American Institute of Mathematical Sciences

Advanced
October  2010, 6(4): 795-810. doi: 10.3934/jimo.2010.6.795

Externality of contracts on supply chains with two suppliers and a common retailer

Juliang Zhang 1, and  Jian Chen 2,

1. 

Department of Logistics Management, School of Economics and Management, Beijing Jiaotong University, Beijing, 100044
2. 

Department of Management Science and Engineering, School of Economics and Management, Tsinghua University, Beijing, 100084, China

Received  October 2009 Revised  May 2010 Published  September 2010

This paper addresses the impact of different contracts on supply chains with different suppliers and a common retailer. Especially, we consider a supply chain system consists of a retailer and two suppliers (supplier1 and supplier 2 and the supply chain consisting of supplier $i$ ($i = 1,2)$and the retailer is named supply chain $i$ ($i = 1,2)$for simplicity) in which supplier 1 and the retailer agree to simple wholesale price contract and supplier 2 and the retailer agree to revenue sharing contract. The products provided by these two suppliers are complement or substitution. We study the external effect of these two contracts. The main findings of this study are as follows: When the two products are not independent, the design of a coordinative contract depends the stocking quantity of another product; Under the same external conditions, both simple wholesale price contract and revenue sharing contract perform the same when the products are complement, and revenue sharing contract performs better than simple wholesale price contract when the products are substitutive or independent; we can also design a wholesale price contract and a revenue sharing contract which coordinate these two supply chains simultaneously when the products are complement. Moreover, we consider the case that the demand depends on costly retailer's effort. We show that wholesale price contract always distorts the retailer's decision on effort in supply chain 1 and we can design a revenue sharing contract coordinating supply chain 2. Whether wholesale price contract or revenue sharing contract is more incentive to encourage retailer's promotion effort depends on the problem and contract parameters. These findings are different from the well known properties of these two contracts in a supply chain consisting of 1-supplier and 1-retailer. As retailers always sell multi-items in reality, we believe that our findings could help managers manage channels efficiently.
Keywords: external effects., supply chain coordination, sale effort, revenue sharing contract, wholesale price contract.
Mathematics Subject Classification: Primary: 90B50, 91B06; Secondary: 91A1.
Citation: Juliang Zhang, Jian Chen. Externality of contracts on supply chains with two suppliers and a common retailer. Journal of Industrial and Management Optimization, 2010, 6 (4) : 795-810. doi: 10.3934/jimo.2010.6.795
References:
[1]

R. Anupindi and Y. Bassok, Supply contracts with quantity commitments and stochastic demand, in "Quantitative Models for Supply Chain Management" (eds. S. Tayur, M. Magazine and R. Ganeshan), Kluwer Academic Publishers, 1999.

[2]

G. P. Cachon and M. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 5 (2005), 30-44. doi: 10.1287/mnsc.1040.0215.

[3]

G. P. Cachon, Supply chain coordination with contracts, in "Handbooks in Operations Research and Management Science: Supply Chain Management: Design, Coordination and Operation" (eds. S. C. Graves and A. G. Kok ), North-Holland, 2003. doi: 10.1016/S0927-0507(03)11006-7.

[4]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296. doi: 10.1287/mksc.10.4.271.

[5]

G. D. Eppen and A. V. Iyer, Backup agreements in fashion buying - The value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469.

[6]

Y. Gerchak and Y. Wang, Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand, Production and Operations Management, 13 (2004), 23-33. doi: 10.1111/j.1937-5956.2004.tb00142.x.

[7]

M. A. Lariviere and E. L. Porteus, Selling to the newsvendor: An analysis of price-only contracts, Manufacturing & Service Operations Management, 3 (2001), 293-305. doi: 10.1287/msom.3.4.293.9971.

[8]

S. Lippman and K. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.

[9]

M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demands, Naval Research Logistics, 35 (1988), 397-409. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.

[10]

B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 4 (1985), 166-176. doi: 10.1287/mksc.4.2.166.

