Coordination of a Two-echelon Supply Chain under Demand Uncertainty Using Revised Sales Rebate with Simultaneous Punishment and Rebate Approaches

Document Type: Research Paper


Faculty of Industrial Engineering, University of Tehran, Iran


This paper investigates coordination of a decentralized two-echelon supply chain with a single supplier and retailer with uncertain market demand. The presented model pursuits to coordinate the decisions related to the retailer's order quantity that in addition to increasing the profit of the decentralized supply chain, grow the profit of both two members of the chain to the amount greater than the decentralized mode. The main purpose of the model is to achieve maximum profit of the whole supply chain, beside the provision of incentives to satisfy the chain members to withdraw the decentralized decisions and join the contract. Considering the studied supply chain features, a revised sales rebate contract is applied in which both punishment and rebate approaches have been adopted simultaneously. Furthermore, a new approach of determining the contract's parameters based on the retailer and supplier viewpoints is developed. Finally, some numerical studies are conducted and a sensitivity analysis is done on the parameter of demand variations. Results show that the presented model has the ability of coordinating the ordering quantity in the supply chain.


Main Subjects

1. Cachon, G. P. (2003). “Supply chain coordination with contracts”, Handbooks in Operations Research and Management Science,Vol. 11, No. 1, PP. 227-339.

2. Wong, W.-K., Qi, J. and Leung, S. (2009). “Coordinating supply chains with sales rebate contracts and vendor-managed inventory”, International Journal of Production Economics, Vol. 120, No. 1, PP. 151-161.

3. Taylor, T. A. (2002). “Supply chain coordination under channel rebates with sales effort effects”, Management Science, Vol. 48, No. 8, PP. 992-1007.

4. Li, X. and Wang, Q. (2007). “Coordination mechanisms of supply chain systems”, European Journal of Operational Research, Vol. 179, No. 1, PP. 1-16.

5. Taylor, T. A. and Xiao, W. (2009). “Incentives for retailer forecasting: Rebates vs. returns”, Management Science, Vol. 55, No. 10, PP. 1654-1669.

6. He, Y., Zhao, X., Zhao, L. and He, J. (2009). “Coordinating a supply chain with effort and price dependent stochastic demand”, Applied Mathematical Modelling, Vol. 33, No. 6, PP. 2777-2790.

7. Chiu, C.-H., Choi, T.-M. and Li, X. (2011). “Supply chain coordination with risk sensitive retailer under target sales rebate”, Automatica, Vol. 47, No. 8, PP. 1617-1625.

8. Chiu, C. H., Choi, T. M. and Tang, C. S. (2011). “Price, Rebate, and Returns Supply Contracts for Coordinating Supply Chains with Price‐Dependent Demands”, Production and Operations Management, Vol. 20, No. 1, PP. 81-91.

9. Xing, D. and Liu, T. (2012). “Sales effort free riding and coordination with price match and channel rebate”, European Journal of Operational Research, Vol. 219, No. 2, PP. 264-271.

10. Giannoccaro, I. and Pontrandolfo, P. (2004). “Supply chain coordination by revenue sharing contracts”, International Journal of Production Economics,Vol. 89, No. 2, PP. 131-139.

11. Ding, D. and Chen, J. (2008). “Coordinating a three level supply chain with flexible return policies”, Omega, Vol. 36, No. 5, PP. 865-876.

12. Ruiz-Benitez, R. and Muriel, A. (2014). “Consumer returns in a decentralized supply chain”, International Journal of Production Economics, Vol. 147, No. 1, PP. 573-592.

13. Hou, J., Zeng, A. Z. and Zhao, L. (2009). “Achieving better coordination through revenue sharing and bargaining in a two-stage supply chain”, Computers & Industrial Engineering, Vol. 57, No. 1, PP. 383-394.

14. Xu, G., Dan, B., Zhang, X. and Liu, C. (2014). “Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract”, International Journal of Production Economics, Vol. 147, No. 1,  PP. 171-179.

15. Corbett, C. J. and De Groote, X. (2000). “A supplier's optimal quantity discount policy under asymmetric information”, Management Science, Vol. 46, No. 3, PP. 444-450.

16. Zissis, D., Ioannou, G. and Burnetas, A. (2015). “Supply chain coordination under discrete information asymmetries and quantity discounts”, Omega, Vol. 53, No. 1, PP. 21-29.

17. Tsay, A. A. (1999). “The quantity flexibility contract and supplier-customer incentives”, Management Science, Vol. 45, No. 10, PP. 1339-1358.

18. Lian, Z. and Deshmukh, A. (2009). “Analysis of supply contracts with quantity flexibility”, European Journal of Operational Research, Vol. 196, No. 2, PP. 526-533.

19. Huang, X., Gu, J.-W., Ching, W.-K. and Siu, T.-K. (2014). “Impact of secondary market on consumer return policies and supply chain coordination”, Omega, Vol. 45, No. 1, PP. 57-70.

20. Heydari, J. and Asl-Najafi, J. (2016). “Coordinating inventory decisions in a two-echelon supply chain through the target sales rebate contract”, International Journal of Inventory Research, Vol. 3, No. 1, PP. 49-69.

21. Wang, C. X. (2002). “A general framework of supply chain contract models”, Supply Chain Management: An International Journal, Vol. 7, No. 5, PP. 302-310.