Skip to main content
SpringerLink
Log in

Uncertain Supply Chain Problem with Price and Effort

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

A two-echelon supply chain problem influenced by retail price and sales effort is investigated in this paper, in which the demand, manufacturing cost and sales effort elasticity are considered as uncertain variables. Centralized decision model and decentralized decision model based on information about retailer’s scale parameter are presented, and the optimal solutions are obtained by game theory. In addition, two coordination models under symmetric and asymmetric information situations are developed. Furthermore, the parameters are treated as fuzzy variables and the results prove that fuzzy theory can be used to construct efficient models as well. Numerical examples indicate that the profit of the entire supply chain in two coordination situations are greater than that in the without coordination situation. What’s more, the consumers have to face a higher retail price when under symmetric information situation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Bernstein, F., Federgruen, A.: Decentralized supply chains with competing retailers under demand uncertainty. Manag. Sci. 51(1), 18–29 (2005)

    Article  MATH  Google Scholar 

  2. Cachon, G.: Supply chain coordination with contracts. Handb. Oper. Res. Manag. Sci. 11, 227–339 (2003)

    Google Scholar 

  3. Chen, F.: 94\(\%\)-Effective policies for a two-stage serial inventory system with stochastic demand. Manag. Sci. 45(12), 1679–1696 (1999)

    Article  MATH  Google Scholar 

  4. Chen, S., Ho, Y.: Analysis of the newsboy problem with fuzzy demands and incremental discounts. Int. J. Product. Econ. 129(1), 169–177 (2011)

    Article  Google Scholar 

  5. Chen, L., Peng, J., Liu, Z., Zhao, R.: Pricing and effort decisions for a supply chain with uncertain information. Int. J. Prod. Res. 55(1), 264–284 (2017)

    Article  Google Scholar 

  6. Dash, WuD: Bargaining in supply chain with price and promotional effort dependent demand. Math. Comput. Model. 58(9–10), 1659–1669 (2013)

    Article  MathSciNet  Google Scholar 

  7. Gao, J., Han, H., Hou, L., Wang, H.: Pricing and effort decisions in a closed-loop supply chain under different channel power structures. J. Clean. Prod. 112, 2043–2057 (2016)

    Article  Google Scholar 

  8. Giannoccaro, I., Pontrandolfo, P., Scozzi, B.: A fuzzy echelon approach for inventory management in supply chains. Eur. J. Oper. Res. 149(1), 185–196 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Giri, B., Bardhan, S., Maiti, T.: Coordinating a two-echelon supply chain through different contracts under price and promotional effort-dependent demand. J. Syst. Sci. Syst. Eng. 22(3), 295–318 (2013)

    Article  MATH  Google Scholar 

  10. Han, S., Peng, Z., Wang, S.: The maximum flow problem of uncertain network. Inf. Sci. 265, 167–175 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. He, Y., Zhao, X., Zhao, L., He, J.: Coordinating a supply chain with effort and price dependent stochastic demand. Appl. Math. Model. 33(6), 2777–2790 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hua, Z., Li, S., Liang, L.: Impact of demand uncertainty on supply chain cooperation of single-period products. Int. J. Prod. Econ. 100(2), 268–284 (2006)

    Article  Google Scholar 

  13. Ji, X., Zhou, J.: Option pricing for an uncertain stock model with jumps. Soft Comput. 19(11), 3323–3329 (2015)

    Article  MATH  Google Scholar 

  14. Ke, H., Liu, H., Tian, G.: An uncertain random programming model for project scheduling problem. Int. J. Intell. Syst. 30(1), 66–79 (2015)

    Article  Google Scholar 

  15. Krishnan, H., Kapuscinski, R., Butz, D.: Coordinating contracts for decentralized supply chains with retailer promotional effort. Manag. Sci. 50(1), 48–63 (2004)

    Article  Google Scholar 

  16. Lau, A., Lau, H.: Some two-echelon supply-chain games: Improving from deterministic-symmetric-information to stochastic-asymmetric-information models. Eur. J. Oper. Res. 161(1), 203–223 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lau, A., Lau, H., Zhou, Y.: A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain. Eur. J. Oper. Res. 176(1), 295–316 (2007)

    Article  MATH  Google Scholar 

  18. Li, B., Chen, P., Li, Q., Wang, W.: Dual-channel supply chain pricing decisions with a risk-averse retailer. Int. J. Prod. Res. 52(23), 7132–7147 (2014)

