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Two-echelon supply chain coordination under information asymmetry with multiple types


  • Kerkkamp, R.B.O.
  • van den Heuvel, W.
  • Wagelmans, A.P.M.


We analyse a principal-agent contracting model with asymmetric information between a supplier and a retailer. Both the supplier and the retailer have the classical non-linear economic ordering cost functions consisting of ordering and holding costs. We assume that the retailer has the market power to enforce any order quantity. Furthermore, the retailer has private holding costs. The supplier wants to minimise his expected costs by offering a menu of contracts with side payments as an incentive mechanism. We consider a general number of discrete single-dimensional retailer types with type-dependent default options. A natural and common model formulation is non-convex, but we present an equivalent convex formulation. Hence, the contracting model can be solved efficiently for a general number of retailer types. We also derive structural properties of the optimal menu of contracts. In particular, we completely characterise the optimum for two retailer types and provide a minimal list of candidate contracts for three types. Finally, we prove a sufficient condition to guarantee unique contracts in the optimal solution for a general number of retailer types.

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  • Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2016. "Two-echelon supply chain coordination under information asymmetry with multiple types," Econometric Institute Research Papers EI-2016-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:80104

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    1. Zissis, Dimitris & Ioannou, George & Burnetas, Apostolos, 2015. "Supply chain coordination under discrete information asymmetries and quantity discounts," Omega, Elsevier, vol. 53(C), pages 21-29.
    2. Sucky, Eric, 2006. "A bargaining model with asymmetric information for a single supplier-single buyer problem," European Journal of Operational Research, Elsevier, vol. 171(2), pages 516-535, June.
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    5. Guido Voigt, 2015. "Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(4), pages 554-569, April.
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    8. Pishchulov, Grigory & Richter, Knut, 2016. "Optimal contract design in the joint economic lot size problem with multi-dimensional asymmetric information," European Journal of Operational Research, Elsevier, vol. 253(3), pages 711-733.
    9. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
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    11. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    12. Li, Yina & Xu, Xuejun & Zhao, Xiande & Yeung, Jeff Hoi Yan & Ye, Fei, 2012. "Supply chain coordination with controllable lead time and asymmetric information," European Journal of Operational Research, Elsevier, vol. 217(1), pages 108-119.
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    Cited by:

    1. Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2019. "Two-echelon lot-sizing with asymmetric information and continuous type space," Omega, Elsevier, vol. 87(C), pages 158-176.
    2. Matsui, Kenji, 2019. "A supply chain member should set its margin later if another member's cost is highly uncertain," European Journal of Operational Research, Elsevier, vol. 275(1), pages 127-138.

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    economic order quantity; mechanism design; asymmetric information; hidden convexity;

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