International Journal of Fuzzy Systems

, Volume 21, Issue 8, pp 2354–2372 | Cite as

Integrated Multi-stage Decision-Making for Winner Determination Problem in Online Multi-attribute Reverse Auctions Under Uncertainty

  • Shilei Wang
  • Shaojian QuEmail author
  • Mark Goh
  • M. I. M. Wahab
  • Huan Zhou


Online multi-attribute reverse auctions (OMARA), which include many non-price attributes, aligns better to practice, and is prevalent in many fields such as project bidding and public sector procurement. In such auctions, the decision makers often face varying degrees of cognitive and environmental uncertainty. This renders the traditional winner (supplier) determination method based on deterministic values impracticable. Hence, from the standpoint of the auctioneer (purchaser), a new integrated decision framework under an uncertain situation is proposed. Firstly, the fuzzy set theory is applied to the winner determination problem in OMARA to recognize the uncertainty in the bidding attribute values. Secondly, the detail description of the winner determination problem in OMARA is provided. Thirdly, the comprehensive weights of the evaluation attributes are obtained by using fuzzy AHP and fuzzy deviation maximizing method together. Lastly, the five fuzzy multi-attribute decision-making methods are combined with simple dominant principle to evaluate the bidding alternatives and determine the winner (supplier). A numerical example is used to demonstrate the process of the proposed integrated decision frame-work, and the comparative analysis illustrates its feasibility and effectiveness.


Online multi-attribute reverse auction (OMARA) Winner determination Uncertainty Fuzzy multi-attribute decision-making methods 



This study was supported by the National Natural Science Foundation of China (No. 71571055) and Hujiang Leading Talent Project of Shanghai (101730301725). We gratefully acknowledge the anonymous referees for their valuable comments and suggestions.

