供需不确定条件下基于CVaR的零售商库存鲁棒优化模型

在经典报童模型下考虑供应和需求不确定性，研究了具有风险厌恶的零售商库存优化问题。采用条件风险值（CVaR）对库存绩效进行度量，构建了基于CVaR的零售商库存运作模型；在此基础上，考虑上游供应商供货能力和下游市场需求不确定性，并采用一系列未知概率的离散情景进行描述，给出了供需不确定条件下基于CVaR的零售商库存鲁棒优化模型。进一步，采用区间不确定集对未知情景概率进行建模，给出了基于最大最小准则的鲁棒对应模型。针对同时考虑供需不确定性导致的模型非凸性，采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不同风险厌恶程度和不确定性程度对零售商库存决策以及库存绩效的影响。结果表明，供需不确定性的存在虽然会导致零售商库存绩效损失，但损失值较小。特别地，依据文中模型得到的鲁棒库存策略在多数情况下能够保证零售商获得更优的库存绩效。此外，不确定性和风险厌恶程度的增加虽然会影响零售商库存决策和运作绩效，但在同等风险厌恶态度下，随着不确定性程度的增加，基于文中方法得到的鲁棒库存策略仍能确保零售商获得理想的库存绩效，表明文中所建模型在应对供需不确定性方面具有良好的鲁棒性。

The CVaR-based Robust Optimization Model for Retailer's Inventory Management under Supply and Demand Uncertainties

Inventory management under uncertainty has been extensively studied in the past. However, most of literature focuses on finding optimal inventory policies for management under demand uncertainty while as suming no uncertainty on the supply side.As supply chains have been growing considerably, supply uncertainty that often arises from higher variability in suppliers' operations can adversely impact the performance of an inventory system, which suggests a need to simultaneously incorporate supply and demand uncertainties into inventory management.In this paper, the problem of inventory management for a risk-averse retailer is studied under both supply and demand uncertainties based on the classic newsvendor model. To cope with the risk caused by uncertainty, the conditional value-at-risk (CVaR) is used to measure the retailer's inventory performance, and then a CVaR-based inventory operational model is developed. Based on which the uncertainties in both the upstream supplier's supply capacity and the downstream market demand are considered.A series of discrete scenarios with unknown probabilities are used to describe uncertainties, and the CVaR-based robust optimization model for retailer's inventory management is established. To solve the proposed robust optimization model, the max-min robust counterpart is presented underthe box uncertainty set to which the unknown supply and demand scenarios probabilities belong. To deal with the non-convexity caused by considering supply and demand uncertainties simultaneously, the so-called canonical duality theory is introduced to equivalently transform the developed robust optimization model into a tractable mathematical programming problem.At last, some numerical examples are executed to analyze the impact of different risk aversion levels and uncertainty degrees on retailer's inventory strategy and operational performance. The results show that, although the existence of uncertainty in supply and demand will lead to the loss of inventory performance, the loss is very limited. Specially, the robust inventory strategy derived from the model developed in this paper can ensure a preferable inventory performance for the retailer in most cases. In addition, although the retailer's inventory strategy and performance will deteriorate as the increasing of the risk averse levels and uncertainty degrees, the robust inventory strategy can still ensure the retailer obtain the ideal performance as the increasing of the uncertainty degree under the same risk averse level, which indicates that the model developed in this paper possesses well robustness in dealing with both supply and demand uncertainty.