# American Institute of Mathematical Sciences

• Previous Article
Some characterizations of robust optimal solutions for uncertain fractional optimization and applications
• JIMO Home
• This Issue
• Next Article
Hidden Markov models with threshold effects and their applications to oil price forecasting
April  2017, 13(2): 775-801. doi: 10.3934/jimo.2016046

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

 1 College of Business, Qingdao University, Qingdao, Shandong, China 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

* Corresponding author: Y.C.E. Lee

Received  July 2014 Revised  June 2016 Published  August 2016

Fund Project: 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.

Citation: Cheng Ma, Y. C. E. Lee, Chi Kin Chan, Yan Wei. Auction and contracting mechanisms for channel coordination with consideration of participants' risk attitudes. Journal of Industrial & Management Optimization, 2017, 13 (2) : 775-801. doi: 10.3934/jimo.2016046
##### References:

show all references

##### References:
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
 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
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
 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
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
 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
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
 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
 [1] Tinghai Ren, Kaifu Yuan, Dafei Wang, Nengmin Zeng. Effect of service quality on software sales and coordination mechanism in IT service supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021165 [2] Wei Chen, Yongkai Ma, Weihao Hu. Electricity supply chain coordination with carbon abatement technology investment under the benchmarking mechanism. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020175 [3] Feimin Zhong, Wei Zeng, Zhongbao Zhou. Mechanism design in a supply chain with ambiguity in private information. Journal of Industrial & Management Optimization, 2020, 16 (1) : 261-287. doi: 10.3934/jimo.2018151 [4] Jing Feng, Yanfei Lan, Ruiqing Zhao. Impact of price cap regulation on supply chain contracting between two monopolists. Journal of Industrial & Management Optimization, 2017, 13 (1) : 349-373. doi: 10.3934/jimo.2016021 [5] Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103 [6] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effect of disruption risk on a supply chain with price-dependent demand. Journal of Industrial & Management Optimization, 2020, 16 (6) : 3083-3103. doi: 10.3934/jimo.2019095 [7] K. F. Cedric Yiu, S. Y. Wang, K. L. Mak. Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains. Journal of Industrial & Management Optimization, 2008, 4 (1) : 81-94. doi: 10.3934/jimo.2008.4.81 [8] Zhi-tang Li, Cui-hua Zhang, Wei Kong, Ru-xia Lyu. The optimal product-line design and incentive mechanism in a supply chain with customer environmental awareness. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021204 [9] Dingzhong Feng, Xiaofeng Zhang, Ye Zhang. Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021117 [10] Xumei Zhang, Jiafeng Yuan, Bin Dan, Ronghua Sui, Wenbo Li. The evolution mechanism of the multi-value chain network ecosystem supported by the third-party platform. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021148 [11] Jingzhen Liu, Lihua Bai, Ka-Fai Cedric Yiu. Optimal investment with a value-at-risk constraint. Journal of Industrial & Management Optimization, 2012, 8 (3) : 531-547. doi: 10.3934/jimo.2012.8.531 [12] Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021042 [13] Bin Chen, Wenying Xie, Fuyou Huang, Juan He. Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2903-2924. doi: 10.3934/jimo.2020100 [14] Chuan Ding, Kaihong Wang, Shaoyong Lai. Channel coordination mechanism with retailers having fairness preference ---An improved quantity discount mechanism. Journal of Industrial & Management Optimization, 2013, 9 (4) : 967-982. doi: 10.3934/jimo.2013.9.967 [15] Jian Chen, Lei Guan, Xiaoqiang Cai. Analysis on Buyers' cooperative strategy under group-buying price mechanism. Journal of Industrial & Management Optimization, 2013, 9 (2) : 291-304. doi: 10.3934/jimo.2013.9.291 [16] Junling Han, Nengmin Wang, Zhengwen He, Bin Jiang. Optimal return and rebate mechanism based on demand sensitivity to reference price. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021087 [17] Juliang Zhang. Coordination of supply chain with buyer's promotion. Journal of Industrial & Management Optimization, 2007, 3 (4) : 715-726. doi: 10.3934/jimo.2007.3.715 [18] Na Song, Ximin Huang, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu. Impact of reorder option in supply chain coordination. Journal of Industrial & Management Optimization, 2017, 13 (1) : 449-475. doi: 10.3934/jimo.2016026 [19] Jun Pei, Panos M. Pardalos, Xinbao Liu, Wenjuan Fan, Shanlin Yang, Ling Wang. Coordination of production and transportation in supply chain scheduling. Journal of Industrial & Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399 [20] Helmut Mausser, Oleksandr Romanko. CVaR proxies for minimizing scenario-based Value-at-Risk. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1109-1127. doi: 10.3934/jimo.2014.10.1109

2020 Impact Factor: 1.801