具损失厌恶和损失概率厌恶的报童问题研究
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摘要
研究了具损失厌恶和损失概率厌恶行为的考虑缺货成本报童模型。利用订购量小于和大于最大损失等量订购量时的随机利润分布函数以及随机获利和损失的排名函数,获得了报童的前景值函数,分析了报童的前景值函数性质。结果表明:前景值函数为订货量的连续不可微凹函数,不可微点位于最大损失等量订购量处;而且仅具损失厌恶或仅具风险中性的报童模型是本模型的特例。解析分析表明:当最优订购量小于最大损失等量订购量时,最优订购量随极端获利和不利结果重视程度的提高而增加;当最优订购量大于最大损失等量订购量时,最优订购量随极端获利结果重视程度的提高而增加,最优订购量随极端不利结果重视程度的提高而减少。数值结果表明:最优订购量随非极端获利和非极端损失结果敏感度的提高而增加;最优订购量随损失厌恶系数的提高而减少。
It is found that the newsboy has loss of disgust and loss of probability aversion characteristics.In the paper,the Newsboy model with loss aversion and probabilistic loss aversion under shortage cost is studied.Using stochastic profit distribution functions and ranking functions when order quantity is less than maximum loss equivalent and order quantity is greater than maximum loss equivalent,its prospect value function is derived,and the nature of prospect value is revealed.The results show that the prospect value function is a continuous and non differentiable convex function,in which non differentiable points is in maximum loss equivalent;and Newsboy models with loss aversion or risk neutral are its special case.The analysis shows that:under the optimal order quantity being less than the maximum loss equivalent,the optimal order quantity increases with the increase of the degree on the extreme gain and unfavorable results.Under the optimal order quantity being greater than the maximum loss equivalent,the optimal order quantity increases with the increase of the degree on the extreme gain,and the optimal order quantity reduces with the degree on the extreme unfavorable results.The numerical results show that the optimal order quantity increases with the increase of the sensitivity of non extreme gain and non extreme loss.With the increase of the loss aversion coefficient,the optimal order quantity decreases.This study is helpful to understand the impact of the behavioral characteristics of newsboy on decision making.
It is found that the newsboy has loss of disgust and loss of probability aversion characteristics.In the paper,the Newsboy model with loss aversion and probabilistic loss aversion under shortage cost is studied.Using stochastic profit distribution functions and ranking functions when order quantity is less than maximum loss equivalent and order quantity is greater than maximum loss equivalent,its prospect value function is derived,and the nature of prospect value is revealed.The results show that the prospect value function is a continuous and non differentiable convex function,in which non differentiable points is in maximum loss equivalent;and Newsboy models with loss aversion or risk neutral are its special case.The analysis shows that:under the optimal order quantity being less than the maximum loss equivalent,the optimal order quantity increases with the increase of the degree on the extreme gain and unfavorable results.Under the optimal order quantity being greater than the maximum loss equivalent,the optimal order quantity increases with the increase of the degree on the extreme gain,and the optimal order quantity reduces with the degree on the extreme unfavorable results.The numerical results show that the optimal order quantity increases with the increase of the sensitivity of non extreme gain and non extreme loss.With the increase of the loss aversion coefficient,the optimal order quantity decreases.This study is helpful to understand the impact of the behavioral characteristics of newsboy on decision making.
引文
[1]陈杰,唐萍,高腾.带有多元马氏需求的多产品报童模型[J].中国管理科学,2017,25(2):57-67.
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[12]周永务,肖旦,李绩才.损失规避零售商订货量与广告费用的联合决策[J].系统工程理论与实践,2012,32(8):1727-1738.
[13]柳键,邱国斌,黄健.面对损失厌恶顾客的零售商订货定价策略及激励问题[J].控制与决策,2014,29(1):107-112.
[14]Baron O,Hu Ming,Najafi-Asadolahi S,et al.Newsvendor selling to loss-averse consumers with stochastic reference points[J].Manufacturing&Service Operations Management,2015,17(4):456-469.
