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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:
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Zemel, Sourcing through auctions and audits, Production and Operations Management, 17 (2008), 121-138. doi: 10.3401/poms.1080.0018. Google Scholar [7] Y.-J. Chen and G. Vulcano, Effects of information disclosure under first-and second-price auctions in a supply chain setting, Manufacturing & Service Operations Management, 11 (2008), 299-316. doi: 10.1287/msom.1080.0220. Google Scholar [8] C. J. Corbett, Stochastic inventory systems in a supply chain with asymmetric information: Cycle stocks, safety stocks, and consignment stock, Operations Research, 49 (2001), 487-500. doi: 10.1287/opre.49.4.487.11223. Google Scholar [9] C. J. Corbett and X. De Groote, A supplier's optimal quantity discount policy under asymmetric information, Management Science, 46 (2000), 444-450. doi: 10.1287/mnsc.46.3.444.12065. Google Scholar [10] C. J. Corbett and C. S. Tang, Designing supply contracts: Contract type and information asymmetry, Quantitative Models for Supply Chain Management, 17 (1999), 269-297. doi: 10.1007/978-1-4615-4949-9_9. Google Scholar [11] W. Elmaghraby and P. Keskinocak, Combinatorial auctions in procurement, The Practice of Supply Chain Management: Where Theory and Application Converge, 62 (2004), 245-258. doi: 10.1007/0-387-27275-5_15. Google Scholar [12] X. Gan, S. P. Sethi and H. Yan, Coordination of supply chains with risk-averse agents, Production and Operations Management, 13 (2004), 135-149. Google Scholar [13] X. Gan, S. P. Sethi and H. Yan, Channel coordination with a risk-neutral supplier and a downside-risk-averse retailer, Production and Operations Management, 14 (2005), 80-89. Google Scholar [14] J. S. Gans and S. P. King, Exclusionary contracts and competition for large buyers, International Journal of Industrial Organization, 20 (2002), 1363-1381. doi: 10.1016/S0167-7187(02)00008-5. Google Scholar [15] S. 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Wang, How a dominant retailer might design a purchase contract for a newsvendor-type product with price-sensitive demand, European Journal of Operational Research, 190 (2008), 443-458. doi: 10.1016/j.ejor.2007.06.042. Google Scholar [21] C. Li and A. Scheller-Wolf, Push or pull? auctioning supply contracts, Production and Operations Management, 20 (2011), 198-213. Google Scholar [22] F. Mathewson and R. A. Winter, Buyer groups, International Journal of Industrial Organization, 15 (1997), 137-164. doi: 10.1016/0167-7187(95)00517-X. Google Scholar [23] D. C. Parkes and J. Kalagnanam, Models for iterative multiattribute procurement auctions, Management Science, 51 (2005), 435-451. doi: 10.1287/mnsc.1040.0340. Google Scholar [24] K. Shi and T. Xiao, Coordination of a supply chain with a loss-averse retailer under two types of contracts, International Journal of Information and Decision Sciences, 1 (2008), 5-25. doi: 10.1504/IJIDS.2008.020033. Google Scholar [25] The Organization for Economic Development (OECD) Background Report In: OECD conference on empowering E-consumers, Washington, 2009. Available from: http://www.oecd.org/dataoecd/44/13/44047583.pdf.Google Scholar [26] T. I. Tunca and Q. Wu, Multiple sourcing and procurement process selection with bidding events, Management Science, 55 (2009), 763-780. doi: 10.1287/mnsc.1080.0972. Google Scholar [27] United States Securities and Exchange Commission (SEC) Form 10-K (eBay Inc: ), 2009. Available from: http://investor.ebay.com/secfiling.cfm?filingID=950134-09-3306.Google Scholar [28] G. Van Ryzin and G. Vulcano, Optimal auctioning and ordering in an infinite horizon inventory-pricing system, Operations Research, 52 (2004), 346-367. doi: 10.1287/opre.1040.0105. Google Scholar [29] L. Zhang, S. Song and C. Wu, Supply chain coordination of loss-averse newsvendor with contract, Tsinghua Science & Technology, 10 (2005), 133-140. doi: 10.1016/S1007-0214(05)70044-4. Google Scholar

show all references

##### References:
 [1] F. Branco, The design of multidimensional auctions, The RAND Journal of Economics, 28 (1997), 63-81. Google Scholar [2] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339. doi: 10.1016/S0927-0507(03)11006-7. Google Scholar [3] Y.-K. Che, Design competition through multidimensional auctions, The RAND Journal of Economics, 24 (1993), 668-680. Google Scholar [4] J. Chen, J. Feng and A. B. Whinston, Keyword auctions, unit-price contracts, and the role of commitment, Production and Operations Management, 19 (2010), 305-321. Google Scholar [5] K. Chen, Procurement strategies and coordination mechanism of the supply chain with one manufacturer and multiple suppliers, International Journal of Production Economics, 138 (2012), 125-135. doi: 10.1016/j.ijpe.2012.03.009. Google Scholar [6] Y.