不确定条件下的零售商库存鲁棒均值-CVaR决策模型

Robust mean-CVaR-based inventory decision model for retailer under uncertainty

针对风险厌恶零售商,考虑上游供给和下游需求不确定性,研究了权衡期望利润和条件风险值(CVaR)的库存优化问题。针对供需不确定性,采用离散情景进行描述,并将情景概率建模为椭球不确定集,给出了鲁棒对应模型。针对鲁棒对应模型的非凸性,利用标准对偶理论将其转化为易于求解的数学规划问题。最后,通过数值计算分析了风险厌恶程度、乐观系数以及不确定性程度对库存决策、期望利润及CVaR的影响,给出了期望利润和CVaR两个目标权衡的帕累托有效前沿。结果表明,依据所提方法获得的库存策略能够有效抑制供需不确定性扰动。在特定风险厌恶程度和乐观水平下,随着不确定程度的增加,基于文中模型获得的库存策略仍能确保较低的绩效损失,具有良好的鲁棒性。

Aiming at the risk-averse retailers,the inventory model was developed by making trade-off between the expected profit and the Conditional Value-at-Risk(CVaR).Both the demand uncertainty from the downstream markets and the supply uncertainty from the upstream suppliers were considered into the model.The discrete scenarios were used to represent these uncertainties and the ellipsoid uncertainty set was constructed to describe the unknown probabilities,based on which the robust counterpart was presented.To deal with the non-convexity of the robust counterpart,the canonical duality theory was introduced to transform it into a tractable mathematical programming problem.The numerical studies were conducted to investigate the impacts of the risk averse level,the optimism coefficient and the uncertainty level on the order decision,the expected profit and the performance of CVaR.Moreover,the Pareto effective frontier was obtained by making tradeoff between the expected profit and CVaR.Simulation results suggested that the corresponding inventory policies could restrain the disturbance of uncertain parameters effectively.Furthermore,for retailers with the same risk averse level and optimism coefficient,inventory policies obtained by this study could ensure a low performance loss regardless of the increase in uncertainty level,demonstrating the favorable robustness of the proposed inventory model.