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July 2018, 14(3): 1023-1040. doi: 10.3934/jimo.2017088

## Optimal decisions for a dual-channel supply chain under information asymmetry

 1 Hunan provincial Engineering Research Center of Electric Transportation, and Smart Distributed Network, College of Economics and Management, Changsha University of Science and Technology, Changsha 410114, China 2 Hunan Province Key Laboratory of Logistics Information and Simulation Technology, College of Economics and Trade, Hunan University, Changsha 410079, China 3 Commonwealth Scientific and Industrial Research Organization, Energy Center, Mayfield West, NSW2304, Australia

* Corresponding author: Erbao Cao

Received  February 2016 Revised  May 2017 Published  September 2017

Fund Project: The authors are supported by the National Natural Science Foundation of China under Grants 71420107027,71671061,71331001 and 91547113, the Program for New Century Excellent Talents in University under Grants NCET-13-0181, the Science and Technology Projects of Hunan Province under Grants 2016WK2015 and 2017CT5015

We discuss the optimal pricing and production decisions in a channel supply chain under symmetric and asymmetric information cases. We compare the optimum policies between the asymmetric information and the full information cases. We analyze the effect of the reseller's cost information on the profits of the partners. We find that information asymmetry is beneficial to the reseller, but is inefficient to the manufacturer and the whole supply chain. The information value increases with uncertainties arising from the reseller's cost structure. The dual-channel supply chain can share information and achieve coordination, if the lump-sum side payment from the manufacturer can make up the loss of the reseller due to sharing information. Finally, the effectiveness of the proposed models is verified by numerical examples.

Citation: Mingyong Lai, Hongzhao Yang, Erbao Cao, Duo Qiu, Jing Qiu. Optimal decisions for a dual-channel supply chain under information asymmetry. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1023-1040. doi: 10.3934/jimo.2017088
##### References:
 [1] A. Arya, B. Mittendorf and M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. [2] T. Boyaci, Competitive stoking and coordination in a multi-channel distribution system, IIE Transactions, 37 (2005), 407-427. [3] G. P. Cachon, Supplier encroachment under asymmetric information, Handbooks in Operations Research & Management Science, 11 (2003), 227-339. [4] G. P. Cachon and M. A. Lariviere, Supply Chain Coordination with Revenue-Sharing Contracts: Strength and Limitations, Management Science, 51 (2005), 30-44. [5] G. Cai, Channel selection and coordination in dual-channel supply chains, Journal of Retailing, 86 (2010), 22-36. [6] B. Cao, Coordination of dual-channel supply chains under demand disruptions management decisions, International Journal of Production Research, 52 (2014), 7114-7131. [7] B. Cao, J. Ma, C. Wan and Y. Lai, Contracting with asymmetric cost information in a dual-channel supply chain, Operations Research Letters, 41 (2013), 410-414. doi: 10.1016/j.orl.2013.04.013. [8] K. Y. Chen, M. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing & Service Operations Management, 10 (2008), 654-675. [9] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [10] W. K. Chiang, Product availability in competitive and cooperative dual-channel distribution with stock-out based substitution, European Journal of Operational Research, 200 (2010), 111-126. [11] W. K. Chiang, D. Chhajed and J. D. Hess, Direct Marketing, Indirect profits: A Strategic Analysis of Dual-channel supply chain Design, Management Science, 49 (2003), 1-20. [12] C. J. Corbett, D. Zhou and C. S. Tang, Designing supply contracts: Contract type and information asymmetry, Management Science, 50 (2004), 550-559. [13] Q. Geng and S. Mallik, Inventory competition and allocation in a multi-channel distribution system, European Journal of Operational Research, 182 (2007), 704-729. [14] G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126. [15] S. Huang, C. Yang and X. Zhang, Pricing and production decisions in a channel supply chain with demand disruptions, Computers & Industrial Engineering, 62 (2012), 70-83. [16] C. A. Ingene and M. E. Parry, Mathematical Models of Distribution Channels, Springer, 2004. [17] Z. Li, G. M. Stephen and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. [18] S. K. Mukhopadhyay, X. Zhu and X. Yue, Optimal contract design for mixed channels under information asymmetry, Production and Operations Management, 17 (2008), 641-650. [19] J. Swaminathan and S. Tayur, Models for supply chains in e-business, Management Science, 49 (2003), 1387-1406. [20] Y. Wang, L. Jiang and Z. Shen, Channel performance under consignment contract with revenue sharing, Management Science, 50 (2004), 34-47. [21] T. Xiao and X. Qi, A two-stage supply chain with demand sensitive to price, delivery time, and reliability of delivery, Annals of Operations Research, 241 (2016), 475-496. doi: 10.1007/s10479-012-1085-6. [22] R. Yan, Pricing strategy for companies with mixed online and traditional reselling distribution markets, Journal of Production and Brand Management, 17 (2008), 48-56. [23] R. L. Yan and Z. Pei, Information asymmetry, pricing strategy and firm's performance in the reseller multi-channel manufacturer supply chain, Journal of Business Research, 64 (2011), 377-384. [24] H. M. Yang, C. Y. Chuang and K. P. Wong, Optimal fuel, power and load-based emissions trades for electric power supply chain equilibrium, IEEE Transactions on Power Systems, 27 (2012), 1147-1157. [25] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retailer competition, European Journal of Operational Research, 186 (2008), 637-651. doi: 10.1016/j.ejor.2007.01.049. [26] C. C. Yu and C. S. Wang, A hybrid mining approach for optimizing returns policies in e-retail, Expert Systems with Applications, 35 (2008), 1575-1582.

