Abstract: 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.

Key words: inventory, supply and demand uncertainty, conditional value-at-risk, robust optimization, model