# Coordination of fuzzy closed-loop supply chain with price dependent demand under symmetric and asymmetric information conditions

## Abstract

This paper investigates the coordination issue of a two-echelon fuzzy closed-loop supply chain. Two coordinating models with symmetric and asymmetric information about retailer’s collecting scale parameter are established by using game theory, and the corresponding analytical solutions are obtained. Theoretical analysis and numerical example show that the maximal expected profits of the fuzzy closed-loop supply chain in two coordination situations are equal to that in the centralized decision case and greater than that in the decentralized decision scenario. Furthermore, under asymmetric information contract, the maximal expected profit obtained by the low-collecting-scale-level retailer is higher than that under symmetric information contract.

## Keywords

Coordination Fuzzy closed-loop supply chain Game theory Symmetric information Asymmetric information## Notes

### Acknowledgments

The authors wish to express their sincerest thanks to the editors and anonymous referees for their constructive comments and suggestions on the paper. We gratefully acknowledge the support of (i) National Natural Science Foundation of China (NSFC), Research Fund Nos. 71371186, 61403213 for J. Wei; (ii) National Natural Science Foundation of China, Nos. 71301116, 71302005 for J. Zhao.

## References

- Anupindi, R., & Bassok, Y. (1999). Centralization of stocks: Retailers vs. manufacturer.
*Management Science*,*45*, 78–91.CrossRefGoogle Scholar - Atasu, A., Toktay, B., & Van Wassenhove, L. (2013). How collection cost structure drives a manufacturers reverse channel choice.
*Production and Operations Management*,*22*, 1089–1102.Google Scholar - Cachon, G. (2003). Supply chain coordination with contracts. In A. G. de Kok & S. C. Graves (Eds.),
*Handbooks in operations research and management science: Supply chain management: design coordination and operation*. Amsterdam: Elsevier.Google Scholar - Cachon, P., & Lariviere, A. M. (2005). Supply chain coordination with revenue-sharing contracts: Strengths and limitations.
*Management Science*,*51*, 30–44.CrossRefGoogle Scholar - Choi, T., Li, Y., & Xu, L. (2013). Channel leadership, performance and coordination in closed loop supply chains.
*International Journal of Production Economics*,*146*, 371–380.CrossRefGoogle Scholar - Corbett, C. J., Zhou, D., & Tang, C. S. (2004). Designing supply contracts: Contract type and information asymmetry.
*Management Science*,*50*, 550–559.CrossRefGoogle Scholar - Guide, V., Teunter, R., & VanWassenhove, L. (2003). Matching demand and supply to maximize profits from remanufacturing.
*Manufacturing and Service Operations Management*,*5*, 303–316.CrossRefGoogle Scholar - Ha, A. (2001). Suppliercbuyer contracting: Asymmetric cost information and cutoff level policy for buyer participation.
*Naval Research Logistics*,*48*, 41–64.CrossRefGoogle Scholar - Hsieh, C., Wu, C., & Huang, Y. (2008). Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information.
*European Journal of Operational Research*,*190*, 509–525.CrossRefGoogle Scholar - Krishnan, H., Kapuscinski, R., & Butz, D. (2004). Coordination contracts for decentralized supply chain with retailer promotional effort.
*Management Science*,*50*, 48–63.CrossRefGoogle Scholar - Lau, A., & Lau, H.-S. (2005). Some two-echelon supply-chain games: improving from deterministic-symmetric-information to stochastic-asymmetric-information models.
*European Journal of Operational Research*,*161*, 203–223.CrossRefGoogle Scholar - Lau, A., Lau, H., & Zhou, Y. (2006). Considering asymmetrical manufacturing cost information in a two-echelon system that uses price-only contracts.
*IIE Transactions*,*38*, 253–271.CrossRefGoogle Scholar - Lau, A., Lau, H.-S., & Zhou, Y.-W. (2007). A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain.
