# 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 & Management Optimization, 2010, 6 (4) : 795-810. doi: 10.3934/jimo.2010.6.795
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