Fuzzy multi-objective optimization for multi-site integrated production and distribution planning in two echelon supply chain

  • Gaurav Kumar Badhotiya
  • Gunjan SoniEmail author
  • M. L. Mittal


This paper addresses an integrated production and distribution planning problem for a two-echelon supply chain network comprising of multiple manufacturers serving multiple selling locations. A novel fuzzy multi-objective mixed integer programming model is formulated considering multi-product, multi-period, and multi-site manufacturing environment. Minimization of total cost, delivery time, and backorder level are the three fuzzy objectives represented by piecewise linear membership function. Three important production and distribution aspects viz. capacity of the heterogeneous transportation, backordering for unfulfilled demand, and set-up cost/time for different products at manufacturing site are incorporated in an integrated manner to represent closeness to the real-life problem. An illustrative example inspired from a real-world case of an automobile industry is taken to demonstrate analytical results of the proposed approach. The outcome of the research indicates the practical applicability of the approach. Sensitivity analysis on objective function values is conducted for analyzing the effect of change in aspiration levels of objective function values on decision maker’s satisfaction level.


Multi-site manufacturing Production planning Distribution planning Fuzzy multi-objective programming Optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Torabi SA, Moghaddam M (2012) Multi-site integrated production-distribution planning with trans-shipment: a fuzzy goal programming approach. Int J Prod Res 50(6):1726–1748CrossRefGoogle Scholar
  2. 2.
    Guinet A (2001) Multi-site planning: a transshipment problem. Int J Prod Econ 74(1–3):21–32CrossRefGoogle Scholar
  3. 3.
    Moon C, Kim J, Hur S (2002) Integrated process planning and scheduling with minimizing total tardiness in multi-plants supply chain. Comput Ind Eng 43(1–2):331–349CrossRefGoogle Scholar
  4. 4.
    Zegordi SH, Nia MA (2009) Integrating production and transportation scheduling in a two-stage supply chain considering order assignment. Int J Adv Manuf Technol 44(9–10):928–939CrossRefGoogle Scholar
  5. 5.
    Rafiei H, Safaei F, Rabbani M (2018) Integrated production-distribution planning problem in a competition-based four-echelon supply chain. Comput Ind Eng 119:85–99CrossRefGoogle Scholar
  6. 6.
    Fahimnia B, Farahani RZ, Marian R, Luong L (2013) A review and critique on integrated production–distribution planning models and techniques. J Manuf Syst 32(1):1–9CrossRefGoogle Scholar
  7. 7.
    Badhotiya GK, Soni G, Mittal ML (2018) An analysis of mathematical models for multi-site production and distribution planning. Int J Intell Enterp 5(4):309–332CrossRefGoogle Scholar
  8. 8.
    Chan FT, Chung SH, Wadhwa S (2005) A hybrid genetic algorithm for production and distribution. Omega 33(4):345–355CrossRefGoogle Scholar
  9. 9.
    Lei L, Liu S, Ruszczynski A, Park S (2006) On the integrated production, inventory, and distribution routing problem. IIE Trans 38(11):955–970CrossRefGoogle Scholar
  10. 10.
    Alemany MM, Boj JJ, Mula J, Lario FC (2010) Mathematical programming model for centralised master planning in ceramic tile supply chains. Int J Prod Res 48(17):5053–5074CrossRefzbMATHGoogle Scholar
  11. 11.
    H'Mida F, Lopez P (2013) Multi-site scheduling under production and transportation constraints. Int J Comput Integr Manuf 26(3):252–266CrossRefGoogle Scholar
  12. 12.
    Entezaminia A, Heydari M, Rahmani D (2016) A multi-objective model for multi-product multi-site aggregate production planning in a green supply chain: considering collection and recycling centers. J Manuf Syst 40:63–75CrossRefGoogle Scholar
  13. 13.
    Park YB (2005) An integrated approach for production and distribution planning in supply chain management. Int J Prod Res 43(6):1205–1224CrossRefzbMATHGoogle Scholar
  14. 14.