*European Journal of Operational Research*,*176*, 295–316.CrossRefGoogle Scholar - Liu, B. (2002).
*Theory and practice of uncertain programming*. Heidelberg: Physica-Verlag.CrossRefGoogle Scholar - Liu, B. (2004).
*Uncertainty theory: An introduction to its axiomatic foundations*. Berlin: Springer.CrossRefGoogle Scholar - Liu, B., & Liu, Y. (2002). Excepted value of fuzzy variable and fuzzy expected value models.
*IEEE Transactions on Fuzzy Systems*,*10*, 445–450.CrossRefGoogle Scholar - Liu, Y., & Liu, B. (2003). Expected value operator of random fuzzy variable and random fuzzy expected value models.
*International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems*,*11*, 195–215.CrossRefGoogle Scholar - Majumder, P., & Groenevelt, H. (2001). Competition in remanufacturing.
*Production and Operations Management*,*10*, 125–141.CrossRefGoogle Scholar - Pasternack, B. A. (2005). Optimal pricing and return policies for perishable commodities.
*Management Science*,*4*, 166–176.Google Scholar - Petrovic, D., Roy, R., & Petrovic, R. (1999). Supply chain modelling using fuzzy sets.
*International Journal of Production Economics*,*59*, 443–453.CrossRefGoogle Scholar - Savaskan, R., & Van Wassenhove, L. (2006). Reverse channel design: The case of competing retailers.
*Management Science*,*52*, 1–14.CrossRefGoogle Scholar - Savaskan, R., Bhattacharya, S., & Van Wassenhove, L. (2004). Closed-loop supply chain models with product remanufacturing.
*Management Science*,*50*, 239–252.CrossRefGoogle Scholar - Spengler, J. (1950). Vertical restraints and antitrust policy.
*The Journal Political Economy*,*58*, 347–352.CrossRefGoogle Scholar - Taylor, T. A. (2002). Supply chain coordination under channel rebates with sales effort effects.
*Management Science*,*48*, 992–1007.CrossRefGoogle Scholar - Wang, C., Tang, W., & Zhao, R. (2007). On the continuity and convexity analysis of the expected value function of a fuzzy mapping.
*Journal of Uncertain Systems*,*1*, 148–160.Google Scholar - Wei, J., & Zhao, J. (2013). Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments.
*Annals of Operations Research*,. doi: 10.1007/s10479-014-1541-6.Google Scholar - Wei, J., Zhao, J., & Li, Y. (2012). Pricing decisions for a closed-loop supply chain in a fuzzy environment.
*Asia-Pacific Journal of Operational Research*,*29*, 1–30.CrossRefGoogle Scholar - Wong, B., & Lai, V. (2011). A survey of the application of fuzzy set theory in production and operations management: 1998–2009.
*International Journal of Production Economics*,*129*, 157–168.CrossRefGoogle Scholar - Xie, Y., Petrovic, D., & Burnham, K. (2006). A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand.
*International Journal Production Economics*,*102*, 37–50.CrossRefGoogle Scholar - Yao, J., Chen, M., & Lu, H. (2006). A fuzzy stochastic single-period model for cash management.
*European Journal of Operational Research*,*170*, 72–90.CrossRefGoogle Scholar - Zadeh, L. (1978). Fuzzy sets as a basis for a theory of possibility.
*Fuzzy Sets and Systems*,*1*, 3–28.CrossRefGoogle Scholar - Zhao, J., Tang, W., & Wei, J. (2012a). Pricing decision for substitutable products with retail competition in a fuzzy environment.
*International Journalof Production Economics*,*135*, 144–153.CrossRefGoogle Scholar - Zhao, J., Tang, W., Zhao, R., & Wei, J. (2012b). Pricing decisions for substitutable products with a common retailer in fuzzy environments.
*European Journal of Operational Research*,*216*, 409–419.CrossRefGoogle Scholar - Zhou, C., Zhao, R., & Tang, W. (2008). Two-echelon supply chain games in a fuzzy environment.
*Computers and Industrial Engineering*,*55*, 390–405.CrossRefGoogle Scholar - Zimmermann, H. (2000). An application-oriented view of modelling uncertainty.
*European Journal of Operational Research*,*122*, 190–198.CrossRefGoogle Scholar