Skip to main content
SpringerLink
Log in

Integrating IVFRN-BWM and Goal Programming to Allocate the Order Quantity Considering Discount for Green Supplier

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

A Correction to this article was published on 08 January 2022

This article has been updated

Abstract

One of the serious supply chain management (SCM) challenges is the effective selection of suppliers and the right allocation of orders to achieve an SCM's suitable financial and technical status. This paper introduced a multi-objective linear programming model to prioritize and weigh suppliers using the modified best–worst method (BWM). The proposed model uses evaluation criteria and used fuzzy variables to determine the right numbers of suppliers as well as order quantity of raw materials each supplier should provide. The model has been made up of four objective functions, and the required constraints have been solved using the goal programming method. The proposed model can take a set of opposing goals into account and prioritize the goals to maximize access to each goal. The uncertain concepts such as fuzzy and rough theories in some criteria enabled the proposed model to use the imprecise information in the best possible manner. This study has solved an example using the proposed model through analytic network process and BWM. Then, the obtained results were compared with our findings for adopting interval-valued fuzzy-rough numbers BWM (IVFRN-BWM) and it was shown that the modified BWM approach generates lower costs and better criteria.

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
Fig. 4

Similar content being viewed by others

Change history

References

  1. Gitinavard, H., Ghaderi, H., Pishvaee, M.S.: Green supplier evaluation in manufacturing systems: a novel interval-valued hesitant fuzzy group outranking approach. Soft Comput. 22, 6441–6460 (2018). https://doi.org/10.1007/s00500-017-2697-1

    Article  Google Scholar 

  2. Li, G., Kou, G., Peng, Y.: A group decision making model for integrating heterogeneous information. IEEE Trans. Syst. Man Cybern. Syst. 48, 982–992 (2018). https://doi.org/10.1109/TSMC.2016.2627050

    Article  Google Scholar 

  3. Mousavi, S.M., Foroozesh, N., Zavadskas, E.K., Antucheviciene, J.: A new soft computing approach for green supplier selection problem with interval type-2 trapezoidal fuzzy statistical group decision and avoidance of information loss. Soft Comput. 24, 12313–12327 (2020). https://doi.org/10.1007/s00500-020-04675-4

    Article  Google Scholar 

  4. Duan, L., Ventura, J.A.: A dynamic supplier selection and inventory management model for a serial supply chain with a novel supplier price break scheme and flexible time periods. Eur. J. Oper. Res. 272, 979–998 (2019). https://doi.org/10.1016/J.EJOR.2018.07.031

    Article  MathSciNet  MATH  Google Scholar 

  5. PrasannaVenkatesan, S., Goh, M.: Multi-objective supplier selection and order allocation under disruption risk. Transp. Res. Part E Logist. Transp. Rev. 95, 124–142 (2016). https://doi.org/10.1016/J.TRE.2016.09.005

    Article  Google Scholar 

  6. Liu, P., Hendalianpour, A., Razmi, J., Sangari, M.S.: A solution algorithm for integrated production-inventory-routing of perishable goods with transshipment and uncertain demand. Complex Intell. Syst. 1, 3 (2021). https://doi.org/10.1007/s40747-020-00264-y

    Article  Google Scholar 

  7. Hendalianpour, A., Razmi, J., Gheitasi, M.: Comparing clustering models in bank customers: based on fuzzy relational clustering approach. Accounting. 3, 81–94 (2017). https://doi.org/10.5267/j.ac.2016.8.003

    Article  Google Scholar 

  8. Hendalianpour, A.: Optimal lot size and price of perishable goods: a novel game-theoretic model using double interval grey numbers. Comput. Ind. Eng. 149, 106780 (2020). https://doi.org/10.1016/j.cie.2020.106780

    Article  Google Scholar 

  9. Hendalianpour, A., Razmi, J., Rameshi Sarvestani, A.: Applying decision tree models to SMEs: a statistics-based model for customer relationship management. Manag. Sci. Lett. 509, 520 (2016). https://doi.org/10.5267/j.msl.2016.5.002

    Article  Google Scholar 

  10. Meyer, A., Amberg, B.: Transport concept selection considering supplier milk runs—an integrated model and a case study from the automotive industry. Transp. Res. Part E Logist. Transp. Rev. 113, 147–169 (2018). https://doi.org/10.1016/J.TRE.2017.07.004

    Article  Google Scholar 

  11. Wan, N., Chen, X.: The role of put option contracts in supply chain management under inflation. Int. Trans. Oper. Res. 26, 1451–1474 (2019). https://doi.org/10.1111/itor.12372

    Article  MathSciNet  Google Scholar 

  12. Liu, P., Hendalianpour, A., Hamzehlou, M.: Pricing model of two-echelon supply chain for substitutable products based on double-interval grey-numbers. J. Intell. Fuzzy Syst. (2021). https://doi.org/10.3233/JIFS-201206

    Article  Google Scholar 

  13. Gupta, S., Chatterjee, P., Yazdani, M., Santibanez Gonzalez, E.D.R.: A multi-level programming model for green supplier selection. Manag. Decis. (2021). https://doi.org/10.1108/MD-04-2020-0472

    Article  Google Scholar 

  14. Hendalianpour, A., Razmi, J., Fakhrabadi, M., Kokkinos, K., Papageorgiou, E.I.: A linguistic multi-objective mixed-integer programming model for multi-echelon supply chain network at bio-refinery. EuroMed J. Manag. 2, 329 (2018). https://doi.org/10.1504/emjm.2018.096453

    Article  Google Scholar 

  15. Zailani, S., Jeyaraman, K., Vengadasan, G., Premkumar, R.: Sustainable supply chain management (SSCM) in Malaysia: a survey. Int. J. Prod. Econ. 140, 330–340 (2012). https://doi.org/10.1016/j.ijpe.2012.02.008

    Article  Google Scholar 

  16. Amirghodsi, S., Bonyadi Naeini, A., Makui, A.: A dual model for selecting technology and technology transfer method using a combination of the best-worst method (BWM) and goal programing. Sci. Iran. (2020). https://doi.org/10.24200/SCI.2020.53925.3511

    Article  Google Scholar 

  17. Dhouib, D.: An extension of MACBETH method for a fuzzy environment to analyze alternatives in reverse logistics for automobile tire wastes. Omega (United Kingdom). 42, 25–32 (2014). https://doi.org/10.1016/j.omega.2013.02.003

    Article  Google Scholar 

  18. Zhao, M., Wei, G., Wei, C., Wu, J.: TODIM method for interval-valued pythagorean fuzzy MAGDM based on cumulative prospect theory and its application to green supplier selection. Arab. J. Sci. Eng. 46, 1899–1910 (2021). https://doi.org/10.1007/s13369-020-05063-8

    Article  Google Scholar 

  19. Wei, C., Wu, J., Guo, Y., Wei, G.: Green supplier selection based on codas method in probabilistic uncertain linguistic environment. Technol. Econ. Dev. Econ. (2021). https://doi.org/10.3846/tede.2021.14078

    Article  Google Scholar 

  20. Mabrouk, N.: Ben: Green supplier selection using fuzzy Delphi method for developing the sustainable supply chain. Decis. Sci. Lett. 10, 63–70 (2020). https://doi.org/10.5267/j.dsl.2020.10.003

    Article  Google Scholar 

  21. Li, X., Ventura, J.A., Venegas, B.B., Kweon, S.J., Hwang, S.W.: An integrated acquisition policy for supplier selection and lot sizing considering total quantity discounts and a quality constraint. Transp. Res. Part E Logist. Transp. Rev. 119, 19–40 (2018). https://doi.org/10.1016/j.tre.2018.09.003

    Article  Google Scholar 

  22. Cai, Y.J., Choi, T.M.: A United Nations’ sustainable development goals perspective for sustainable textile and apparel supply chain management. Transp. Res. Part E Logist. Transp. Rev. 141, 102010 (2020). https://doi.org/10.1016/j.tre.2020.102010

    Article  Google Scholar 

  23. Torabi, S.A., Baghersad, M., Mansouri, S.A.: Resilient supplier selection and order allocation under operational and disruption risks. Transp. Res. Part E Logist. Transp. Rev. 79, 22–48 (2015). https://doi.org/10.1016/J.TRE.2015.03.005

    Article  Google Scholar 

  24. Moon, I., Feng, X.: Supply chain coordination with a single supplier and multiple retailers considering customer arrival times and route selection. Transp. Res. Part E Logist. Transp. Rev. 106, 78–97 (2017). https://doi.org/10.1016/J.TRE.2017.08.004

    Article  Google Scholar 

  25. Wu, C.-C., Gupta, J.N.D., Cheng, S.-R., Lin, B.M.T., Yip, S.-H., Lin, W.-C.: Robust scheduling for a two-stage assembly shop with scenario-dependent processing times. Int. J. Prod. Res. 1, 16 (2020). https://doi.org/10.1080/00207543.2020.1778208

    Article  Google Scholar 

  26. Pamučar, D., Petrović, I., Ćirović, G.: Modification of the Best-Worst and MABAC methods: a novel approach based on interval-valued fuzzy-rough numbers. Expert Syst. Appl. 91, 89–106 (2018). https://doi.org/10.1016/J.ESWA.2017.08.042

    Article  Google Scholar 

  27. Rathi, K., Balamohan, S.: A mathematical model for subjective evaluation of alternatives in fuzzy multi-criteria group decision making using COPRAS method. Int. J. Fuzzy Syst. 19, 1290–1299 (2017). https://doi.org/10.1007/s40815-016-0256-z

    Article  Google Scholar 

  28. Liu, P., Hendalianpour, A., Hamzehlou, M., Feylizadeh, M.R., Razmi, J.: Identify and rank the challenges of implementing sustainable supply chain blockchain technology using the bayesian best worst method. Technol. Econ. Dev. Econ. (2021). https://doi.org/10.3846/tede.2021.14421

    Article  Google Scholar 

  29. Hendalianpour, A., Fakhrabadi, M., Zhang, X., Feylizadeh, M.R., Gheisari, M., Liu, P., Ashktorab, N.: Hybrid model of IVFRN-BWM and robust goal programming in agile and flexible supply chain, a case study: automobile industry. IEEE Access. 7, 71481–71492 (2019). https://doi.org/10.1109/ACCESS.2019.2915309

    Article  Google Scholar 

  30. Hendalianpour, A., Hamzehlou, M., Feylizadeh, M.R., Xie, N., Shakerizadeh, M.H.: Coordination and competition in a two-echelon supply chain using grey revenue-sharing contracts. Grey Syst. Theory Appl. (2020). https://doi.org/10.1108/GS-04-2020-0056

    Article  Google Scholar 

  31. Hendalianpour, A., Fakhrabadi, M., Sangari, M.S., Razmi, J.: A combined benders decomposition and lagrangian relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system. Sci. Iran (2020). https://doi.org/10.24200/sci.2020.53644.3349

    Article  Google Scholar 

  32. Perçin, S.: Use of fuzzy AHP for evaluating the benefits of information-sharing decisions in a supply chain. J. Enterp. Inf. Manag. 21, 263–284 (2008). https://doi.org/10.1108/17410390810866637

    Article  Google Scholar 

  33. Craighead, C.W., Blackhurst, J., Rungtusanatham, M.J., Handfield, R.B.: The severity of supply chain disruptions: design characteristics and mitigation capabilities. Decis. Sci. 38, 131–156 (2007). https://doi.org/10.1111/j.1540-5915.2007.00151.x

    Article  Google Scholar 

  34. Deng, X., Jiang, W.: Evaluating green supply chain management practices under fuzzy environment: a novel method based on d number theory. Int. J. Fuzzy Syst. (2019). https://doi.org/10.1007/s40815-019-00639-5

    Article  Google Scholar 

  35. Zhou, Q., Huang, W., Zhang, Y.: Identifying critical success factors in emergency management using a fuzzy DEMATEL method. Saf. Sci. 49, 243–252 (2011). https://doi.org/10.1016/J.SSCI.2010.08.005

    Article  Google Scholar 

  36. Chen, Y.-H., Wang, T.-C., Wu, C.-Y.: Strategic decisions using the fuzzy PROMETHEE for IS outsourcing. Expert Syst. Appl. 38, 13216–13222 (2011). https://doi.org/10.1016/J.ESWA.2011.04.137

    Article  Google Scholar 

  37. Hsu, C.-C., Liou, J.J.H.: An outsourcing provider decision model for the airline industry. J. Air Transp. Manag. 28, 40–46 (2013). https://doi.org/10.1016/J.JAIRTRAMAN.2012.12.009

    Article  Google Scholar 

  38. Routroy, S., Sunil Kumar, C.V.: Analyzing supplier development program enablers using fuzzy DEMATEL. Meas. Bus. Excell. 18, 1–26 (2014). https://doi.org/10.1108/MBE-08-2013-0046

    Article  Google Scholar 

  39. Uygun, Ö., Kaçamak, H., Kahraman, Ü.A.: An integrated DEMATEL and Fuzzy ANP techniques for evaluation and selection of outsourcing provider for a telecommunication company. Comput. Ind. Eng. 86, 137–146 (2015). https://doi.org/10.1016/J.CIE.2014.09.014

    Article  Google Scholar 

  40. Yu, D., Li, D.-F., Merigó, J.M.: Dual hesitant fuzzy group decision-making method and its application to supplier selection. Int. J. Mach. Learn. Cybern. 7, 819–831 (2016). https://doi.org/10.1007/s13042-015-0400-3

    Article  Google Scholar 

  41. Lima-Junior, F.R., Carpinetti, L.C.R.: A multicriteria approach based on fuzzy QFD for choosing criteria for supplier selection. Comput. Ind. Eng. 101, 269–285 (2016). https://doi.org/10.1016/J.CIE.2016.09.014

    Article  Google Scholar 

  42. Ren, J.: Technology selection for ballast water treatment by multi-stakeholders: a multi-attribute decision analysis approach based on the combined weights and extension theory. Chemosphere 191, 747–760 (2018). https://doi.org/10.1016/j.chemosphere.2017.10.053

    Article  Google Scholar 

  43. Rezaei, J., Kothadiya, O., Tavasszy, L., Kroesen, M.: Quality assessment of airline baggage handling systems using SERVQUAL and BWM. Tour. Manag. 66, 85–93 (2018). https://doi.org/10.1016/J.TOURMAN.2017.11.009

    Article  Google Scholar 

  44. Haeri, S.A.S., Rezaei, J.: A grey-based green supplier selection model for uncertain environments. J. Clean. Prod. 221, 768–784 (2019). https://doi.org/10.1016/j.jclepro.2019.02.193

    Article  Google Scholar 

  45. Wu, L., Chen, Y., Feylizadeh, M.R.: Study on the estimation, decomposition, and application of China’s provincial carbon marginal abatement costs. J. Clean. Prod. (2019). https://doi.org/10.1016/j.jclepro.2018.10.082

    Article  Google Scholar 

  46. Đalić, I., Stević, Ž, Karamasa, C., Puška, A.: A Novel Integrated Fuzzy PIPRECIA–Interval Rough Saw Model: Green Supplier Selection. Decis. Mak. Appl. Manag. Eng. 3, 80–95 (2020). https://doi.org/10.31181/dmame2003114d

    Article  Google Scholar 

  47. Oroojeni Mohammad Javad, M., Darvishi, M., Oroojeni Mohammad Javad, A.: Green supplier selection for the steel industry using BWM and fuzzy TOPSIS: A case study of Khouzestan steel company. Sustain. Futur. 2, 100012 (2020). https://doi.org/10.1016/j.sftr.2020.100012

    Article  Google Scholar 

  48. Kilic, H.S., Yalcin, A.S.: Modified two-phase fuzzy goal programming integrated with IF-TOPSIS for green supplier selection. Appl. Soft Comput. J. 93, 106371 (2020). https://doi.org/10.1016/j.asoc.2020.106371

    Article  Google Scholar 

  49. Gupta, S., Soni, U., Kumar, G.: Green supplier selection using multi-criterion decision making under fuzzy environment: a case study in the automotive industry. Comput. Ind. Eng. 136, 663–680 (2019). https://doi.org/10.1016/j.cie.2019.07.038

    Article  Google Scholar 

  50. Akman, G.: Evaluating suppliers to include green supplier development programs via fuzzy c-means and VIKOR methods. Comput. Ind. Eng. 86, 69–82 (2015). https://doi.org/10.1016/j.cie.2014.10.013

    Article  Google Scholar 

  51. Demirtas, O.: Evaluating the core capabilities for strategic outsourcing decisions at aviation maintenance industry. Procedia-Soc. Behav. Sci. 99, 1134–1143 (2013). https://doi.org/10.1016/J.SBSPRO.2013.10.587

    Article  Google Scholar 

  52. Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., Diabat, A.: Integrated fuzzy multi-criteria decision-making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. J. Clean. Prod. 47, 355–367 (2013). https://doi.org/10.1016/J.JCLEPRO.2013.02.010

    Article  Google Scholar 

  53. Li, D.-F., Wan, S.-P.: Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information. Appl. Soft Comput. 13, 4333–4348 (2013). https://doi.org/10.1016/J.ASOC.2013.06.019

    Article  Google Scholar 

  54. Pun, H., Sebastian Heese, H.: Outsourcing to suppliers with unknown capabilities. Eur. J. Oper. Res. 234, 108–118 (2014). https://doi.org/10.1016/J.EJOR.2013.10.068

    Article  MathSciNet  MATH  Google Scholar 

  55. Li, D.-F.: Notes on “Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making.” Comput. Ind. Eng. 73, 1–4 (2014). https://doi.org/10.1016/J.CIE.2014.04.004

    Article  Google Scholar 

  56. Azadi, M., Jafarian, M., Farzipoor Saen, R., Mirhedayatian, S.M.: A new fuzzy DEA model for evaluation of efficiency and effectiveness of suppliers in sustainable supply chain management context. Comput. Oper. Res. 54, 274–285 (2015). https://doi.org/10.1016/J.COR.2014.03.002

    Article  MathSciNet  MATH  Google Scholar 

  57. Vahidi, F., Torabi, S.A., Ramezankhani, M.J.: Sustainable supplier selection and order allocation under operational and disruption risks. J. Clean. Prod. 174, 1351–1365 (2018). https://doi.org/10.1016/J.JCLEPRO.2017.11.012

    Article  Google Scholar 

  58. Hamdan, S., Cheaitou, A.: Supplier selection and order allocation with green criteria: an MCDM and multi-objective optimization approach. Comput. Oper. Res. 81, 282–304 (2017). https://doi.org/10.1016/j.cor.2016.11.005

    Article  MathSciNet  MATH  Google Scholar 

  59. Liu, C., Chen, W., Mu, J.: Retailer’s multi-tier green procurement contract in the presence of suppliers’ reference point effect. Comput. Ind. Eng. 131, 242–258 (2019). https://doi.org/10.1016/j.cie.2019.03.013

    Article  Google Scholar 

  60. Zhou, F., Chen, T.-Y.: Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures. Comput. Ind. Eng. 148, 106670 (2020). https://doi.org/10.1016/j.cie.2020.106670

    Article  Google Scholar 

  61. Wu, Y., Xu, C., Huang, Y., Li, X.: Green supplier selection of electric vehicle charging based on Choquet integral and type-2 fuzzy uncertainty. Soft Comput. 24, 3781–3795 (2020). https://doi.org/10.1007/s00500-019-04147-4

    Article  Google Scholar 

  62. Miranda-Ackerman, M.A., Azzaro-Pantel, C., Aguilar-Lasserre, A.A.: A green supply chain network design framework for the processed food industry: application to the orange juice agro-food cluster. Comput. Ind. Eng. 109, 369–389 (2017). https://doi.org/10.1016/j.cie.2017.04.031

    Article  Google Scholar 

  63. Sarkar, B., Omair, M., Choi, S.-B.: A multi-objective optimization of energy, economic, and carbon emission in a production model under sustainable supply chain management. Appl. Sci. 8, 1744 (2018). https://doi.org/10.3390/app8101744

    Article  Google Scholar 

  64. Deveci, M., Özcan, E., John, R., Covrig, C.F., Pamucar, D.: A study on offshore wind farm siting criteria using a novel interval-valued fuzzy-rough based Delphi method. J. Environ. Manag. 270, 110916 (2020). https://doi.org/10.1016/j.jenvman.2020.110916

    Article  Google Scholar 

  65. Gorzałczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21, 1–17 (1987). https://doi.org/10.1016/0165-0114(87)90148-5

    Article  MathSciNet  MATH  Google Scholar 

  66. Gao, H., Ran, L., Wei, G., Wei, C., Wu, J.: Vikor method for MAGDM based on Q-rung interval-years, given the advantages of considering the compromise between and its application to supplier selection of medical consumption products. Int. J. Environ. Res. Public Health. 17, 525 (2020). https://doi.org/10.3390/ijerph17020525

    Article  Google Scholar 

  67. Wan, S., Dong, J., Chen, S.-M.: Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making. Inf. Sci. (NY). (2021). https://doi.org/10.1016/j.ins.2021.03.038

    Article  MATH  Google Scholar 

  68. Ali, A., Rashid, T.: Hesitant fuzzy best-worst multi-criteria decision-making method and its applications. Int. J. Intell. Syst. 34, 1953–1967 (2019). https://doi.org/10.1002/int.22131

    Article  Google Scholar 

  69. Guo, S., Zhao, H.: Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Syst. 121, 23–31 (2017). https://doi.org/10.1016/j.knosys.2017.01.010

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu

  2. School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, 1439955961, Iran

    Ayad Hendalianpour

  3. Department of Business and Management Science, NHH Norwegian School of Economics, 5045, Bergen, Norway

    Mahnaz Fakhrabadi

  4. Department of Industrial Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

    Mohamdreza Feylizadeh

Authors
  1. Peide Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ayad Hendalianpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mahnaz Fakhrabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamdreza Feylizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ayad Hendalianpour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Hendalianpour, A., Fakhrabadi, M. et al. Integrating IVFRN-BWM and Goal Programming to Allocate the Order Quantity Considering Discount for Green Supplier. Int. J. Fuzzy Syst. 24, 989–1011 (2022). https://doi.org/10.1007/s40815-021-01181-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01181-z

Keywords

Search

Navigation