Skip to main content
SpringerLink
Log in

A fuzzy bi-objective mixed-integer programming method for solving supply chain network design problems under ambiguous and vague conditions

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Supply chain (SC) network design problems are complex problems with multi-layer levels and dynamic relationships which involve a considerable amount of uncertainty concerning customer demand, facility capacity, or lead times, among others. A large number of optimization methods (i.e., fuzzy mathematical programming, stochastic programming, and interval mathematical programming) have been proposed to cope with the uncertainties in SC network design problems. We propose a fuzzy bi-objective mixed-integer linear programming (MILP) model to enhance the material flow in dual-channel, multi-item, and multi-objective SCs with multiple echelons under both ambiguous and vague conditions, concurrently. We use a computationally efficient ranking method to resolve the ambiguity of the parameters and propose two methods for resolving the vagueness of the objective functions in the proposed fuzzy MILP model. The preferences of the decision makers (DMs) on the priority of the fuzzy goals are represented with crisp importance weights in the first method and fuzzy preference relations in the second method. The fuzzy preference relations in the second method present a unique practical application of type-II fuzzy sets. The performance of the two methods is compared using comprehensive statistical analysis. The results show the perspicuous dominance of the method which uses fuzzy preference relations (i.e., type-II fuzzy sets). We present a case study in the food industry to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms. To the best of our knowledge, a concurrent interpretation of both ambiguous and vague uncertainties, which is applicable to many real-life problems, is novel and has not been reported in the literature.

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

Similar content being viewed by others

References

  1. Amiri A (2006) Designing a distribution network in a supply chain system: formulation and efficient solution procedure. Eur J Oper Res 171(2):567–576

    Article  MATH  MathSciNet  Google Scholar 

  2. Arenas Parra M, Bilbao Terol A, Perez Gladish B, Rodriguez Uria M (2005) Solving a multiobjective possibilistic problem through compromise programming. Eur J Oper Res 164(3):748–759

    Article  MATH  MathSciNet  Google Scholar 

  3. Azadeh A, Keramati A, Karimi A, Jiryaei Sharahi Z, Pourhaji P (2014) Design of integrated information system and supply chain for selection of new facility and suppliers by a unique hybrid meta-heuristic computer simulation algorithm. Int J Adv Manuf Technol 71(5–8):775–793

    Article  Google Scholar 

  4. Azaron A, Brown KN, Tarim SA, Modarres M (2008) A multi-objective stochastic programming approach for supply chain design considering risk. Int J Prod Econ 116:129–138

    Article  Google Scholar 

  5. Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164

    MathSciNet  Google Scholar 

  6. Bhatnagar R, Sohal AS (2005) Supply chain competitiveness: measuring the impact of location factors, uncertainty and manufacturing practices. Technovation 25(5):443–456

    Article  Google Scholar 

  7. Bidhandi HM, Mohd Yusuff R (2011) Integrated supply chain planning under uncertainty using an improved stochastic approach. Appl Math Model 35(6):2618–2630

    Article  MATH  MathSciNet  Google Scholar 

  8. Bidhandi HM, Mohd Yusuff R, Megat Ahmad MMH, Abu Bakar MR (2009) Development of a new approach for deterministic supply chain network design. Eur J Oper Res 198(1):121–128

    Article  MATH  Google Scholar 

  9. Bozorgi-Amiri A, Jabalameli M-S, Alinaghian M, Heydari M (2012) A modified particle swarm optimization for disaster relief logistics under uncertain environment. Int J Adv Manuf Technol 60(1–4):357–371

    Article  Google Scholar 

  10. Buckley JJ (1984) Multiple goal non-cooperative conflicts under uncertainty: a fuzzy set approach. Fuzzy Sets Syst 13:107–124