[11]

N. Sabbaghi, Y. Sheffi and J. N.Tsitsiklis, Coordination capability of linear wholesale price contracts, preprint, LIDS-P-2749, Laboratory for Information and Decision Systems, MIT, February 2007.

[12]

S. P. Sethi , H. Yan, H. Zhang and J.B. Zhou, Information updated supply chain with service-level constraints, Journal of Industrial and Management Optimization, 1 (2005), 513-531.

[13]

T. Taylor, Supply chain coordination under channel rebates with sales effort effects, Management Science, 48 (2002), 992-1007. doi: 10.1287/mnsc.48.8.992.168.

[14]

J. Tirole, "The Theory of Industrial Organization," MIT Press, Cambridge, MA. 1988.

[15]

A. Tsay, S. Nahmias and N. Agrawal, Modeling supply chain contracts: A review, in "Quantitative Models for Supply Chain Management" (eds. S. Tayur, R. Ganeshan, M.Magazine ), Norwell, MA, Kluwer Academic Publisher, (1999).

[16]

A. Tsay, The quantity flexibility contract and supplier-customer incentives, Management Science, 45 (1999), 1339-1358. doi: 10.1287/mnsc.45.10.1339.

[17]

R. Tyagi, On the effects of downstream entry, Management Science, 45 (1999), 59-73. doi: 10.1287/mnsc.45.1.59.

[18]

Z. K. Weng, Channel coordination and quantity discounts, Management Science, 41 (1995), 1509-1522. doi: 10.1287/mnsc.41.9.1509.

[19]

J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial and Management Optimization, 3 (2007), 715-726.

show all references

References:
[1]

R. Anupindi and Y. Bassok, Supply contracts with quantity commitments and stochastic demand, in "Quantitative Models for Supply Chain Management" (eds. S. Tayur, M. Magazine and R. Ganeshan), Kluwer Academic Publishers, 1999.

[2]

G. P. Cachon and M. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 5 (2005), 30-44. doi: 10.1287/mnsc.1040.0215.

[3]

G. P. Cachon, Supply chain coordination with contracts, in "Handbooks in Operations Research and Management Science: Supply Chain Management: Design, Coordination and Operation" (eds. S. C. Graves and A. G. Kok ), North-Holland, 2003. doi: 10.1016/S0927-0507(03)11006-7.

[4]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296. doi: 10.1287/mksc.10.4.271.

[5]

G. D. Eppen and A. V. Iyer, Backup agreements in fashion buying - The value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469.

[6]

Y. Gerchak and Y. Wang, Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand, Production and Operations Management, 13 (2004), 23-33. doi: 10.1111/j.1937-5956.2004.tb00142.x.

[7]

M. A. Lariviere and E. L. Porteus, Selling to the newsvendor: An analysis of price-only contracts, Manufacturing & Service Operations Management, 3 (2001), 293-305. doi: 10.1287/msom.3.4.293.9971.

[8]

S. Lippman and K. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.

[9]

M. Parlar, Game theoretic analysis of the substitutable product inventory problem with random demands, Naval Research Logistics, 35 (1988), 397-409. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.

[10]

B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 4 (1985), 166-176. doi: 10.1287/mksc.4.2.166.

[11]

N. Sabbaghi, Y. Sheffi and J. N.Tsitsiklis, Coordination capability of linear wholesale price contracts, preprint, LIDS-P-2749, Laboratory for Information and Decision Systems, MIT, February 2007.

[12]

S. P. Sethi , H. Yan, H. Zhang and J.B. Zhou, Information updated supply chain with service-level constraints, Journal of Industrial and Management Optimization, 1 (2005), 513-531.

[13]

T. Taylor, Supply chain coordination under channel rebates with sales effort effects, Management Science, 48 (2002), 992-1007. doi: 10.1287/mnsc.48.8.992.168.

