# Risk Analysis of a Two-Level Supply Chain Subject to Misplaced Inventory
## 2 Literature Review
CVaR was originally developed to measure the risk of possible losses in portfolio selections, and its use has recently been expanded to the field of supply chain management. [PERSON] et al. [38] introduced the concept of CVaR as the evaluation criterion in a supply contract context. They specifically showed that CVaR has advantages over mean-variance and VaR in both theory and practice, such as its coherent, sub-additive, positively homogeneous, and translation invariant characteristics. Moreover, the CVaR approach avoids the computational difficulties encountered by using the VaR approach and the mean-variance approach, and can thus obtain a closed-form solution which offers an explicit relationship between the decision maker's risk attitude and the optimal decisions. We therefore model the retailer's risk aversion by adopting the CVaR decision criterion. There exist some studies applying CVaR to the newsvendor problem. [PERSON] and [PERSON] [39] first adopted CVaR minimization in a newsvendor problem with a risk averse retailer. They showed the good computational characteristics of CVaR such that the CVaR minimization problem can be represented as a linear program. [PERSON] and [PERSON] [40] utilized CVaR as the retailer's objective in a newsvendor model where the demand depended on the marketing effort level and the price. [PERSON] et al. [41] investigated the combined order quantity and price decisions of a risk-averse retailer under the CVaR framework, and established the conditions under which the optimal policy uniquely exists. A supply chain contract under the CVaR framework has recently attracted considerable attention. [PERSON] et al. [42] studied the coordination of the supply chain involving a risk-neutral supplier and a risk-averse retailer with the CVaR criterion. They showed that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff, and quantity flexibility contracts. [PERSON] et al. [43] analyzed a supply chain rebates contract problem and measured the retailer's risk aversion attitude with CVaR. [PERSON] et al. [44] considered a dual channel supply chain consisting of a risk-averse retailer and a risk-neutral supplier under the CVaR framework. A risk-sharing contract is proposed to coordinate the dual-channel supply chain. Although all of these studies incorporate a risk aversion attitude into the decision making process, they do not consider the discrepancy between the actual physical inventory and the recorded inventory information, which is quite a realistic problem in supply chain management. [PERSON] et al. [45] also utilized CVaR to explore the optimal ordering policy of a risk-averse retailer subject to inventory inaccuracy. However, the research only analyzed the problem from the retailer's perspective, and focused on the retailer's incentive for RFID adoption. It has been pointed out that RFID should be implemented in the entire supply chain to improve the supply chain performance [46]. On the other hand, one of the major barriers for RFID implementation in a supply chain is the free-rider problem, which is the phenomenon where the retailer can take advantage of RFID without bearing any cost once RFID tags are attached to the products by the upstream supplier. Consequently, this study extends the previous work by analyzing the inventory inaccuracy problem in a two-level supply chain framework, focusing on synchronizing the incentives of both partners in RFID implementation and deciding how the costs and benefits should be distributed between them. The remainder of this paper is organized as follows. In Section 3, we describe the problem and investigate the decision policies of two cases: (1) information asymmetry about inventory errors exists; and (2) the retailer shares information about inventory errors with the supplier. We further explore the benefits of information sharing by comparing the two cases. Section 4 presents another case when RFID is implemented in the supply chain to enable information integration, as well as to reduce inventory errors.