二阶随机占优约束下考虑订购能力的多产品报童问题  

Multi-product Newsvendor Problem with Constraints of Second Order Stochastic Dominance and Order Capability

作　　者：付永彬 孙海琳 FU Yong-bin;SUN Hai-lin(School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023)

机构地区：[1]南京师范大学数学科学学院

出　　处：《工程数学学报》2020年第1期1-15,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11571178;11571056)~~

摘　　要：在不确定环境下的报童问题中,利用风险度量去对抗未来的不确定性,是帮助决策者规避风险的重要方法.二阶随机占优(Second order Sto chastic Dominance,SSD)是一种稳健的风险度量.本文首先提出一种带有SSD约束及订购能力约束的风险厌恶多产品报童模型(SSD模型).其次,采用样本均值逼近(Sample Average Approximation,SAA)方法近似该问题,并对SAA问题进行收敛性分析.最后,在数值实验部分,用切平面法求解SAA问题,并同时与基于风险中性(无风险约束)和风险厌恶(以方差为风险约束)假设下的参照模型进行比较.数值结果表明相对于参照模型,在样本外预测下SSD模型可以更好地规避风险,得到更高的收益.Under on uncertain environment,using risk measure to resist the future uncer-tainties is an imp ortant way to avoid risks in newsvendor problem.Second order Stochastic Dominance(SSD)can be used as a robust risk measure.In this paper,we propose a risk aversion multi-product newsvendor mo del(SSD model)with SSD constraints and capability constraint.Moreover,the sample average approximation(SAA)method is used to approxi-mate the problem,and the convergence analysis of the SAA problem is studied.Finally,in the numerical exp eriments section,we use the cutting plane metho d to solve SAA problem,at the same time it is compared with the reference mo dels based on risk neutral(without risk constraints)and risk aversion(with variance as risk constraints).The numerical results show that the SSD model can avoid risks b etter and get higher return than the reference mo dels under out-of-sample forecast.

关 键 词：报童问题 二阶随机占优 订购能力 切平面法 样本均值逼近 

分 类 号：O221.5[理学—运筹学与控制论] F224.3[理学—数学]