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针对具有风险厌恶的零售商,建立了权衡期望利润和条件风险值(CVaR)的均值-风险库存优化模型,给出了离散需求分布不确定条件下能实现帕累托最优但具有较高保守性和非帕累托最优但具有较低保守性的两种鲁棒对应。针对不确定需求分布,在仅知历史需求样本数据情况下,应用统计推断理论构建了满足一定置信水平的基于似然估计的需求概率分布不确定集。在此基础上,运用拉格朗日对偶理论,将上述两种鲁棒对应模型转化为易于求解的凹优化问题,并证明了其与原问题的等价性。最后,针对实际案例进行了数值计算,分析了不同系统参数和样本规模对零售商最优库存决策及其运作绩效的影响,并给出了零售商期望利润和条件风险值两个目标权衡的帕累托有效前沿。结果表明,采用基于似然估计的鲁棒优化方法得到的零售商库存策略具有良好鲁棒性,能够有效抑制需求分布不确定性对零售商库存绩效的影响。而且,历史需求样本规模越大,鲁棒库存策略下的零售商运作绩效越接近最优情况。进一步,通过对比发现,两种鲁棒对应模型虽然保守性不同,但在最终库存策略上保持一致。
Aiming at a retailer with risk aversion, an averaging-risk inventory optimization model is proposed to weigh the expected profit and condition risk value (CVaR). The optimal Pareto-optimal but highly conservative Both robust and non-Pareto optimal but low-conservative robust correspondences. In view of the distribution of uncertain demand, based on the historical demand sample data, the set of uncertain demand probability distributions based on the likelihood estimation is constructed by applying statistical inference theory. On this basis, Lagrange’s duality theory is used to convert the above two robust corresponding models into easy-to-solve concave optimization problems, and to prove its equivalence with the original problem. Finally, the numerical calculation is carried out for the actual case, the influence of different system parameters and sample size on the optimal inventory decision of retailer and its operational performance is analyzed, and the relationship between retailer’s expected profit and conditional risk value is given. Efficient frontier. The results show that the retailer’s inventory strategy, which is based on the robust optimization method based on likelihood estimation, has good robustness and can effectively restrain the impact of uncertainty of demand distribution on retailer’s inventory performance. Moreover, the larger the sample size of historical demand, the closer the retailer’s operational performance under the robust inventory strategy is to the optimal situation. Further, by comparison, we found that although the two robust corresponding models are conservative, they are consistent in the final inventory strategy.