Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

doi:10.12005/orms.2020.0100

运筹与管理 ›› 2020, Vol. 29 ›› Issue (4): 138-146.DOI: 10.12005/orms.2020.0100

Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

周赛玉, 王长军, 邵栗

东华大学旭日工商管理学院,上海 200051

收稿日期:2017-05-17 出版日期:2020-04-25
作者简介:周赛玉(1995-),女,安徽宿州人,硕士研究生,研究方向:运筹建模与优化;王长军(1976-),通讯作者,男,安徽巢湖人,副教授, 研究生导师,研究方向:运筹优化及其应用, 运作管理等;邵栗(1993-),女,湖南石门人,硕士研究生, 研究方向:报童建模与应用。
基金资助:
国家自然科学基金资助项目(71572033,71832001);上海市哲学社会科学规划基金项目(2019BGL036)

Decision on Single-Period Optimal Order Quantity by Using Copula-CVaR Based on Stochastic Cost and Price

ZHOU Sai-yu, WANG Chang-jun, SHAO Li

Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China

Received:2017-05-17 Online:2020-04-25

摘要/Abstract

摘要： 不确定环境下的单周期最优订货量决策具有重要且广泛的应用价值。与传统的仅考虑需求不确定性的报童模型不同,本文考虑市场价格恒定,但成本和需求随机变化且相关联下的报童决策问题。为此,采用Copula函数构建成本和需求之间的关联,考虑决策者可能具有的风险态度,建立了相应的Copula-CVaR模型,证明了模型解的存在性和唯一性,并将模型离散化为易求解的线性规划问题。最后,通过不同的风险水平和多种Copula函数下的仿真,分析了随机成本与需求的相关性和波动性对最优决策结果影响,并得到相关结论,为相关企业决策提供依据。

关键词: Copula函数, 条件风险价值, 报童模型, 蒙特卡洛模拟, 线性规划

Abstract: The decision of single-period optimal order quantity under uncertain environment is a very important issue which has been widely applied. Different from the traditional newsvendor model concerning uncertain demand merely, a newsvendor decision-making problem under given price and stochastic and correlative demand and cost is investigated in this paper. Therefore, a corresponding Copula-CVaR model is proposed, and then, the existence and uniqueness of the solution are proved. Moreover, by discretization, a tractable linear programming model is developed. Finally, the experiment simulation is conducted to analyse the relation between optimal decisions with correlation and violation of uncertain cost and demand under different Copulafunctions and different risk attitudes. Several results are obtained which can provide the guidance for the enterprises.

Key words: copula function, conditional value-at-risk, newsvendor model, monte carlo simulation, linear programming

中图分类号:

C934

周赛玉, 王长军, 邵栗. Copula-CVaR下考虑随机成本和需求的单周期订货决策研究[J]. 运筹与管理, 2020, 29(4): 138-146.

ZHOU Sai-yu, WANG Chang-jun, SHAO Li. Decision on Single-Period Optimal Order Quantity by Using Copula-CVaR Based on Stochastic Cost and Price[J]. Operations Research and Management Science, 2020, 29(4): 138-146.

参考文献

[1] Haresh G, Christopher Tang S. Note: optimal ordering decisions with uncertain cost and demand forecast updating[J]. Management Science, 1999, 45(10): 1456-1462.
[2] Chen S, Lee H, Moinzadeh K. Supply chain coordination with multiple shipments: the optimal inventory subsidizing contracts[J]. Operations Research, 2016, 64(6): 1320-1337.
[3] Khouja M. The single-period(news-vendor)problem: literature review and suggestions for future research[J]. Omega, 1999, 27(5): 537-553.
[4] Qin Y, Wang R, Vakharia A J, et al. The newsvendor problem: review and directions for future research[J]. European Journal of Operational Research, 2011, 213(2): 361-374.
[5] 许民利,李展.需求依赖于价格情境下基于Copula-CVaR的报童决策[J].控制与决策,2014(6):1083-1090.
[6] Sklar A. Fonctions de répartition àn dimensions et leurs marges[J]. Publication Institute Statistical University Paris, 1959, 8(2): 229-231.
[7] Embrechts P, Resnick S I, Samorodnitsky G. Extreme value theory as a risk management tool[J]. North American Actuarial Journal, 1999, (3): 1-22.
[8] 任仙玲,张世英.基于核估计及多元阿基米德Copula的投资组合风险分析[J].管理科学,2007,20(5):92-97.
[9] 周孝华,张保帅,董耀武.基于Copula-SV-GPD模型的投资组合风险度量[J].管理科学学报,2012,15(12):70-78.
[10] Koliai L. Extreme risk modeling: an EVT-pair-copulas approach for financial stress tests[J]. Journal of Banking & Finance, 2016, 70: 1-22.
[11] Aydln B, Guler K, Kayls E. A copula approach to inventory pooling problems with newsvendor products[J]. Mathematics, 2012, 176: 81-101.
[12] Artzner P, Delbaen F. Coherent measure of risk[J]. Mathematical Finance, 1999, 9(3): 203-228.
[13] Carlo A, Claudio N, Carlo S. Expected shortfall as a tool for financial risk management[DB/OL]. http://www.gloriamundi.org/VaR/VW, 2001.
[14] Ben-Tal A, El Ghaoui L, Nemirovski A. Robust optimization[M]. New Jersey: Princeton University Press, 2009.
[15] 刘慧,杨超.需求不确定的服务设施网络设计模型鲁棒性研究[J].运筹与管理,2016,25(1):117-125.
[16] Rockafellar R T, Uryasev S. Optimization of conditional Value-at-risk[J]. Journal of Risk, 1999, 29(1): 1071-1074.
[17] Jammernegg W, Kischka P. Handbook of newsvendor problems[M]. Springer, International Series in Operations Research and Management Science, 2012. 197-216.
[18] Adam K, Sylwia S. Portfolio optimization with a copula-based extension of conditional value-at-risk[M]. Annals of operations research, 2016, 237(1): 219-236.
[19] 杨湘豫,赵婷.基于Copula的沪、深、港股票市场的组合风险度量[J].统计与决策,2010,(14):125-127.
[20] Nelson R B. An introduction to copulas[M]. New York: Springer, 2006. 18-22.
[21] 杨士林,彭良雪.二重积分定义的函数求导[J].高等数学研究,2006,9(2):40-41.
[22] Kao L J, Wu P C, Lee C F. An assessment of copula functions approach in conjunction with factor model in portfolio credit risk management[M]. New York: Springer, 2015.
[23] Renard B, Lang M. Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology[J]. Advances in Water Resources, 2007, 30(4): 897-912.
[24] 战雪丽,张世英.基于Copula-SV模型的金融投资组合风险分析[J].系统管理学报,2007,16(3):302-306.
[25] 陆静,张佳.基于极值理论和多元Copula函数的商业银行操作风险计量研究[J].中国管理科学,2013,21(3):11-19.
[26] 王久胜,包卫军,胡杰.基于多维Gumbel Copula函数的投资组合VaR分析[J].数理统计与管理,2010,29(1):137-143.
[27] Mccullough B D. Random number generation and Monte Carlo methods[J]. Technometrics, 2004, 46(2): 252-253.

Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

Decision on Single-Period Optimal Order Quantity by Using Copula-CVaR Based on Stochastic Cost and Price

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