CVaR下基于Ф-散度的单周期库存鲁棒优化模型

The Ф-divergence-based robust optimization model of a single-period inventory under CVaR

在离散随机需求情景及概率不确定条件下,针对风险厌恶的库存管理者,建立了基于条件风险值(CVaR)的单周期库存鲁棒优化模型.在仅知离散需求情景条件下,结合统计学理论,采用Ф-散度构建了一定置信水平下的不确定需求概率的置信域;运用拉格朗日对偶理论,将单周期库存鲁棒优化模型转化为易于求解的数学规划问题.特别地,给出了仅知需求情景数据下,基于数据驱动的单周期库存策略.最后,进行了数值计算,分析了不同风险厌恶程度、Ф-函数形式和抽样规模对库存策略和库存管理者绩效的影响.结果表明,基于Ф-散度的鲁棒库存策略具有良好的鲁棒性,能够有效抑制需求概率不确定性对库存绩效的影响.进一步,与数据驱动结果对比,发现基于Ф-散度的鲁棒库存策略能够保证库存管理者获得更为理想的绩效,表明对需求数据所蕴含的统计信息的挖掘能够有效改进库存管理者的运作绩效.

The robust optimization model of a single-period inventory based on conditional value-at-risk（CVaR） is established for risk-aversion inventory managers under the discrete stochastic demand with uncertain probability.Using φdivergence,the confidence region of the uncertain demand probability with a certain confidence level is constructed based on statistical theory when only knowing discrete demand scenarios.The robust optimization model of a single period inventory is transformed into a tractable one by Lagrange dual theory.Specially,an inventory strategy based on data-driven is proposed in the setting of only demand scenarios are known.At last,some numerical examples are executed to analyze the impacts of the degree of risk-aversion,the different forms of φ-divergence and the number of sampling on inventory strategy and managers＇ performance.The results show that the robust inventory strategy based on φ-divergence is robust to restrain the effects of the uncertain demand probability on the inventory performance.Furthermore,comparing with the results derived by data-driven method,the robust inventory strategy based on φ-divergence can ensure inventory managers to get a more ideal performance which indicates that the mining for statistical information implicit in demand data can effectively improve the inventory managers＇ operation performance.