    Article  MATH  MathSciNet  Google Scholar 

  11. Charnes A, Cooper WW (1961) Management models and industrial application of linear programming. Wiley, New York

    Google Scholar 

  12. Chen CL, Lee WC (2004) Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Comput Chem Eng 28(6–7):1131–1144

    Article  Google Scholar 

  13. Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97:33–48

    Article  MATH  MathSciNet  Google Scholar 

  14. Chiclana F, Herrera F, Herrera-Viedma E (2001) Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277–291

    Article  MATH  MathSciNet  Google Scholar 

  15. Christopher M (1998) Logistics and supply chain management. Pitman, London

    Google Scholar 

  16. Croom S, Romano P, Giannakis M (2000) Supply chain management: an analytical framework for critical literature review. Euro J Purch Supply Manag 6(1):67–83

    Article  Google Scholar 

  17. Dalkey NC, Helmer O (1963) An experimental application of the Delphi method to the use of experts. Manag Sci 9:458–467

    Google Scholar 

  18. Degraeve Z, Roodhooft F (2000) A mathematical programming approach for procurement using activity based costing. J Bus Financ Account 27(1–2):69–98

    Article  Google Scholar 

  19. Dubois D, Fargier H, Fortemps P (2003) Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge. Eur J Oper Res 147(2):231–252

    Article  MATH  MathSciNet  Google Scholar 

  20. Dubois D, Prade H (1980) Systems of linear fuzzy constraints. Fuzzy Sets Syst 3(1):37–48

    Article  MATH  Google Scholar 

  21. Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30(3):183–224

    Article  MATH  MathSciNet  Google Scholar 

  22. Dullaert W, Bräysy O, Goetschalckx M, Raa B, Center A (2007) Supply chain (re) design: support for managerial and policy decisions. Eur Transp Infrastruct Res 7(2):73–92

    Google Scholar 

  23. ElMaraghy H, Majety R (2008) Integrated supply chain design using multi-criteria optimization. Int J Adv Manuf Technol 37(3):371–399

    Article  Google Scholar 

  24. Eskigun E, Uzsoy R, Preckel PV, Beaujon G, Krishnan S, Tew JD (2005) Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers. Eur J Oper Res 165(1):182–206

    Article  MATH  MathSciNet  Google Scholar 

  25. Eskigun E, Uzsoy R, Preckel PV, Beaujon G, Krishnan S, Tew JD (2007) Outbound supply chain network design with mode selection and lead time considerations. Nav Res Logist 54(3):282–300

    Article  MATH  MathSciNet  Google Scholar 

  26. Fan Z-P, Hu G-F, Xiao S-H (2004) A method for multiple attribute decision-making with the fuzzy preference relation on alternatives. Comput Ind Eng 46:321–327

    Article  Google Scholar 

  27. Fan Z-P, Ma J, Jiang Y-P, Sun Y-H, Ma L (2006) A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations. Eur J Oper Res 174:311–321

    Article  MATH  Google Scholar 

  28. Fazel Zarandi M-H, Haddad Sisakht A, Davari S (2011) Design of a closed-loop supply chain (CLSC) model using an interactive fuzzy goal programming. Int J Adv Manuf Technol 56(5–8):809–821

    Article  Google Scholar 

  29. Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets Syst 47(1):81–86

    Article  MATH  MathSciNet  Google Scholar 

  30. Ho C, Chi Y, Tai Y (2005) A structural approach to measuring uncertainty in supply chains. Int J Electron Commer 9(3):91–114

    Google Scholar 

  31. Inuiguchi M, Ichihashi H (1990) Relative modalities and their use in possibilistic linear programming. Fuzzy Sets Syst 35(3):303–323

    Article  MATH  MathSciNet  Google Scholar 

  32. Inuiguchi M, Ichihashi H, Kume Y (1992) Relationships between modality constrained programming problems and various fuzzy mathematical programming problems. Fuzzy Sets Syst 49(3):243–259

    Article  MATH  MathSciNet  Google Scholar 

  33. Inuiguchi M, Ramík J (2000) Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst 111(1):3–28

    Article  MATH  Google Scholar 

  34. Inuiguchi M, Sakawa M, Kume Y (1994) The usefulness of possibilistic programming in production planning problems. Int J Prod Econ 33(1–3):45–52

