy Sets&Systems,2000,109(1):97-106.
[12]LIU B.Uncertainty theory[M].Berlin:Springer-Verlag,2004.
[13]LIU B.Theory and practice of uncertain programming[M].2nd ed.Berlin:Springer,2009.
[14]LIU B,CHEN X.Uncertain multiobjective programming and uncertain goal programming[J].Journal of Uncertainty Analysis&Applications,2015,3(1):1-8.
[15]LIU B,YAO K.Uncertain multilevel programming:algorithm and applications[J].Computers&Industrial Engineering,2015,89:235-240.
[16]GUO J S,WANG Z T,ZHENG M F,et al.Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm[J].Chinese Journal of Aeronautics,2014,27(6):1477-1487.
[17]MA W,CHE Y,HUANG H,et al.Resource-constrained project scheduling problem with uncertain durations and renewable resources[J].International Journal of Machine Learning&Cybernetics,2016,7(4):613-621.
[18]DALMAN H.Uncertain programming model for multi-item solid transportation problem[J].International Journal of Machine Learning&Cybernetics,2018,9(4):559-567.
[19]GUO J,WANG Z,ZHENG M,et al.An approach for UAV reconnaissance mission planning problem under uncertain environment[J].International Journal of Imaging&Robotics,2014,14(3):1-15.
[20]LIU B.Uncertainty theory:a branch of mathematics for modeling human uncertainty[M].Berlin:Springer-Verlag,2010:56-60.
[2]LIU B.Dependent-chance programming:a class of stochastic optimization[J].Computers&Mathematics with Applications,1997,34(12):89-104.
[3]KAHNEMAN D,TVERSKY A.Prospect theory:an analysis of decisions under risk[J].Econometrica,1979,47(2):263-291.
[4]KAHNEMAN D,TVERSKY A.Rational choice and the framing of decisions[J].Journal of Business,1986,59(4):S251-S278.
[5]ZADEH L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[6]ZADEH L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets&Systems,1978,1(1):3-28.
[7]LIU B,LIU Y K.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Trans.on Fuzzy Systems,2002,10(4):445-450.
[8]LIU B,IWAMURA K.Chance constrained programming with fuzzy parameters[J].Fuzzy Sets&Systems,1998,94(2):227-237.
[9]LIU B,IWAMURA K.A note on chance constrained programming with fuzzy coefficients[J].Fuzzy Sets&Systems,1998,100(1/3):229-233.
[10]LIU B.Minimax chance constrained programming models for fuzzy decision systems[J].Information Sciences,1998,112(1/4):25-38.
[11]LIU B.Dependent-chance programming in fuzzy environments[J].Fuzzy Sets&Systems,2000,109(1):97-106.
[12]LIU B.Uncertainty theory[M].Berlin:Springer-Verlag,2004.
[13]LIU B.Theory and practice of uncertain programming[M].2nd ed.Berlin:Springer,2009.
[14]LIU B,CHEN X.Uncertain multiobjective programming and uncertain goal programming[J].Journal of Uncertainty Analysis&Applications,2015,3(1):1-8.
[15]LIU B,YAO K.Uncertain multilevel programming:algorithm and applications[J].Computers&Industrial Engineering,2015,89:235-240.
[16]GUO J S,WANG Z T,ZHENG M F,et al.Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm[J].Chinese Journal of Aeronautics,2014,27(6):1477-1487.
[17]MA W,CHE Y,HUANG H,et al.Resource-constrained project scheduling problem with uncertain durations and renewable resources[J].International Journal of Machine Learning&Cybernetics,2016,7(4):613-621.
[18]DALMAN H.Uncertain programming model for multi-item solid transportation problem[J].International Journal of Machine Learning&Cybernetics,2018,9(4):559-567.
[19]GUO J,WANG Z,ZHENG M,et al.An approach for UAV reconnaissance mission planning problem under uncertain environment[J].International Journal of Imaging&Robotics,2014,14(3):1-15.
[20]LIU B.Uncertainty theory:a branch of mathematics for modeling human uncertainty[M].Berlin:Springer-Verlag,2010:56-60.