Compliance with Ethical Standards

Conflict of interest

The authors declare that that they have no conflicts of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. 1.
    Pinker, E.J., Seidmann, A., Vakrat, Y.: Managing online auctions: current business and research issues. Manag. Sci. 49(11), 1457–1484 (2003)Google Scholar
  2. 2.
    Long, P., Teich, J.E., Wallenius, J.: Multi-attribute online reverse auctions: recent research trends. Eur. J. Oper. Res. 242(1), 1–9 (2015)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Na, Y., Liao, X., Huang, W.W.: Decision support for preference elicitation in multi-attribute electronic procurement auctions through an agent-based intermediary. Decis. Support Syst. 57(1), 127–138 (2014)Google Scholar
  4. 4.
    Talluri, S., Narasimhan, R., Viswanathan, S.: Information technologies for procurement decisions: a decision support system for multi-attribute e-reverse auctions. Int. J. Product. Res. 45(11), 2615–2628 (2007)zbMATHGoogle Scholar
  5. 5.
    Bichler, M.: An experimental analysis of multi-attribute auctions. Decis. Support Syst. 29(3), 249–268 (2000)Google Scholar
  6. 6.
    Qu, S.J., Zhou, Y.Y., Zhang, Y.L., Wahab, M.I.M., Zhang, G., Ye, Y.Y.: Optimal strategy for a green supply chain considering shipping policy and default risk. Comput. Ind. Eng. 131, 172–186 (2019)Google Scholar
  7. 7.
    Weber, C.A., Current, J.R., Benton, W.C.: Vendor selection criteria and methods. Eur. J. Oper. Res. 50(1), 2–18 (1991)zbMATHGoogle Scholar
  8. 8.
    Govindan, K., Rajendran, S., Sarkis, J., Murugesan, P.: Multicriteria decision making approaches for green supplier evaluation and selection: a literature review. J. Clean. Prod. 98, 66–83 (2015)Google Scholar
  9. 9.
    Liao, C.N., Kao, H.P.: An integrated fuzzy TOPSIS and MCGP approach to supplier selection in supply chain management. Expert Syst. Appl. 38(9), 10803–10811 (2011)Google Scholar
  10. 10.
    Wan, S.P., Li, D.F.: Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees. Omega 41(6), 925–940 (2013)Google Scholar
  11. 11.
    Chen, C.T., Lin, C.T., Huang, S.F.: A fuzzy approach for supplier evaluation and selection in supply chain management. Int. J. Prod. Econ. 102(2), 289–301 (2006)Google Scholar
  12. 12.
    Lee, A.H.I.: A fuzzy supplier selection model with the consideration of benefits, opportunities, costs and risks. Expert Syst. Appl. 36(2), 2879–2893 (2009)Google Scholar
  13. 13.
    Büyüközkan, G., Çifçi, G.: A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers. Expert Syst. Appl. 39(3), 3000–3011 (2012)Google Scholar
  14. 14.
    Liu, Z.M., Liu, P.D., Liang, X.: Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. Int. J. Intel. Syst. 33(9), 1900–1928 (2018)Google Scholar
  15. 15.
    Che, Y.K.: Design competition through multidimensional auctions. RAND J. Econ. 24(4), 668–680 (1993)Google Scholar
  16. 16.
    David, E.: Bidding in sealed-bid and English multi-attribute auctions. Decis. Support Syst. 42(2), 527–556 (2006)Google Scholar
  17. 17.
    Durán, O., Aguilo, J.: Computer-aided machine-tool selection based on a fuzzy-AHP approach. Expert Syst. Appl. 34(3), 1787–1794 (2008)Google Scholar
  18. 18.
    Xu, Z.S.: Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl. Based Syst. 24(6), 749–760 (2011)Google Scholar
  19. 19.
    Sandholm, T.: Very large-scale generalized combinatorial multi-attribute auctions. Oxford University Press, UK (2013)Google Scholar
  20. 20.
    Bichler, M., Kalagnanam, J.: Configurable offers and winner determination in multi-attribute auctions. Eur. J. Oper. Res. 160(2), 380–394 (2005)zbMATHGoogle Scholar
  21. 21.
    Bellosta, M.J., Kornman, S., Vanderpooten, D.: Preference-based English reverse auctions. Artif. Intel. 175(7), 1449–1467 (2011)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Cheng, C.B.: Solving a sealed-bid reverse auction problem by multiple-criterion decision-making methods. Comput. Math. Appl. 56(12), 3261–3274 (2008)zbMATHGoogle Scholar
  23. 23.
    Singh, R.K., Benyoucef, L.: Fuzzy logic and interval arithmetic-based TOPSIS method for multi-criteria reverse auctions. Serv. Sci. 4(2), 101–117 (2012)Google Scholar
  24. 24.