    Article  Google Scholar 

  35. Jayaraman V, Pirkul H (2001) Planning and coordination of production and distribution facilities for multiple commodities. Eur J Oper Res 133(2):394–408

    Article  MATH  Google Scholar 

  36. Jiménez M, Arenas M, Bilbao A (2007) Linear programming with fuzzy parameters: an interactive method resolution. Eur J Oper Res 177(3):1599–1609

    Article  MATH  Google Scholar 

  37. Kacprzyk J (1986) Group decision making with a fuzzy majority. Fuzzy Sets Syst 18:105–118

    Article  MATH  MathSciNet  Google Scholar 

  38. Kacprzyk J, Fedrizzi M, Nurmi H (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst 49:21–31

    Article  MATH  MathSciNet  Google Scholar 

  39. Keeney S, Hasson RE, McKenna H (2006) Consulting the oracle: 10 lessons from using the Delphi technique in nursing research. J Adv Nurs 53(2):205–212

    Article  Google Scholar 

  40. Khalili-Damghani K, Sadi-Nezhad S (2013) A decision support system for fuzzy multi-objective multi-period sustainable project selection. Comput Ind Eng 64:1045–1060

    Article  Google Scholar 

  41. Khalili-Damghani K, Sadi-Nezhad S, Tavana M (2013) Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation. Inf Sci. doi:10.1016/j.ins.2013.05.005

    MATH  MathSciNet  Google Scholar 

  42. Khalili-Damghani K, Tavana M (2013) A new fuzzy network data envelopment analysis model for measuring the performance of agility in supply chains. Int J Adv Manuf Technol 69(1–4):291–318

    Article  Google Scholar 

  43. Kristianto Y, Zhu L (2013) An integration of assembly planning by design into supply chain planning. Int J Adv Manuf Technol 69(5–8):1593–1604

    Article  Google Scholar 

  44. Lai YJ, Hwang CL (1993) Possibilistic linear programming for managing interest rate risk. Fuzzy Sets Syst 54(2):135–146

    Article  MathSciNet  Google Scholar 

  45. Lee BK, Kang KH, Lee YH (2008) Decomposition heuristic to minimize total cost in a multi-level supply chain network. Comput Ind Eng 54(4):945–959

    Article  Google Scholar 

  46. Liang TF (2008) Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain. Comput Ind Eng 55(3):676–694

    Article  Google Scholar 

  47. Liu L, Huang GH, Liu Y, Fuller GA, Zeng GM (2003) A fuzzy-stochastic mixed integer robust linear programming approach for regional air quality management. Eng Optim 35(2):177–199

    Article  MathSciNet  Google Scholar 

  48. Lu Z, Bostel N (2007) A facility location model for logistics systems including reverse flows: the case of remanufacturing activities. Comput Oper Res 34(2):299–323

    Article  MATH  MathSciNet  Google Scholar 

  49. Lu J, Zhang G, Ruan D, Wu F (2007) Multi-objective group decision making: methods software and applications with fuzzy set techniques. Imperial College Press, London

    Book  Google Scholar 

  50. Luhandjula MK (1986) Satisfying solutions for a possibilistic linear program. Inf Sci 40(3):247–265

    Article  MATH  MathSciNet  Google Scholar 

  51. Mirzapour Al-e-Hashem SMJ, Aryanezhad MB, Sadjadi SJ (2012) An efficient algorithm to solve a multi-objective robust aggregate production planning in an uncertain environment. Int J Adv Manuf Technol 58(5–8):765–782

    Article  Google Scholar 

  52. Negoita C (1981) The current interest in fuzzy optimization. Fuzzy Sets Syst 6(3):261–269

    Article  MATH  MathSciNet  Google Scholar 

  53. Nikolopoulou A, Ierapetritou MG (2012) Optimal design of sustainable chemical processes and supply chains: a review. Comput Chem Eng 44:94–103