[15]张鹏,张杰,马俊.两种需求情形下损失规避零售商的最优订货-定价联合决策[J].控制与决策,2015,30(10):820-827.
[16]周艳菊,应仁仁,陈晓红,等.基于前景理论的两产品报童的订货模型[J].管理科学学报,2013,16(11):17-29.
[17]Geng Wei,Zhao Xiaobo,Gao Deng.A single-period inventory system with a general S-shaped utility and exponential demand[J].Journal of Systems Science and Systems Engineering,2010,19(2):227-236.
[18]刘咏梅,成尚汶,谢虎.具有损失厌恶偏好零售商的供应链弹性数量契约[J].控制与决策,2012,27(7):975-982.
[19]胡劲松,赵光丽.具有损失规避零售商的模糊供应链网络均衡[J].控制与决策,2014,(10):1899-1906.
[20]胡劲松,朱太硕,王永波.损失概率厌恶和损失厌恶行为零售商的供应链网络均衡[J].控制与决策,2016,31(7):1296-1304.
[2]张永,张卫国,徐维军.无统计信息假设下的多阶段报童决策[J].中国管理科学,2015,23(5):107-115.
[3]陈杰,陈志祥,邢灵博,等.带有能力约束的多元马氏需求报童模型[J].管理科学学报,2016,(7):37-49.
[4]Loewensteiin G F,Weber E U,Hsee C K,et al.Risk as feelings[J].Psychological bulletin,2001,127(2):267-286.
[5]Tversky A,Kahneman D.Advances in prospect theory:Cumulative representation of uncertainty[J].Journal of Risk and uncertainty,1992,5(4):297-323.
[6]Quiggin J.A theory of anticipated utility[J].Journal of Economic Behavior&Organization,1982,3(4):323-343.
[7]Schmidt U,Zank H.Risk aversion in cumulative prospect theory[J].Management Science,2008,54(1):208
[8]Schweitzer M E,Cachon G P.Decision bias in the newsvendor problem with a known demand distribution:Experimental evidence[J].Management Science,2000,46(3):404-420.
[9]文平.损失厌恶的报童-预期理论下的报童问题新解[J].中国管理科学,2005,13(6):64-68.
[10]Wang C X,Webster S.The loss-averse newsvendor problem[J].Omega,2009,37(1):93-105.
[11]Shen Houcai,Pang Zhan,Cheng T C E.The component procurement problem for the loss-averse manufacturer with spot purchase[J].International Journal of Production Economics,2011,132(1):146-153.
[12]周永务,肖旦,李绩才.损失规避零售商订货量与广告费用的联合决策[J].系统工程理论与实践,2012,32(8):1727-1738.
[13]柳键,邱国斌,黄健.面对损失厌恶顾客的零售商订货定价策略及激励问题[J].控制与决策,2014,29(1):107-112.
[14]Baron O,Hu Ming,Najafi-Asadolahi S,et al.Newsvendor selling to loss-averse consumers with stochastic reference points[J].Manufacturing&Service Operations Management,2015,17(4):456-469.
[15]张鹏,张杰,马俊.两种需求情形下损失规避零售商的最优订货-定价联合决策[J].控制与决策,2015,30(10):820-827.
[16]周艳菊,应仁仁,陈晓红,等.基于前景理论的两产品报童的订货模型[J].管理科学学报,2013,16(11):17-29.
[17]Geng Wei,Zhao Xiaobo,Gao Deng.A single-period inventory system with a general S-shaped utility and exponential demand[J].Journal of Systems Science and Systems Engineering,2010,19(2):227-236.
[18]刘咏梅,成尚汶,谢虎.具有损失厌恶偏好零售商的供应链弹性数量契约[J].控制与决策,2012,27(7):975-982.
[19]胡劲松,赵光丽.具有损失规避零售商的模糊供应链网络均衡[J].控制与决策,2014,(10):1899-1906.
[20]胡劲松,朱太硕,王永波.损失概率厌恶和损失厌恶行为零售商的供应链网络均衡[J].控制与决策,2016,31(7):1296-1304.