    Article  Google Scholar 

  19. Liu, B.: Uncertainty Theory, 2nd edn. Springer, Berlin (2007)

    MATH  Google Scholar 

  20. Liu, B.: Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer, Berlin (2010)

    Book  Google Scholar 

  21. Liu, B.: Some research problems in uncertainty theory. J. Uncertain Syst. 3(1), 3–10 (2009)

    Google Scholar 

  22. McGuire, T., Staelin, R.: An industry equilibrium analyses of down stream vertical integration. Marketing Sci. 2(2), 161–191 (1983)

    Article  Google Scholar 

  23. Petrovic, D., Roy, R., Petrovic, R.: Supply chain modelling using fuzzy sets. Int. J. Prod. Econ. 59(1–3), 443–453 (1999)

    Article  Google Scholar 

  24. Qin, Z., Kar, S.: Single-period inventory problem under uncertain environment. Appl. Math. Comput. 219(18), 9630–9638 (2013)

    MathSciNet  MATH  Google Scholar 

  25. Shen, J., Zhu, Y.: Scheduling in a two-stage supply chain with uncertain parameters. J. Intell. Fuzzy Syst. 30(6), 3439–3449 (2016)

    Article  MATH  Google Scholar 

  26. Sheng, Y., Gao, J.: Chance distribution of the maximum flow of uncertain random network. J. Uncertain. Anal. Appl. 2(1), 15 (2014)

    Article  Google Scholar 

  27. Sun, J., Chen, X.: Asian option pricing formula for uncertain financial market. J. Uncertain. Anal. Appl. 3, 11 (2015)

    Article  Google Scholar 

  28. Taylor, T.: Supply chain coordination under channel rebates with sales effort effects. Manag. Sci. 48(8), 992–1007 (2002)

    Article  MATH  Google Scholar 

  29. Tse, Y., Tan, K.: Managing product quality risk and visibility in multi-layer supply chain. Int. J. Prod. Econ. 139(1), 49–57 (2012)

    Article  Google Scholar 

  30. Wang, J., Shu, Y.: Fuzzy decision modeling for supply chain management. Fuzzy Sets and Syst. 150(1), 107–127 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang, K., Yang, Q.: Hierarchical facility location for the reverse logistics network design under uncertainty. J. Uncertain Syst. 8(4), 255–270 (2014)

    Google Scholar 

  32. Wei, J., Zhao, J.: Pricing decisions with retail competition in a fuzzy closed loop supply chain. Expert Syst. Appl. 38(9), 11209–11216 (2011)

    Article  Google Scholar 

  33. Wei, J., Zhao, J.: Reverse channel decisions for a fuzzy closed-loop supply chain. Appl. Math. Model. 37(3), 1502–1513 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Wei, J., Pang, G., Liu, Y., Ma, Q.: Pricing decisions of a two-echelon supply chain in fuzzy environment. Disc. Dyn. Nat. Soc. 971504, 11 (2013)

    MathSciNet  MATH  Google Scholar 

  35. Wei, J., Govindan, K., Li, Y., Zhao, J.: Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information. Comput. Oper. Res. 54, 257–265 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wen, M., Qin, Z., Kang, K.: The \(\alpha\)-cost minimization model for capacitated facility location-allocation problem with uncertain demands. Fuzzy Optim. Decis. Making 13(3), 345–356 (2014)

    Article  MathSciNet  Google Scholar 

  37. Wong, B., Lai, V.: A survey of the application of fuzzy set theory in production and operations management: 1998–2009. Int. J. Prod. Econ. 129(1), 157–168 (2011)

    Article  Google Scholar 

  38. Xu, G., Dan, B., Zhang, X., Liu, C.: Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract. Int. J. Prod. Econ. 147, 171–179 (2014)

    Article  Google Scholar 

  39. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  40. Zhang, X., Zeephongsekul, P.: Asymmetric information supply chain models with credit option. Ind. Eng. Manag. Syst. 12(3), 264–273 (2013)

    Google Scholar 

  41. Zhang, B., Peng, J.: Uncertain programming model for uncertain optimal assignment problem. Appl. Math. Model. 37(9), 6458–6468 (2013)

    Article  MathSciNet  Google Scholar 

  42. Zhao, J., Tang, W., Wei, J.: Pricing decision for substitutable products with retailer competition in a fuzzy environment. Int. J. Prod. Econ. 135(1), 144–153 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Jiayu Shen

  2. School of Automobile and Traffic Engineering, Jiangsu University of Technology, Changzhou, 213001, Jiangsu, People’s Republic of China

    Kai Zhu

Authors
  1. Jiayu Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiayu Shen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shen, J., Zhu, K. Uncertain Supply Chain Problem with Price and Effort. Int. J. Fuzzy Syst. 20, 1145–1158 (2018). https://doi.org/10.1007/s40815-017-0407-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0407-x

Keywords

Mathematics Subject Classification

Search

Navigation