Article Contents
Article Contents

# Auction and contracting mechanisms for channel coordination with consideration of participants' risk attitudes

• * Corresponding author: Y.C.E. Lee
This research was supported by the Research Committee of The Hong Kong Polytechnic University, the National Natural Science Foundation of China (No.11401331), China Postdoctoral Foundation (No.2016M592148) and the Foundation for Guide Scientific and Technological Achievements of Qingdao (No. 14-2-4-57-jch).
• This paper considers a two-supplier one-retailer coordinated supply chain system with auction and contracting mechanism incorporating participants' risk attitudes. The risk attitude is quantified using the value-at-risk (VaR) measure and the retailer faces a stochastic linear price-dependent demand function. In the supply chain, the suppliers (providing identical products) compete with each other in order to win the ordering contract of the retailer. Several auction and contracting mechanisms are developed and compared. It can be analytically shown that the retail price of the risk-averse system is higher than that of the risk-neutral system, but the order quantity is lower than that of the risk-neutral system.

Mathematics Subject Classification: Primary: 91B26, 91B42; Secondary: 91B24.

 Citation:

• Table 1.  Comparison of the optimal ordering quantities and optimal retail prices obtained under the complete information and asymmetric information situations

 Demand Disturbance $\thicksim$ Exponential Demand Disturbance $\thicksim$ Normal Complete Information Asymmetric Information Complete Information Asymmetric Information $\alpha$ $s_1$ $q_{1,\alpha}^\star$ $r_{1,\alpha}^\star$ $\bar{q}_{1,\alpha}^\star$ $\bar{r}_{1,\alpha}^\star$ $q_{2,\alpha}^\star$ $r_{2,\alpha}^\star$ $\ \bar{q}_{2,\alpha}^\star$ $\bar{r}_{2,\alpha}^\star$ 0.1 10 23.15 19.79 16.47 21.46 24.64 20.16 17.94 21.83 15 13.15 22.29 14.64 22.26 0.05 10 23.50 19.87 16.82 21.54 24.82 20.21 18.14 21.88 15 13.50 22.37 14.82 22.71 0.01 10 24.30 20.08 17.62 21.75 25.17 20.29 18.49 21.96 15 14.30 22.58 15.17 22.79

Table 2.  Comparison of the performance of the simple model with the two-part contract model when the demand disturbance follows an exponential distribution

 Coordinated Policy Independent Policy Two-Part Contract $\alpha$ $s_1$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ 0.1 13 134.00 0.00 134.00 33.50 67.00 100.50 73.54 60.46 134.00 15 43.24 90.76 17 20.94 113.06 0.05 13 138.04 0.00 138.04 34.51 69.02 103.53 76.54 61.50 138.04 15 45.55 92.49 17 22.55 115.49 0.01 13 147.65 0.00 147.65 36.91 73.83 110.74 83.75 63.90 147.65 15 51.14 96.51 17 26.54 121.11

Table 3.  Comparison of the performance of the simple model with the two-part contract model when the demand disturbance follows a normal distribution

 Coordinated Policy Independent Policy Two-Part Contract $\alpha$ $s_1$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ $\Pi_{1,r,\alpha}^\star$ $\Pi_{1,s_1,\alpha}^\star$ $\Pi_{1,SC,\alpha}^\star$ 0.1 13 151.78 0.00 151.78 37.95 75.89 113.84 86.86 64.92 151.78 15 53.58 98.20 17 28.30 123.48 0.05 13 154.04 0.00 154.04 38.51 77.02 115.53 88.57 65.47 154.04 15 54.93 99.11 17 29.28 124.76 0.01 13 158.32 0.00 158.32 39.58 79.16 118.74 91.82 66.50 158.32 15 57.49 100.83 17 31.16 127.16

Table 4.  Comparison of the optimal ordering quantity and the optimal retail price of a risk-averse and a risk neutral supply chain

 Demand Disturbance $\thicksim$ Exponential Demand Disturbance $\thicksim$ Normal Risk Averse Risk Neutral Risk Averse Risk Neutral $\alpha$ $q_{1,\alpha}^\star$ $r_{1,\alpha}^\star$ $q_{1,N}^\star$ $r_{1,N}^\star$ $SL(r_{1,N}^\star)$ $q_{2,\alpha}^\star$ $r_{2,\alpha}^\star$ $q_{2,N}^\star$ $r_{2,N}^\star$ $SL(r_{2,N}^\star)$ 0.1 5.88 12.85 6.62 11.45 0.91 7.37 15.83 8.17 14.52 0.92 0.05 6.22 13.55 7.55 16.19 0.01 7.03 15.16 7.89 16.88
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