    Article  Google Scholar 

  54. Okoli C, Pawloski S (2004) The Delphi method as a research tool: an example, design considerations and applications. Inf Manag 42:15–29

    Article  Google Scholar 

  55. Paksoy T, Pehlivan NY, Özceylan E (2012) Application of fuzzy optimization to a supply chain network design: a case study of an edible vegetable oils manufacturer. Appl Math Model 36(6):2762–2776

    Article  MATH  MathSciNet  Google Scholar 

  56. Peidro D, Mula J, Jiménez M, del Mar Botella M (2010) A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment. Eur J Oper Res 205(1):65–80

    Article  MATH  Google Scholar 

  57. Peidro D, Mula J, Poler R, Lario FC (2009) Quantitative models for supply chain planning under uncertainty: a review. Int J Adv Manuf Technol 43(3–4):400–420

    Article  Google Scholar 

  58. Peidro D, Mula J, Poler R, Verdegay JL (2009) Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets Syst 160(18):2640–2657

    Article  MATH  MathSciNet  Google Scholar 

  59. Pishvaee MS, Kianfar K, Karimi B (2010) Reverse logistics network design using simulated annealing. Int J Adv Manuf Technol 47(1):269–281

    Article  Google Scholar 

  60. Pishvaee MS, Torabi SA (2010) A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets Syst 161(20):2668–2683

    Article  MATH  MathSciNet  Google Scholar 

  61. PrasannaVenkatesan S, Kumanan S (2012) Multi-objective supply chain sourcing strategy design under risk using PSO and simulation. Int J Adv Manuf Technol 61(1–4):325–337

    Article  Google Scholar 

  62. Ramezani M, Bashiri M, Tavakkoli-Moghaddam R (2013) A robust design for a closed-loop supply chain network under an uncertain environment. Int J Adv Manuf Technol 66(5–8):825–843

    Article  Google Scholar 

  63. Ramik J, Rommelfanger H (1993) A single- and multi-valued order on fuzzy numbers and its use in linear programming with fuzzy coefficients. Fuzzy Sets Syst 57(2):203–208

    Article  MATH  MathSciNet  Google Scholar 

  64. Ramik J, Rommelfanger H (1996) Fuzzy mathematical programming based on some new inequality relations. Fuzzy Sets Syst 81(1):77–88

    Article  MATH  MathSciNet  Google Scholar 

  65. Romero C (1986) A survey of generalized goal programming (1970–1982). Eur J Oper Res 25:183–191

    Article  MATH  Google Scholar 

  66. Romero C (2004) A general structure of achievement functions for a goal programming model. Eur J Oper Res 153:675–686

    Article  MATH  Google Scholar 

  67. Rommelfanger H, Slowinski R (1998) Fuzzy linear programming with single or multiple objective functions. Fuzzy sets in decision analysis, operations research and statistics. The handbooks of fuzzy sets series. Kluwer Academic Publ, Boston, pp 179–213

    Book  Google Scholar 

  68. Roodhooft F, Konings J (1997) Vendor selection and evaluation an activity based costing approach. Eur J Oper Res 96(1):97–102

    Article  MATH  Google Scholar 

  69. Rubin PA, Narasimhan R (1984) Fuzzy goal programming with nested priorities. Fuzzy Sets Syst 14:115–129

    Article  MATH  MathSciNet  Google Scholar 

  70. Sadjady H, Davoudpour H (2012) Two-echelon, multi-commodity supply chain network design with mode selection, lead-times and inventory costs. Comput Oper Res 39(7):1345–1354

    Article  MATH  MathSciNet  Google Scholar 

  71. Selim H, Ozkarahan I (2008) A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. Int J Adv Manuf Technol 36(3):401–418

    Article  Google Scholar 

  72. Singh AR, Jain R, Mishra PK (2013) Capacities-based supply chain network design considering demand uncertainty using two-stage stochastic programming. Int J Adv Manuf Technol 69(1–4):555–562