    Li, D.F., Chen, G.H., Huang, Z.G.: Linear programming method for multiattribute group decision making using IF sets. Inf. Sci. 180(9), 1591–1609 (2010)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Ho, W., Xu, X., Dey, P.K.: Multi-criteria decision making approaches for supplier evaluation and selection: a literature review. Eur. J. Oper. Res. 202(1), 16–24 (2010)zbMATHGoogle Scholar
  26. 26.
    Gencer, C., Gürpinar, D.: Analytic network process in supplier selection: a case study in an electronic firm. Appl. Math. Model. 31(11), 2475–2486 (2007)zbMATHGoogle Scholar
  27. 27.
    Yilmaz, B., Dagdeviren, M.: A combined approach for equipment selection: F-PROMETHEE method and zero–one goal programming. Expert Syst. Appl. 38(9), 11641–11650 (2011)Google Scholar
  28. 28.
    Chou, S.Y., Chang, Y.H.: A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach. Expert Syst. Appl. 34(4), 2241–2253 (2008)Google Scholar
  29. 29.
    Kwong, C.K., Ip, W.H., Chan, J.W.K.: Combining scoring method and fuzzy expert systems approach to supplier assessment: a case study. Integr. Manuf. Sys. 13(7), 512–519 (2002)Google Scholar
  30. 30.
    Tavana, M., Fallahpour, A., Di Caprio, D., Santos-Artega, F.J.: A hybrid intelligent fuzzy predictive model with simulation for supplier evaluation and selection. Expert Syst. Appl. 61, 129–144 (2016)Google Scholar
  31. 31.
    Opricovic, S., Tzeng, G.H.: Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156(2), 445–455 (2004)zbMATHGoogle Scholar
  32. 32.
    Roy, B.: The outranking approach and the foundations of the ELECTRE methods. Theor. Decis. 31(1), 49–73 (1991)MathSciNetGoogle Scholar
  33. 33.
    Gomes, L.F.A.M., Lima, M.M.P.P.: TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Found. Comput. Decis. Sci. 16(4), 113–127 (1992)zbMATHGoogle Scholar
  34. 34.
    Anojkumar, L., Ilangkumaran, M., Sasirekha, V.: Comparative analysis of MCDM methods for pipe material selection in sugar industry. Expert Syst. Appl. 41(6), 2964–2980 (2014)Google Scholar
  35. 35.
    Kaya, I., Colak, M., Terzi, F.: A comprehensive review of fuzzy multi-criteria decision making methodologies for energy policy making. Energy Strateg. Rev. 24, 207–228 (2019)Google Scholar
  36. 36.
    Ilbahar, E., Cebi, S., Kahraman, C.: A state-of-the-art review on multi-attribute renewable energy decision making. Energy Strateg. Rev. 25, 18–33 (2019)Google Scholar
  37. 37.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)Google Scholar
  38. 38.
    Babbar, C., Amin, S.H.: A multi-objective mathematical model integrating environmental concerns for supplier selection and order allocation based on fuzzy QFD in beverages industry. Expert Syst. Appl. 92, 27–38 (2018)Google Scholar
  39. 39.
    Amin, S.H., Razm, J.: An integrated fuzzy model for supplier management: a case study of ISP selection and evaluation. Expert Syst. Appl. 36(4), 8639–8648 (2009)Google Scholar
  40. 40.
    Xu, Z.S.: Linguistic decision making: theory and methods. Springer, Berlin (2012)zbMATHGoogle Scholar
  41. 41.
    Wind, Y., Saaty, T.L.: Marketing applications of the analytic hierarchy process. Manag. Sci. 26(7), 641–658 (1980)Google Scholar
  42. 42.
    Huang, C.C., Chu, P.Y., Chiang, Y.H.: A fuzzy AHP application in government-sponsored R&D project selection. Omega 36(6), 1038–1052 (2008)Google Scholar
  43. 43.
    Kilincci, O., Onal, S.A.: Fuzzy AHP approach for supplier selection in a washing machine company. Expert Syst. Appl. 38(8), 9656–9664 (2011)Google Scholar
  44. 44.
    Ayhan, M.B., Kilic, H.S.: A two stage approach for supplier selection problem in multi-item/multi-supplier environment with quantity discounts. Comput. Indust. Eng. 85, 1–12 (2015)Google Scholar
  45. 45.
    Paksoy, T., Pehlivan, N.Y., Kahraman, C.: Organizational strategy development in distribution channel management using fuzzy AHP and hierarchical fuzzy TOPSIS. Expert Syst. Appl. 39(3), 2822–2841 (2012)Google Scholar
  46. 46.
    Hwang, C.L., Yoon, K.: Multiple attribute decision making: methods and applications. Springer, Berlin (1981)zbMATHGoogle Scholar
  47. 47.
    Li, P., Wu, J., Hui, Q.: Assessment of ground-water quality for irrigation purposes and identification of hydrogeochemical evolution mechanisms in Pengyang County, China. Environ. Earth Sci. 69(7), 2211–2225 (2012)Google Scholar
  48. 48.
    Ertuğrul, İ.: Fuzzy group decision making for the selection of facility location. Group Decis. Negotia. 20(6), 725–740 (2011)Google Scholar
  49. 49.
