1. Analyzing Risks Measurement and Transmission of Supply Chain with Retail Price Fluctuation Yonghong Li Lindu Zhao 2009-10-31

2. Contents 1. Introduction 2. Risks Model of a Supply Chain 3. Transmission Mode Analysis 4. Numerical Example 5. Conclusions and Extensions

3. 1. Introduction Knight the publication of risk, uncertainty and profit March & Shapira et al. define risks as uncertainties Guo and Pu hold risks are the possibility of the risks outcome Kaminsky & Reinhart study the credit risk transfer between different countries Beretta study the risk transmission of financial crisis between different countries and companies

4. 1. Introduction Kraljic propose a combination management framework of procurement Hallikas divide risk factors of network of suppliers into four categories Ojala and Hallikas analyze supplier investment risk, and how each could be managed Wu et al. classify a broader set of supply chain risks as internal and external by the level of controllability Li model supplier risk attitude with respect to risk aversion Ye and Deng analyze the transfer of costs structure when producers implemented VMI services, the transfer of costs structure would cause change of the profits function of the main decision-making agents

5. 1. Introduction Wu & Olson consider three types of risk evaluation models within supply chains Lee et al. consider pricing as a main cause of bullwhip effect, creates adverse effects such as excess inventories, backorders and inefficient use of resources. Özelkan &Cakanyildirim analyze the impact of procurement price variability in the upstream of a supply chain on the downstream Li & Zhao use the variances of profits of supplier and retailer to characterize their risk, respectively and analyze the transmission mode of risk by the difference of variances of profits of retailer and supplier

6. Most papers generalize and introduce supply chain risk just from the micro level Few papers analyze quantificationally the measurement methods, transfer process, and impact extent of risk in a supply chain caused by the fluctuation of price.

7. 2. Risks model of a supply chain c Production cost w Wholesale price d Distribution priceRetail price QdQd The orders of distributor QrQr The orders of retailer M The purchases of supplierMarket demand a The maximum market demand b The price-sensitive coefficient Figure 1. Supply chain flowing model without inventory S upplie r Distribut or Retailer Materials flowCapital flow pdwc

8. To simplify the analysis, assumptions of the paper are as follows: (1)The information of costs structure and market demand of supplier, distributor and retailer are perfect information, and all of the supplier, distributor and retailer are risk-neutral; (2)The supplier, distributor and retailer are independent economic entities; (3)The situations of out of stock and holding inventory are irrespective; (4)The retail price is a random variable;

9. The market demand: The relationships among the orders of retailer, distributor, purchases of supplier and the market demand:

10. The variance of profits of retailer : The variance of profits of distributor : The variance of profits of supplier:

11. 3. Transmission mode analysis There is a ripple effect in a supply chain. Because of the ripple effect, the risk caused by a certain factor will flow along the supply chain when the factor of the chain flows. That is, the risk of downstream echelon caused by factors has changed, there are a series of ripple effects and it will cause the risk of upstream echelon arising from the relevant factors to change. There is reduction effect, invariable effect and amplification effect for the change.

12. Measuring the risk of retailer and distributor by the variances of profits, so the difference of risk is the difference of variances :

13. The difference of risk between distributor and supplier is the difference of variances :

14. Theory: In a three-supply chain system, a reduction effect on risks caused by retail price fluctuation takes place when the wholesale price and distribution price satisfy conditions of

15. 4. Numerical Example Assume that the production cost and wholesale price are c=0.2, the maximum market demand and the price- sensitive coefficient are a=50 and b=0.1. The random variable subjects to the probability density function

16. Table 1. Expectations of retail price The conditions of risks reduction effect is:

17. Figure 2. Cures of distribution price d, wholesale price w and differences

18. From the simulation model: when the wholesale price and distribution price satisfy certain conditions in a three-echelon supply chain, risks of upstream echelon are lower than that of the downstream echelon and it is a reduction effect.

19. 5. Conclusions and Extensions Characterize the risks of supply chain members by variances of profits Analyze the influence of distribution price and wholesale price on the transmission mode of risks caused by price fluctuation in a supply chain When the distribution price and wholesale price satisfy certain conditions, the upstream will suffer lower risks caused by retail price fluctuation than the downstream echelon

20. Further research to characterize the risk of multi-echelon supply chains to research the risk of three-echelon supply chains with inventories to measure the risk when considering the retail price as a random variable by other methods