    Article  Google Scholar 

  73. Singh AR, Mishra PK, Jain R, Khurana MK (2012) Design of global supply chain network with operational risks. Int J Adv Manuf Technol 60(1–4):273–290

    Article  Google Scholar 

  74. Steuer RE (1986) Multiple criteria optimization, theory, computation and application. Wiley, New York

    MATH  Google Scholar 

  75. Syarif A, Yun YS, Gen M (2002) Study on multi-stage logistic chain network: a spanning tree-based genetic algorithm approach. Comput Ind Eng 43(1–2):299–314

    Article  Google Scholar 

  76. Tanaka H, Okuda T, Asai K (1973) On fuzzy-mathematical programming. J Cybern 3(4):37–46

    Article  MATH  MathSciNet  Google Scholar 

  77. Tanino T (1990) On group decision making under fuzzy preference. In: Kacprzyk J, Fedrizzi M (eds) Multiperson decision making using fuzzy sets and possibility theory. Kluwer Academic Publishers, Dordrecht, pp 172–185

    Chapter  Google Scholar 

  78. Tiwari RN, Dharmar S, Rao JR (1987) Fuzzy goal programming—an additive model. Fuzzy Sets Syst 24:27–34

    Article  MATH  MathSciNet  Google Scholar 

  79. Torabi SA, Hassini E (2008) An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst 159(2):193–214

    Article  MATH  MathSciNet  Google Scholar 

  80. Torabi SA, Hassini E (2009) Multi-site production planning integrating procurement and distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming approach. Int J Prod Res 47(19):5475–5499

    Article  MATH  Google Scholar 

  81. Tsiakis P, Papageorgiou LG (2008) Optimal production allocation and distribution supply chain networks. Int J Prod Econ 111(2):468–483

    Article  Google Scholar 

  82. van der Vorst JGAJ, Beulens AJM (2002) Identifying sources of uncertainty to generate supply chain redesign strategies. Int J Phys Distrib Logist Manag 32(6):409–430

    Article  Google Scholar 

  83. Vlajic JV, van der Vorst JGAJ, Haijema R (2012) A framework for designing robust food supply chains. Int J Prod Econ 137(1):176–189

    Article  Google Scholar 

  84. Wang W, Fung RYK, Chai Y (2004) Approach of just-in-time distribution requirements planning for supply chain management. Int J Prod Econ 91(2):101–107

    Article  Google Scholar 

  85. Wang F, Lai X, Shi N (2011) A multi-objective optimization for green supply chain network design. Decis Support Syst 51(2):262–269

    Article  Google Scholar 

  86. Wang RC, Liang TF (2005) Applying possibilistic linear programming to aggregate production planning. Int J Prod Econ 98(3):328–341

    Article  Google Scholar 

  87. Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1(1):3–28

    Article  MATH  MathSciNet  Google Scholar 

  88. Zanjirani Farahani R, Elahipanah M (2008) A genetic algorithm to optimize the total cost and service level for just-in-time distribution in a supply chain. Int J Prod Econ 111(2):229–243

    Article  Google Scholar 

  89. Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55

    Article  MATH  Google Scholar 

  90. Zimmermann HJ (1996) Fuzzy set theory and its applications, 3rd edn. Kluwer Academic Publishers, Boston, pp 11–38

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

    Kaveh Khalili-Damghani & Mohammad Amirkhan

  2. Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

Authors
  1. Kaveh Khalili-Damghani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madjid Tavana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Amirkhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Madjid Tavana.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khalili-Damghani, K., Tavana, M. & Amirkhan, M. A fuzzy bi-objective mixed-integer programming method for solving supply chain network design problems under ambiguous and vague conditions. Int J Adv Manuf Technol 73, 1567–1595 (2014). https://doi.org/10.1007/s00170-014-5891-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-014-5891-7

Keywords

Search

Navigation