二阶随机占优约束下考虑订购能力的多产品报童问题

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 Stochastic 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．

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

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.