基于CVaR准则下的二层报童问题模型研究
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摘要
报童问题是供应链管理中的经典库存决策模型之一,也被称为单周期库存问题。它研究的是在随机市场环境下,零售商寻求使其利润达到最大化的订购量。随着其在经济生活中作用的日益突出,报童问题已经成为众多学者研究的热门课题。
本文首先对经典报童问题做了简要的介绍。随着它受到众多学者的关注,出现了多方面的扩展模型。对于这些扩展模型做了相关综述,并对其中一种十分重要的扩展模型——二层报童问题进行了阐述。
接着,本文阐述了带有风险规避的报童问题。结合主要的三种风险度量准则,对报章问题分别在其度量下的相关模型的发展状况进行了介绍。作为一种应用非常广泛的风险度量准则,条件风险值CVaR具有良好的计算特性和应用性,为此特别阐述了基于CVaR准则下的报童问题研究情况。
随后,结合条件风险值CVaR和二层报童问题,讨论了两种基于CVaR准则下的二层报童问题模型。一种是没有缺货惩罚时上层供应商为风险中性,下层零售商为风险厌恶的二层报童问题模型;另一种是没有缺货惩罚时上层供应商和下层零售商都为风险厌恶的二层报童问题模型。考虑到随机市场需求的不确定性和部分商品的不可储存性,决策者一般都是风险厌恶的,他们希望在规避风险的情况下获得最大利润。因此,利用CVaR准则对风险进行度量建立了上述两种模型。针对这两种模型分别设计了相应的求解算法并给出了两个算例。通过实例分析表明,在两种模型的条件下,供应商可确定适当的批发价格,零售商可以对买进多少订购量做出最佳的决策,使得各自获得最大的利润。
Newsboy problem is a classical inventory model of supply chain management, and it's also a single period inventory problem .It is to find the order quantity which maximizes the profit of retailer in the random market. Along with newsboy problem development, a lot of scholars study it.
Firstly, this paper introduces the classical newsboy problem. With its attention by many scholars, the expansions of newsboy problem have been proposed. We give a summary of these expansions, and elaborate an important model of the expansions -tow-echelon newsboy problem.
Secondly, this paper elaborates the newsboy problem with risk aversion. Based three of the major risk measurement criteria, the newsboy problem in its measurement of the development of related models are introduced. As a widely used risk measurement criteria, Conditional Value-at-Risk has a good calculating character and application. For this reason, we elaborate the research situation of newsboy problem with CVaR criteria specially.
Finally, combined with CVaR and tow-echelon newsboy problem, two models for tow-echelon newsboy problem with CVaR are studied when there is no lost sale penalty cost. In one model, the upper level is supplier with risk neutral and the lower level is retailer with risk aversion. In the other model, the supplier and retailer are all risk averse. Considering the random market demand is uncertain and some products can not be stored, decision-makers who want to gain the greatest profits under the lowest risk are risk averse. We design corresponding algorithms and give two examples for the models. According to the analyzing results of concrete examples, it shows that the suppliers can confirm an optimum price and the retailers can make the best decision for the purchasing amount to maximize their profit in the models.
本文首先对经典报童问题做了简要的介绍。随着它受到众多学者的关注,出现了多方面的扩展模型。对于这些扩展模型做了相关综述,并对其中一种十分重要的扩展模型——二层报童问题进行了阐述。
接着,本文阐述了带有风险规避的报童问题。结合主要的三种风险度量准则,对报章问题分别在其度量下的相关模型的发展状况进行了介绍。作为一种应用非常广泛的风险度量准则,条件风险值CVaR具有良好的计算特性和应用性,为此特别阐述了基于CVaR准则下的报童问题研究情况。
随后,结合条件风险值CVaR和二层报童问题,讨论了两种基于CVaR准则下的二层报童问题模型。一种是没有缺货惩罚时上层供应商为风险中性,下层零售商为风险厌恶的二层报童问题模型;另一种是没有缺货惩罚时上层供应商和下层零售商都为风险厌恶的二层报童问题模型。考虑到随机市场需求的不确定性和部分商品的不可储存性,决策者一般都是风险厌恶的,他们希望在规避风险的情况下获得最大利润。因此,利用CVaR准则对风险进行度量建立了上述两种模型。针对这两种模型分别设计了相应的求解算法并给出了两个算例。通过实例分析表明,在两种模型的条件下,供应商可确定适当的批发价格,零售商可以对买进多少订购量做出最佳的决策,使得各自获得最大的利润。
Newsboy problem is a classical inventory model of supply chain management, and it's also a single period inventory problem .It is to find the order quantity which maximizes the profit of retailer in the random market. Along with newsboy problem development, a lot of scholars study it.
Firstly, this paper introduces the classical newsboy problem. With its attention by many scholars, the expansions of newsboy problem have been proposed. We give a summary of these expansions, and elaborate an important model of the expansions -tow-echelon newsboy problem.
Secondly, this paper elaborates the newsboy problem with risk aversion. Based three of the major risk measurement criteria, the newsboy problem in its measurement of the development of related models are introduced. As a widely used risk measurement criteria, Conditional Value-at-Risk has a good calculating character and application. For this reason, we elaborate the research situation of newsboy problem with CVaR criteria specially.