-J. Chen, S. Seshadri and E. Zemel, Sourcing through auctions and audits, Production and Operations Management, 17 (2008), 121-138. doi: 10.3401/poms.1080.0018. Google Scholar [7] Y.-J. Chen and G. Vulcano, Effects of information disclosure under first-and second-price auctions in a supply chain setting, Manufacturing & Service Operations Management, 11 (2008), 299-316. doi: 10.1287/msom.1080.0220. Google Scholar [8] C. J. Corbett, Stochastic inventory systems in a supply chain with asymmetric information: Cycle stocks, safety stocks, and consignment stock, Operations Research, 49 (2001), 487-500. doi: 10.1287/opre.49.4.487.11223. Google Scholar [9] C. J. Corbett and X. De Groote, A supplier's optimal quantity discount policy under asymmetric information, Management Science, 46 (2000), 444-450. doi: 10.1287/mnsc.46.3.444.12065. Google Scholar [10] C. J. Corbett and C. S. Tang, Designing supply contracts: Contract type and information asymmetry, Quantitative Models for Supply Chain Management, 17 (1999), 269-297. doi: 10.1007/978-1-4615-4949-9_9. Google Scholar [11] W. Elmaghraby and P. Keskinocak, Combinatorial auctions in procurement, The Practice of Supply Chain Management: Where Theory and Application Converge, 62 (2004), 245-258. doi: 10.1007/0-387-27275-5_15. Google Scholar [12] X. Gan, S. P. Sethi and H. Yan, Coordination of supply chains with risk-averse agents, Production and Operations Management, 13 (2004), 135-149. Google Scholar [13] X. Gan, S. P. Sethi and H. Yan, Channel coordination with a risk-neutral supplier and a downside-risk-averse retailer, Production and Operations Management, 14 (2005), 80-89. Google Scholar [14] J. S. Gans and S. P. King, Exclusionary contracts and competition for large buyers, International Journal of Industrial Organization, 20 (2002), 1363-1381. doi: 10.1016/S0167-7187(02)00008-5. Google Scholar [15] S. Gupta, C. Koulamas and G. J. Kyparisis, E-business: A review of research published in production and operations management (1992–2008), Production and Operations Management, 18 (2009), 604-620. Google Scholar [16] A. Y. Ha, Supplier-buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation, Naval Research Logistics, 48 (2001), 41-64. doi: 10.1002/1520-6750(200102)48:1<41::AID-NAV3>3.0.CO;2-M. Google Scholar [17] G. Iyengar and A. Kumar, Optimal procurement mechanisms for divisible goods with capacitated suppliers, Review of Economic Design, 12 (2008), 129-154. doi: 10.1007/s10058-008-0046-7. Google Scholar [18] M. Jin and S. D. Wu, Supply chain coordination in electronic markets: Auction and contracting mechanisms, in E-Commerce Research Forum, December, 2001.Google Scholar [19] V. Krishna, Auction Theory, Academic press, New York, 2009.Google Scholar [20] A. H. L. Lau, H.-S. Lau and J.-C. Wang, How a dominant retailer might design a purchase contract for a newsvendor-type product with price-sensitive demand, European Journal of Operational Research, 190 (2008), 443-458. doi: 10.1016/j.ejor.2007.06.042. Google Scholar [21] C. Li and A. Scheller-Wolf, Push or pull? auctioning supply contracts, Production and Operations Management, 20 (2011), 198-213. Google Scholar [22] F. Mathewson and R. A. Winter, Buyer groups, International Journal of Industrial Organization, 15 (1997), 137-164. doi: 10.1016/0167-7187(95)00517-X. Google Scholar [23] D. C. Parkes and J. Kalagnanam, Models for iterative multiattribute procurement auctions, Management Science, 51 (2005), 435-451. doi: 10.1287/mnsc.1040.0340. Google Scholar [24] K. Shi and T. Xiao, Coordination of a supply chain with a loss-averse retailer under two types of contracts, International Journal of Information and Decision Sciences, 1 (2008), 5-25. doi: 10.1504/IJIDS.2008.020033. Google Scholar [25] The Organization for Economic Development (OECD) Background Report In: OECD conference on empowering E-consumers, Washington, 2009. Available from: http://www.oecd.org/dataoecd/44/13/44047583.pdf.Google Scholar [26] T. I. Tunca and Q. Wu, Multiple sourcing and procurement process selection with bidding events, Management Science, 55 (2009), 763-780. doi: 10.1287/mnsc.1080.0972. Google Scholar [27] United States Securities and Exchange Commission (SEC) Form 10-K (eBay Inc: ), 2009. Available from: http://investor.ebay.com/secfiling.cfm?filingID=950134-09-3306.Google Scholar [28] G. Van Ryzin and G. Vulcano, Optimal auctioning and ordering in an infinite horizon inventory-pricing system, Operations Research, 52 (2004), 346-367. doi: 10.1287/opre.1040.0105. Google Scholar [29] L. Zhang, S. Song and C. Wu, Supply chain coordination of loss-averse newsvendor with contract, Tsinghua Science & Technology, 10 (2005), 133-140. doi: 10.1016/S1007-0214(05)70044-4. Google Scholar
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
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