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##### References:
 [1] A. Arya, B. Mittendorf and M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. [2] T. Boyaci, Competitive stoking and coordination in a multi-channel distribution system, IIE Transactions, 37 (2005), 407-427. [3] G. P. Cachon, Supplier encroachment under asymmetric information, Handbooks in Operations Research & Management Science, 11 (2003), 227-339. [4] G. P. Cachon and M. A. Lariviere, Supply Chain Coordination with Revenue-Sharing Contracts: Strength and Limitations, Management Science, 51 (2005), 30-44. [5] G. Cai, Channel selection and coordination in dual-channel supply chains, Journal of Retailing, 86 (2010), 22-36. [6] B. Cao, Coordination of dual-channel supply chains under demand disruptions management decisions, International Journal of Production Research, 52 (2014), 7114-7131. [7] B. Cao, J. Ma, C. Wan and Y. Lai, Contracting with asymmetric cost information in a dual-channel supply chain, Operations Research Letters, 41 (2013), 410-414. doi: 10.1016/j.orl.2013.04.013. [8] K. Y. Chen, M. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing & Service Operations Management, 10 (2008), 654-675. [9] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [10] W. K. Chiang, Product availability in competitive and cooperative dual-channel distribution with stock-out based substitution, European Journal of Operational Research, 200 (2010), 111-126. [11] W. K. Chiang, D. Chhajed and J. D. Hess, Direct Marketing, Indirect profits: A Strategic Analysis of Dual-channel supply chain Design, Management Science, 49 (2003), 1-20. [12] C. J. Corbett, D. Zhou and C. S. Tang, Designing supply contracts: Contract type and information asymmetry, Management Science, 50 (2004), 550-559. [13] Q. Geng and S. Mallik, Inventory competition and allocation in a multi-channel distribution system, European Journal of Operational Research, 182 (2007), 704-729. [14] G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126. [15] S. Huang, C. Yang and X. Zhang, Pricing and production decisions in a channel supply chain with demand disruptions, Computers & Industrial Engineering, 62 (2012), 70-83. [16] C. A. Ingene and M. E. Parry, Mathematical Models of Distribution Channels, Springer, 2004. [17] Z. Li, G. M. Stephen and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. [18] S. K. Mukhopadhyay, X. Zhu and X. Yue, Optimal contract design for mixed channels under information asymmetry, Production and Operations Management, 17 (2008), 641-650. [19] J. Swaminathan and S. Tayur, Models for supply chains in e-business, Management Science, 49 (2003), 1387-1406. [20] Y. Wang, L. Jiang and Z. Shen, Channel performance under consignment contract with revenue sharing, Management Science, 50 (2004), 34-47. [21] T. Xiao and X. Qi, A two-stage supply chain with demand sensitive to price, delivery time, and reliability of delivery, Annals of Operations Research, 241 (2016), 475-496. doi: 10.1007/s10479-012-1085-6. [22] R. Yan, Pricing strategy for companies with mixed online and traditional reselling distribution markets, Journal of Production and Brand Management, 17 (2008), 48-56. [23] R. L. Yan and Z. Pei, Information asymmetry, pricing strategy and firm's performance in the reseller multi-channel manufacturer supply chain, Journal of Business Research, 64 (2011), 377-384. [24] H. M. Yang, C. Y. Chuang and K. P. Wong, Optimal fuel, power and load-based emissions trades for electric power supply chain equilibrium, IEEE Transactions on Power Systems, 27 (2012), 1147-1157. [25] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retailer competition, European Journal of Operational Research, 186 (2008), 637-651. doi: 10.1016/j.ejor.2007.01.049. [26] C. C. Yu and C. S. Wang, A hybrid mining approach for optimizing returns policies in e-retail, Expert Systems with Applications, 35 (2008), 1575-1582.
Variation of prices with $\theta$ under asymmetric information case
Variation of demands with $\theta$ under asymmetric information case
Variation of the manufacturer's profit for various $B$ under asymmetric information case
The optimum policies under full and asymmetric information cases
 $p_1$ $p_2$ $w$ $L_1$ $D_2$ D $\pi_m$ $\pi_r$ $\pi$ Full Information 630 510 185.9 192.793 326.126 518.919 244226 6188 250414 Asymmetric Information 592.771 510 141.225 326.952 212.091 539.043 230462 17799 248261
 $p_1$ $p_2$ $w$ $L_1$ $D_2$ D $\pi_m$ $\pi_r$ $\pi$ Full Information 630 510 185.9 192.793 326.126 518.919 244226 6188 250414 Asymmetric Information 592.771 510 141.225 326.952 212.091 539.043 230462 17799 248261
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