Optimization Letters

, Volume 12, Issue 3, pp 661–673 | Cite as

On explicit solutions of a two-echelon supply chain coordination game

  • Mustafa Ç. Pınar
Short Communication


A contracting game under asymmetric information specific to two-echelon supply chain coordination between a retailer of unknown type and a supplier is studied. When the parameter which is private information to the retailer (holding cost) is known up to an interval of uncertainty, a uniform discrete approximation for retailer types leads to closed-form solutions where the joint (coordinated) optimal order quantity for a modified holding cost plays a major role. Furthermore, the closed-form solutions result in increasing information rent for higher types under easy-to-verify conditions involving strict lower limits on the total holding costs of retailer and supplier and the difference between uncoordinated optimal costs of consecutive retailer types.


Two-echelon supply chain coordination Incentives Principal-agent problem Convex optimization 



The revised paper benefited from the comments of five anonymous referees. Special thanks are due to Dr. Alper Şen for suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of EngineeringBilkent UniversityAnkaraTurkey

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