CVaR准则下的双层供应链风险决策模型

A Bilevel Risk Decision-making Model in Supply Chain Based on CVaR

在供应商和零售商组成的供应链系统中,我们引入了奖励策略,用于研究在由于需求不确定性和供需双方不平衡性所产生风险损失的条件下,零售商和供应商的双层风险决策问题。首先,证明了零售商在损失条件风险值CVaR(Conditional Value-at-Risk)最小化时最优订货量的解析解。然后,以供应商为领导层,零售商为从属层,给出了基于CVaR准则下的供应链双层风险决策模型(即双层规划)。最后,通过算例分析说明:奖励策略能有效的降低需求不确定性和供需双方不平衡性产生的风险,有效地激励供应链的下游决策者订购更多的商品,达到风险共担利润共享的局面;并且,对于供应链参与双方,风险承担能力越强,获得的利润也越高。

Many multi-level decision problems exist in the supply chain management field. Demand uncertainty underlies these problems and can cause the bullwhip effect and decision-making mistakes. At present, the main method of solving these problems is to integrate the Newsboy model with the expected profit maximum or the expected loss minimization to construct a multi-level programming model. Many scholars have studied supply-chain network equilibrium model, inventory control model, and Staekelberg model, as well as introduced concepts such as contract or marketing strategy. To some extent, these researches have provided clear directions for supply-chain participants to make decisions. However, these studies have the limitation of clearly describing the supply-chain expected loss tail risk. To overcome the limitation, some scholars adopt the conditional value at risk in the financial area and apply such concept to supply-chain procurement- and risk-decision problems. In fact, major risks in a supply cbain come from demand uncertainty and supply-demand disequilibrium. The paper first introduces the conditionalvalue-at-risk （CVaR） model, which is used to measure the tail risk, and defines VaR （value-at-risk） and CVaR. When the supplier＇ s wholesale price is fixed, we present a risk decision-making model of retailer, and solve the optimal order quantity of retailer under a reward strategy, which satisfies the condition of loss condition value-at-risk minimization. Second, when the supplier＇ s wholesale price-is not fixed, we, based on CVaR, present a bilevel risk decision-making model of both retailer and supplier, in which supplier is considered as a decision maker at the upper level and retailer as the follower at the lower level. The upper-level objective function is to maximize the expected profit with the constraint that the loss does not exceed the expected one. The lower-level objective function is to minimize the risk of CVaR loss. Finally, we give a practical example to demonstrate the use of the bilevel risk decision-making model. Four cases are analyzed and compared. Numerical results show that the reward strategy can effectively reduce the risks caused by demand uncertainty and supply-demand disequilibrium, and can stimulate decision-makers in the downstream supply chain to order more goods, share profits, and minimize risks. This study shows that the stronger risk-taking ability, the higher the profit by analyzing the factors that influence the joint decision-making process of retailer and supplier.