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

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Abstract

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.

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References

  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. Long, P., Teich, J.E., Wallenius, J.: Multi-attribute online reverse auctions: recent research trends. Eur. J. Oper. Res. 242(1), 1–9 (2015)

    MathSciNet  MATH  Google Scholar 

  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. 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)

    MATH  Google Scholar 

  5. Bichler, M.: An experimental analysis of multi-attribute auctions. Decis. Support Syst. 29(3), 249–268 (2000)

    Google Scholar 

  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. Weber, C.A., Current, J.R., Benton, W.C.: Vendor selection criteria and methods. Eur. J. Oper. Res. 50(1), 2–18 (1991)

    MATH  Google Scholar 

  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. 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. 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. 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. 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. 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. 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. Che, Y.K.: Design competition through multidimensional auctions. RAND J. Econ. 24(4), 668–680 (1993)

    Google Scholar 

  16. David, E.: Bidding in sealed-bid and English multi-attribute auctions. Decis. Support Syst. 42(2), 527–556 (2006)

    Google Scholar 

  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. 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. Sandholm, T.: Very large-scale generalized combinatorial multi-attribute auctions. Oxford University Press, UK (2013)

    Google Scholar 

  20. Bichler, M., Kalagnanam, J.: Configurable offers and winner determination in multi-attribute auctions. Eur. J. Oper. Res. 160(2), 380–394 (2005)

    MATH  Google Scholar 

  21. Bellosta, M.J., Kornman, S., Vanderpooten, D.: Preference-based English reverse auctions. Artif. Intel. 175(7), 1449–1467 (2011)

    MathSciNet  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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. 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)

    MathSciNet  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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. 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. 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. 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. 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)

    MATH  Google Scholar 

  32. Roy, B.: The outranking approach and the foundations of the ELECTRE methods. Theor. Decis. 31(1), 49–73 (1991)

    MathSciNet  Google Scholar 

  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)

    MATH  Google Scholar 

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

    Google Scholar 

  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. 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. Xu, Z.S.: Linguistic decision making: theory and methods. Springer, Berlin (2012)

    MATH  Google Scholar 

  41. Wind, Y., Saaty, T.L.: Marketing applications of the analytic hierarchy process. Manag. Sci. 26(7), 641–658 (1980)

    Google Scholar 

  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. 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. 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. 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. Hwang, C.L., Yoon, K.: Multiple attribute decision making: methods and applications. Springer, Berlin (1981)

    MATH  Google Scholar 

  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. Ertuğrul, İ.: Fuzzy group decision making for the selection of facility location. Group Decis. Negotia. 20(6), 725–740 (2011)

    Google Scholar 

  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)

    MATH  Google Scholar 

  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. 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. 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. Opricovic, S.: Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade (1998)

    Google Scholar 

  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. 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. 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. Brans, J.P., Vincle, P.: A preference ranking organization method. Manag. Sci. 31(6), 647–656 (2010)

    Google Scholar 

  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. 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)

    MATH  Google Scholar 

  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. 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. 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. Mei, Y., Xie, K.: Evacuation strategy of emergent event in metro station based on the ELECTRE method. Granul. Comput. 3(3), 209–218 (2018)

    MathSciNet  Google Scholar 

  64. Sevkli, M.: An application of the fuzzy ELECTRE method for supplier selection. Int. J. Product. Res. 48(12), 3393–3405 (2010)

    MATH  Google Scholar 

  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. 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)

    MathSciNet  Google Scholar 

  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. 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 

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Acknowledgements

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.

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Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China

    Shilei Wang, Shaojian Qu & Huan Zhou

  2. NUS Business School & The Logistics Institute-Asia Pacific, National University of Singapore, Singapore, Singapore

    Mark Goh

  3. Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canada

    M. I. M. Wahab

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  1. Shilei Wang
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  2. Shaojian Qu
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  3. Mark Goh
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Appendixes

Appendixes

1.1 Appendix 1: Ranking the Bidding Alternatives by F-TOPSIS

See Tables 8, 9 and 10.

Table 8 The weighted normalized evaluation matrix \(\tilde{V}\) of the bidding alternatives
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Table 9 The positive ideal solution \(A^{ + }\) and negative ideal solution \(A^{ - }\)
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Table 10 The distances from \(A^{ + }\) and \(A^{ - }\), relative closeness degree \(RC_{i}^{ + }\), and ranking order
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1.2 Appendix 2: Ranking the Bidding Alternatives by F-TODIM

See Tables 11, 12, 13, 14, 15 and 16.

Table 11 Dominance degree matrix \(\psi_{1}\) regarding the attribute G1
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Table 12 Dominance degree matrix \(\psi_{2}\) regarding the attribute G2
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Table 13 Dominance degree matrix \(\psi_{3}\) regarding the attribute G3
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Table 14 Dominance degree matrix \(\psi_{4}\) regarding the attribute G4
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Table 15 The overall dominance degree \(\varphi (s_{i} ,s_{k} )\) of the alternative \(s_{i}\) over alternative \(s_{k}\)
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Table 16 The ranking order of all bidding alternatives(or suppliers)
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1.3 Appendix 3: Ranking the Bidding Alternatives by F-VIKOR

See Tables 17, 18 and 19.

Table 17 The ideal \(\tilde{p^{\prime}}_{j}^{ + }\) and the worst \(\tilde{p^{\prime}}_{j}^{ - }\) for each attribute
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Table 18 The utility measurement \(H_{i}\) and regret measurement \(R_{i}\) for each bidding alternative
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Table 19 The comprehensive index \(\delta_{i}^{{}}\) and ranking of the bidding alternatives (or suppliers)
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1.4 Appendix 4: Ranking the Bidding Alternatives by F-PROMETHEE II

See Tables 20 and 21.

Table 20 The relative preference degree \(\gamma_{j} (s_{a} ,s_{b} )\) and global preference index \(\pi (s_{a} ,s_{b} )\)
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Table 21 The positive, negative and net outranking flows, and the ranking of the bidding alternatives
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1.5 Appendix 5: Ranking the Bidding Alternatives by F-ELECTRE II

See Tables 22, 23, 24, 25 and 26.

Table 22 The concordance and discordance interval sets Cxy and Dxy
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Table 23 The concordance matrix C
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Table 24 The discordance matrix D
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Table 25 The concordant Boolean matrix \(E\) and the discordant Boolean matrix \(F\)
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Table 26 The global matrix \(U\) and ranking order of bidding alternatives (or suppliers)
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Wang, S., Qu, S., Goh, M. et al. Integrated Multi-stage Decision-Making for Winner Determination Problem in Online Multi-attribute Reverse Auctions Under Uncertainty. Int. J. Fuzzy Syst. 21, 2354–2372 (2019). https://doi.org/10.1007/s40815-019-00757-0

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