Finally, combined with CVaR and tow-echelon newsboy problem, two models for tow-echelon newsboy problem with CVaR are studied when there is no lost sale penalty cost. In one model, the upper level is supplier with risk neutral and the lower level is retailer with risk aversion. In the other model, the supplier and retailer are all risk averse. Considering the random market demand is uncertain and some products can not be stored, decision-makers who want to gain the greatest profits under the lowest risk are risk averse. We design corresponding algorithms and give two examples for the models. According to the analyzing results of concrete examples, it shows that the suppliers can confirm an optimum price and the retailers can make the best decision for the purchasing amount to maximize their profit in the models.
引文
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[3]Khouja M.The single-period newsvendor problem:literature Review and suggestions for future research[J].Omega,1999,27:537-553.
[4]Lau A and Lau H.Maximizing the probability of achieving a target profit level in a two-product newsboy problem[J].Decision Sciences,1988,19:392-408.
[5]Eeckhoudt L,Gollier C and Schlesinger H.The risk averse(and prudent)newsboy[J].Management Science,1995,41:786-794.
[6]Agrawal V and Seshadri S.Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem[J].Manufacturing & Service Operations Management,2000,2:410-423.
[7]Chen F and Federgruen A.Mean-Variance Analysis of Basic Inventory Moodels[R].Columbia University,New York,NY 10027,2000.
[8]Parlar M and Weng Z K.Balancing desirable but conflicting objectives in the newsvendor problem[J].IIE Transactions,2003,35:131-142.
[9]Chen X,Sim M,Simchi-Levi D and Sun P.Risk aversion in inventory management[R].MIT,Cambridge,MA,2003.
[10]许明辉,于刚,张汉勤.带有缺货惩罚的报童问题模型中的CVaR研究[J].系统工程理论与实践,2006,10:1-8.
[11]Gotoh J and Takano Y.Newsvendor solution via conditional value-at-risk minimization[J].European Journal of Operational Research,2007,179:80-96.
[12]Pasternack B A.Optimal pricing and return policies for perishable commodities[J].Marketing Science,1985,4:166-176.
[13]Iyer A V and Bergen M E.Quick response in manufacturer-retailer channels[J].Management Science,1997,43:559-570.
[14]Lau A H L and Lau H S.Some two-echelon style-goods inventory models with asymmetric market information[J].European Journal of Operational Research,2001,13:29-42.
[15]Lau A H L and Lau H S.Comparative normative optimal behavior in two-echelon multiple-retailer distribution systems for a single-period product[J].European Journal of Operational Research,2003,144:659-676.
[16]Yang Shanlin and Zhou Yongwu.Two-echelon supply chain model:Considering duopolistic retailer's different competitive behaviors[J].Inter.J.Production Economics,2006,103:104-116.
[17]万仲平,肖昌育,王先甲等.不确定电力市场下最优竞价策略的一种二层规划模型[J].电力系统自动化,2004,28(19):12-16.
[18]李善良,朱道立.逆向信息和道德风险下的供应链线性激励契约研究[J].运筹学学报,2005,9(2):21-29.
[19]Sethi S P,Yan Houmin and Zhang Hanqin.Inventory and supply chain management with forecast updates[J].Springer,2005.
[20]候阔林.合约决策条件下的二层报童问题模型与算法研究:[硕士学位论文].武汉:武汉大学数学与统计学院,2007.
[21]Jucker J V and Rosenblatt M J.Single-period inventory models with demand uncertainty and quantity discouts:behavioral implications and a new solution procedure[J].Naval Research Logistics Quarterly,1985,32:537-550.
[22]Lin C and Kroll D E.The single-item newsboy problem with dual performance measures and models and quantity discouts[J].European Journal of Operational Reseach,1997,100:562-565.
[23]Lau Amy Hing Ling,Lau Hon-Shiang and Wang Jian-Cai.Designing a quantity discout Scheme for a newsvendor-type product with numerous heterogeneous retailers[J].European Journal of Operational Reseach,2007,180(2):585-600.
[24]Monstard Julien and Teunter Ruud.The newsboy problem with resalable returns:A single period model and case study[J].European Journal of Operational Reseach,2006,169(1):81-96.
[25]Lee Chang Hwan and Rhee Byong-Duk.Channel coordination using product returns for a supply chain with stochastic salvage capacity[J].European Journal of Operational Reseach,2007,177(1):214-238.
[26]Zhang Long,Song Shiji and Wu Cheng.Supply coordination of loss-averse newsvendor with contract[J].Tsinghua Science & Technology,2005,10(2):133-140.
[27]吴鹏.考虑回收再制造的报童模型扩展[J].清华大学学报(哲学社会科学版),2006,21(S1):71-76.
[28]Arecelus F J,Kumar Satyendra and Srinivasan G.Evaluating manufacturer's buyback policies in a single-period two-echelon framework under price-dependent stochastic demand[J].Omega,2008,in press.
[29]Whitin T M.Inventory control and price theory[J].Management Science,1955,2:61-68.
[30]Lau A and Lau H.The newsboy problem with price-dependent demand distribution[J].IIE Trans,1988,20:168-175.
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