# American Institute of Mathematical Sciences

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

 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.
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.

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##### 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.
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