    Gomes, L.F.A.M., Rangel, L.A.D., Maranhão, F.J.C.: Multicriteria analysis of natural gas destination in Brazil: an application of the TODIM method. Math. Comput. Model. 50(1), 92–100 (2009)zbMATHGoogle Scholar
  50. 50.
    Huang, J., Li, Z., Liu, H.C.: New approach for failure mode and effect analysis using linguistic distribution assessments and TODIM method. Reliab. Eng. Syst. Saf. 167, 302–309 (2017)Google Scholar
  51. 51.
    Krohling, R.A., Souza, T.T.M.D.: Combining prospect theory, fuzzy numbers to multi-criteria decision making. Expert Syst. Appl. 39(13), 11487–11493 (2012)Google Scholar
  52. 52.
    Fan, Z.P., Zhang, X., Chen, F.D., Liu, Y.: Extended TODIM method for hybrid multiple attribute decision making problems. Knowl. Based Syst. 42(2), 40–48 (2013)Google Scholar
  53. 53.
    Opricovic, S.: Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade (1998)Google Scholar
  54. 54.
    Ilangkumaran, M., Kumanan, S.: Application of hybrid VIKOR model in selection of main-tenance strategy. Int. J. Inf. Syst. Supply Chain Manag. 5(2), 59–81 (2012)Google Scholar
  55. 55.
    Sanayei, A., Mousavi, S.F., Yazdankhah, A.: Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst. Appl. 37(1), 24–30 (2010)Google Scholar
  56. 56.
    Shemshadi, A., Shirazi, H., Toreihi, M., Tarokh, M.J.: A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst. Appl. 38(10), 12160–12167 (2011)Google Scholar
  57. 57.
    Brans, J.P., Vincle, P.: A preference ranking organization method. Manag. Sci. 31(6), 647–656 (2010)Google Scholar
  58. 58.
    Athawale, V.M., Chatterjee, P., Chakraborty, S.: Decision making for facility location selection using PROMETHEE II method. Int. J. Indust. Syst. Eng. 11(15), 16–30 (2012)Google Scholar
  59. 59.
    Behzadian, M., Kazemzadeh, R.B., Albadvi, A., Aghdasi, M.: PROMETHEE: a comprehensive literature review on methodologies and applications. Eur. J. Oper. Res. 200(1), 198–215 (2010)zbMATHGoogle Scholar
  60. 60.
    Lolli, F., Ishizaka, A., Gamberini, R., Rimini, B., Ferrari, A.M., Marinelli, S., Savazza, R.: Waste treatment: an environmental, economic and social analysis with a new group fuzzy PROMETHEE approach. Clean Tech. Environ. Policy 18(5), 1317–1332 (2016)Google Scholar
  61. 61.
    Benayoun, R., Roy, B., Sussman, B.: ELECTRE: Une methode pour guider le choix en presence de points de vue multiples, Note de travail 49. SEMA-METRA International, Direction Scientifique (1966)Google Scholar
  62. 62.
    Figueira, J., Mousseau, V., Roy, B.: ELECTRE methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple criteria decision analysis: state of the art surveys, pp. 133–162. Springer, Boston (2005)Google Scholar
  63. 63.
    Mei, Y., Xie, K.: Evacuation strategy of emergent event in metro station based on the ELECTRE method. Granul. Comput. 3(3), 209–218 (2018)MathSciNetGoogle Scholar
  64. 64.
    Sevkli, M.: An application of the fuzzy ELECTRE method for supplier selection. Int. J. Product. Res. 48(12), 3393–3405 (2010)zbMATHGoogle Scholar
  65. 65.
    Liao, H.C., Yang, L.Y., Xu, Z.S.: Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets. Appl. Soft Comput. 63, 223–234 (2018)Google Scholar
  66. 66.
    Xu, Y., Wen, X., Sun, H., Wang, H.: Consistency and consensus models with local adjustment strategy for hesitant fuzzy linguistic preference relations. Int. J. Fuzzy Syst. 20(7), 2216–2233 (2018)MathSciNetGoogle Scholar
  67. 67.
    Xu, Y., Xu, A., Wang, H.: Hesitant fuzzy linguistic linear programming technique for multidimensional analysis of preference for multi-attribute group decision making. Int. J. Mach. Learn. Cyber. 7(5), 845–855 (2016)Google Scholar
  68. 68.
    Liu, Z.M., Qu, S.J., Goh, M., Huang, R.P., Wang, S.L.: Optimization of fuzzy demand distribution supply chain using modified sequence quadratic programming approach. J. Intel. Fuzzy Syst. 36(6), 6167–6180 (2019)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  • Shilei Wang
    • 1
  • Shaojian Qu
    • 1
    Email author
  • Mark Goh
    • 2
  • M. I. M. Wahab
    • 3
  • Huan Zhou
    • 1
  1. 1.Business SchoolUniversity of Shanghai for Science and TechnologyShanghaiPeople’s Republic of China
  2. 2.NUS Business School & The Logistics Institute-Asia PacificNational University of SingaporeSingaporeSingapore
  3. 3.Department of Mechanical and Industrial EngineeringRyerson UniversityTorontoCanada

Personalised recommendations