[14]

J. Tirole, "The Theory of Industrial Organization," MIT Press, Cambridge, MA. 1988.

[15]

A. Tsay, S. Nahmias and N. Agrawal, Modeling supply chain contracts: A review, in "Quantitative Models for Supply Chain Management" (eds. S. Tayur, R. Ganeshan, M.Magazine ), Norwell, MA, Kluwer Academic Publisher, (1999).

[16]

A. Tsay, The quantity flexibility contract and supplier-customer incentives, Management Science, 45 (1999), 1339-1358. doi: 10.1287/mnsc.45.10.1339.

[17]

R. Tyagi, On the effects of downstream entry, Management Science, 45 (1999), 59-73. doi: 10.1287/mnsc.45.1.59.

[18]

Z. K. Weng, Channel coordination and quantity discounts, Management Science, 41 (1995), 1509-1522. doi: 10.1287/mnsc.41.9.1509.

[19]

J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial and Management Optimization, 3 (2007), 715-726.

[1]

Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165
[2]

Han Zhao, Bangdong Sun, Hui Wang, Shiji Song, Yuli Zhang, Liejun Wang. Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022021
[3]

Kun Fan, Wenjin Mao, Hua Qu, Xinning Li, Meng Wang. Study on government subsidy in a two-level supply chain of direct-fired biomass power generation based on contract coordination. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022049
[4]

Yafei Zu. Inter-organizational contract control of advertising strategies in the supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021126
[5]

Jun Tu, Zijiao Sun, Min Huang. Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2191-2220. doi: 10.3934/jimo.2021062
[6]

Wenying Xie, Bin Chen, Fuyou Huang, Juan He. Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3393-3415. doi: 10.3934/jimo.2020125
[7]

Jun Wu, Shouyang Wang, Wuyi Yue. Supply contract model with service level constraint. Journal of Industrial and Management Optimization, 2005, 1 (3) : 275-287. doi: 10.3934/jimo.2005.1.275
[8]

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 and Management Optimization, 2021  doi: 10.3934/jimo.2021117
[9]

Wucheng Zi, Jiayu Zhou, Honglei Xu, Guodong Li, Gang Lin. Preserving relational contract stability of fresh agricultural product supply chains. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2505-2518. doi: 10.3934/jimo.2020079
[10]

Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1603-1627. doi: 10.3934/jimo.2021035
[11]

Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169
[12]

Ashkan Mohsenzadeh Ledari, Alireza Arshadi Khamseh, Mohammad Mohammadi. A three echelon revenue oriented green supply chain network design. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 157-168. doi: 10.3934/naco.2018009
[13]

Juliang Zhang. Coordination of supply chain with buyer's promotion. Journal of Industrial and Management Optimization, 2007, 3 (4) : 715-726. doi: 10.3934/jimo.2007.3.715
[14]

Na Song, Ximin Huang, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu. Impact of reorder option in supply chain coordination. Journal of Industrial and Management Optimization, 2017, 13 (1) : 449-475. doi: 10.3934/jimo.2016026
[15]

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 and Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399
[16]

Xiaomei Li, Renjing Liu, Zhongquan Hu, Jiamin Dong. Information sharing in two-tier supply chains considering cost reduction effort and information leakage. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021200
[17]

Kebing Chen, Tiaojun Xiao. Reordering policy and coordination of a supply chain with a loss-averse retailer. Journal of Industrial and Management Optimization, 2013, 9 (4) : 827-853. doi: 10.3934/jimo.2013.9.827
[18]

Chong Zhang, Yaxian Wang, Ying Liu, Haiyan Wang. Coordination contracts for a dual-channel supply chain under capital constraints. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1485-1504. doi: 10.3934/jimo.2020031
[19]

Wei Chen, Fuying Jing, Li Zhong. Coordination strategy for a dual-channel electricity supply chain with sustainability. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021139
[20]

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 and Management Optimization, 2021  doi: 10.3934/jimo.2021165

2021 Impact Factor: 1.411

Tools

Metrics

  • PDF downloads (87)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy