A belief degree-based uncertain scheme for a bi-objective two-stage green supply chain network design problem with direct shipment

Abstract

In the lack of historical data for an uncertain event, the belief degree-based uncertainty becomes more applicable than other types of uncertainty like fuzzy theory, stochastic programming, etc. This study focuses on an uncertain bi-objective two-stage supply chain network design problem. The problem consists of plants, depots, and customers with cost and environmental impacts (CO2 emission) where direct shipment between plants and customers is allowed. As such network could be designed for the first time in a geographical region, such problem is modeled in a belief degree-based uncertain environment. This is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts and direct shipment. Three approaches of expected value model, chance-constrained model, and their combination are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by two multi-objective optimization approaches of goal programming (GP) and global criterion method (GCM). An extensive computational study with various test problems is performed to study the performance of the crisp models and the solution approaches. As result, the obtained crisp formulations are highly sensitive to the changes in the cost parameters’ values, and the GP performs better than the GCM from the solution quality point of view.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Boros P, Fehér O, Lakner Z, Niroomand S, Vizvári B (2016) Modeling supermarket re-layout from the owner’s perspective. Ann Oper Res 238(1–2):27–40

    MathSciNet  Article  Google Scholar 

  2. Chen L, Peng J, Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59

    Article  Google Scholar 

  3. Cheraghalipour A, Paydar MM, Hajiaghaei-Keshteli M (2018) A bi-objective optimization for citrus closed-loop supply chain using Pareto-based algorithms. Appl Soft Comput 69:33–59

    Article  Google Scholar 

  4. Choong SS, Wong LP, Lim CP (2018) A dynamic fuzzy-based dance mechanism for the bee colony optimization algorithm. Comput Intell. https://doi.org/10.1111/coin.12159

    MathSciNet  Article  Google Scholar 

  5. Dalman H (2018a) Uncertain programming model for multi-item solid transportation problem. Int J Mach Learn Cybernet 9(4):559–567

    Article  Google Scholar 

  6. Dalman H (2018b) Entropy-based multi-item solid transportation problems with uncertain variables. Soft Comput. https://doi.org/10.1007/s00500-018-3255-1

    Article  MATH  Google Scholar 

  7. Ding S (2015) The α-maximum flow model with uncertain capacities. Appl Math Model 39(7):2056–2063

    MathSciNet  Article  Google Scholar 

  8. Ding S, Gao Y (2014) The (σ, S) policy for uncertain multi-product newsboy problem. Expert Syst Appl 41(8):3769–3776

    Article  Google Scholar 

  9. Gao Y (2012) Uncertain models for single facility location problems on networks. Appl Math Model 36:2592–2599

    MathSciNet  Article  Google Scholar 

  10. Gao Y, Kar S (2017) Uncertain solid transportation problem with product blending. Int J Fuzzy Syst 19(6):1916–1926

    MathSciNet  Article  Google Scholar 

  11. Govindan K, Darbari JD, Agarwal V, Jha PC (2017) Fuzzy multi-objective approach for optimal selection of suppliers and transportation decisions in an eco-efficient closed loop supply chain network. J Clean Prod 165:1598–1619

    Article  Google Scholar 

  12. Heydari A, Mahmoodirad A, Niroomand S (2016) An entropy-based mathematical formulation for straight assembly line balancing problem. Int J Strat Decis Sci (IJSDS) 7(2):57–68

    Article  Google Scholar 

  13. Huang X, Di H (2016) Uncertain portfolio selection with background risk. Appl Math Comput 276:284–296

    MathSciNet  MATH  Google Scholar 

  14. Izadikhah M, Saeidifar A, Roostaee R (2014) Extending TOPSIS in fuzzy environment by using the nearest weighted interval approximation of fuzzy numbers. J Intel Fuzzy Syst 27(6):2725–2736

  15. Kovács G, Vizvári B (2018) A generalization of Hunter’s bound to hypergraphs. Ann Oper Res. https://doi.org/10.1007/s10479-018-2869-0

  16. Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    Google Scholar 

  17. Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3–10

    Google Scholar 

  18. Liu L, Zhang B, Ma W (2018) Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Comput 22(17):5825–5833

  19. Ma H, Li X (2017) Closed-loop supply chain network design for hazardous products with uncertain demands and returns. Appl Soft Comput 68:889–899

    Article  Google Scholar 

  20. Mahmoodirad A, Dehghan R, Niroomand S (2019) Modelling linear fractional transportation problem in belief degree—based uncertain environment. J Exp Theor Artif Intell 31(3):393–408

    Article  Google Scholar 

  21. Mirzaei N, Niroomand S, Zare R (2016) Application of statistical process control in service industry. J Modell Manag 11(3):763–782

    Article  Google Scholar 

  22. Mohammed A, Wang Q, Li X (2017) A cost-effective decision-making algorithm for an RFID-enabled HMSC network design. Ind Manag Data Syst 117(9):1782–1799

    Article  Google Scholar 

  23. Mohammed A, Harris I, Soroka A, Nujoom R (2019) A hybrid MCDM-fuzzy multi-objective programming approach for a G-Resilient supply chain network design. Comput Ind Eng 127:297–312

    Article  Google Scholar 

  24. Mosallaeipour S, Mahmoodirad A, Niroomand S, Vizvari B (2018) Simultaneous selection of material and supplier under uncertainty in carton box industries: a fuzzy possibilistic multi-criteria approach. Soft Comput 22(9):2891–2905

    Article  Google Scholar 

  25. Mou D, Zhao W, Chang X (2013) A transportation problem with uncertain truck times and unit costs. Ind Eng Manag Syst 12(1):30–35

    Google Scholar 

  26. Nejad ZM, Ghaffari-Hadigheh A (2018) A novel DEA model based on uncertainty theory. Ann Oper Res 264(1–2):367–389

    MathSciNet  Article  Google Scholar 

  27. Niroomand S (2018) A multi-objective based direct solution approach for linear programming with intuitionistic fuzzy parameters. J Intell Fuzzy Syst 35(2):1923–1934

    Article  Google Scholar 

  28. Niroomand S, Vizvári B (2013) A mixed integer linear programming formulation of closed loop layout with exact distances. J Ind Prod Eng 30(3):190–201

    Google Scholar 

  29. Niroomand S, Takács S, Vizvári B (2011) To lay out or not to lay out? Ann Oper Res 191(1):183–192

    MathSciNet  Article  Google Scholar 

  30. Niroomand S, Hadi-Vencheh A, Mirzaei N, Molla-Alizadeh-Zavardehi S (2016) Hybrid greedy algorithms for fuzzy tardiness/earliness minimisation in a special single machine scheduling problem: case study and generalisation. Int J Comput Integr Manuf 29(8):870–888

    Article  Google Scholar 

  31. Niroomand S, Bazyar A, Alborzi M, Mahmoodirad A (2018) A hybrid approach for multi-criteria emergency center location problem considering existing emergency centers with interval type data: a case study. J Ambient Intell Humaniz Comput 9(6):1999–2008

    Article  Google Scholar 

  32. Nujoom R, Mohammed A, Wang Q (2019) Drafting a cost-effective approach towards a sustainable manufacturing system design. Comput Ind Eng 133:317–330

    Article  Google Scholar 

  33. Özceylan E, Paksoy T (2013) A mixed integer programming model for a closed-loop supply-chain network. Int J Prod Res 51(3):718–734

    Article  Google Scholar 

  34. Rezaei S, Kheirkhah A (2018) A comprehensive approach in designing a sustainable closed-loop supply chain network using cross-docking operations. Comput Math Organ Theory 24(1):51–98

    Article  Google Scholar 

  35. Salehi M, Maleki HR, Niroomand S (2017) A multi-objective assembly line balancing problem with worker’s skill and qualification considerations in fuzzy environment. Appl Intell. https://doi.org/10.1007/s10489-017-1065-2

    Article  Google Scholar 

  36. Sanei M, Mahmoodirad A, Niroomand S (2016) Two-stage supply chain network design problem with interval data. Int J e-Navigat Maritime Economy 5:74–84

    Article  Google Scholar 

  37. Sanei M, Mahmoodirad A, Niroomand S, Jamalian A, Gelareh S (2017) Step fixed charge solid transportation problem: a Lagrangian relaxation heuristic approach. Comput Appl Math 36(3):1217–1237

    MathSciNet  Article  Google Scholar 

  38. Taassori M, Taassori M, Niroomand S, Vizvári B, Uysal S, Hadi-Vencheh A (2015) OPAIC: An optimization technique to improve energy consumption and performance in application specific network on chips. Measurement 74:208–220

    Article  Google Scholar 

  39. Tavana M, Santos-Arteaga FJ, Mahmoodirad A, Niroomand S, Sanei M (2018) Multi-stage supply chain network solution methods: hybrid metaheuristics and performance measurement. Int J Syst Sci Oper Logistics 5(4):356–373

    Google Scholar 

  40. Torabi SA, Hassini E (2008) An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst 159:193–214

    MathSciNet  Article  Google Scholar 

  41. Tsao YC, Thanh VV, Lu JC, Yu V (2018) Designing sustainable supply chain networks under uncertain environments: fuzzy multi-objective programming. J Clean Prod 174:1550–1565

    Article  Google Scholar 

  42. Wanke P, Kalam Azad MA, Barros CP, Hadi-Vencheh A (2016) Predicting performance in ASEAN banks: an integrated fuzzy MCDM–neural network approach. Expert Syst 33(3):213–229

    Article  Google Scholar 

  43. Wanke P, Alvarenga H, Correa H, Hadi-Vencheh A, Azad MAK (2017) Fuzzy inference systems and inventory allocation decisions: exploring the impact of priority rules on total costs and service levels. Expert Syst Appl 85:182–193

    Article  Google Scholar 

  44. Wen M, Guo L, Kang R, Yang Y (2014) Data envelopment analysis with uncertain inputs and outputs. J Appl Math. https://doi.org/10.1155/2014/307108

    Article  Google Scholar 

  45. Zheng H, He J, Zhang Y, Huang G, Zhang Z, Liu Q (2019) A general model for fuzzy decision tree and fuzzy random forest. Comput Intell 35(2):310–335. https://doi.org/10.1111/coin.12195

    MathSciNet  Article  Google Scholar 

Download references

Funding

This study was not funded by any organization.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ali Mahmoodirad.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by V. Loia.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mahmoodirad, A., Niroomand, S. A belief degree-based uncertain scheme for a bi-objective two-stage green supply chain network design problem with direct shipment. Soft Comput (2020). https://doi.org/10.1007/s00500-020-05085-2

Download citation

Keywords

  • Green supply chain
  • Supply chain network design problem
  • Uncertainty theory
  • Multi-objective optimization