# 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] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020165 [2] Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020167 [3] Nguyen Huy Tuan. On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020354 [4] Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166 [5] Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347 [6] Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248 [7] Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020052 [8] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442

2019 Impact Factor: 1.366