    Safaei AS, Moattar Husseini SM, Z.-Farahani R, Jolai F, Ghodsypour SH (2010) Integrated multi-site production-distribution planning in supply chain by hybrid modelling. Int J Prod Res 48(14):4043–4069CrossRefzbMATHGoogle Scholar
  15. 15.
    Melo RA, Wolsey LA (2012) MIP formulations and heuristics for two-level production-transportation problems. Comput Oper Res 39(11):2776–2786MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Vercellis C (1999) Multi-plant production planning in capacitated self-configuring two-stage serial systems. Eur J Oper Res 119(2):451–460CrossRefzbMATHGoogle Scholar
  17. 17.
    Khalili-Damghani K, Tajik-Khaveh M (2015) Solving a multi-objective multi-echelon supply chain logistic design and planning problem by a goal programming approach. Int J Mgmt Sci Eng Mgmt 10(4):242–252CrossRefGoogle Scholar
  18. 18.
    Badhotiya GK, Soni G, Mittal ML (2018) Multi-site integrated production and distribution planning: a multi-objective approach. Int J Prod Dev 22(6):488–501CrossRefGoogle Scholar
  19. 19.
    Liang TF (2007) Applying fuzzy goal programming to production/transportation planning decisions in a supply chain. Int J Syst Sci 38(4):293–304MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Azadegan A, Porobic L, Ghazinoory S, Samouei P, Kheirkhah AS (2011) Fuzzy logic in manufacturing: a review of literature and a specialized application. Int J Prod Econ 132(2):258–270CrossRefGoogle Scholar
  21. 21.
    Zadeh LA (1965) Information and control. Fuzzy Sets 8(3):338–353Google Scholar
  22. 22.
    Zimmermann HJ (1976) Description and optimization of fuzzy systems. Int J Gen Syst 2(1):209–215CrossRefzbMATHGoogle Scholar
  23. 23.
    Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):B-141MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Hannan EL (1981) Linear programming with multiple fuzzy goals. Fuzzy Sets Syst 6(3):235–248MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    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):400–420CrossRefGoogle Scholar
  27. 27.
    Sakawa M, Nishizaki I, Uemura Y (2001) Fuzzy programming and profit and cost allocation for a production and transportation problem. Eur J Oper Res 131(1):1–5MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Chen SP, Chang PC (2006) A mathematical programming approach to supply chain models with fuzzy parameters. Eng Optim 38(6):647–669Google Scholar
  29. 29.
    Zadeh LA (1999) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 100:9–34CrossRefGoogle Scholar
  30. 30.
    Bilgen B (2008) Modeling of a blending and marine transportation planning problem with fuzzy mixed-integer programming. Int J Adv Manuf Technol 36(9–10):1041–1050CrossRefGoogle Scholar
  31. 31.
    Bilgen B (2010) Application of fuzzy mathematical programming approach to the production allocation and distribution supply chain network problem. Expert Syst Appl 37(6):4488–4495CrossRefGoogle Scholar
  32. 32.
    Jung H, Jeong SJ (2012) Managing demand uncertainty through fuzzy inference in supply chain planning. Int J Prod Res 50(19):5415–5429CrossRefGoogle Scholar
  33. 33.
    J.-Sharahi S, Khalili-Damghani K, Abtahi AR, Rashidi-Komijan A (2018) Type-II fuzzy multi-product, multi-level, multi-period location–allocation, production–distribution problem in supply chains: modelling and optimisation approach. Fuzzy Infor Eng 10(2):260–283CrossRefGoogle Scholar
  34. 34.
    Chen CL, Wang BW, Lee WC (2003) Multi objective optimization for a multi enterprise supply chain network. Ind Eng Chem Res 42(9):1879–1889CrossRefGoogle Scholar
  35. 35.
    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):1131–1144CrossRefGoogle Scholar
  36. 36.
    Roghanian E, Sadjadi SJ, Aryanezhad MB (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188(1):786–800MathSciNetzbMATHGoogle Scholar
  37. 37.
    Liang TF (2008a) Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain. Comput Ind Eng 55(3):676–694CrossRefGoogle Scholar
  38. 38.
    Liang TF (2008b) Integrating production-transportation planning decision with fuzzy multiple goals in supply chains. Int J Prod Res 46(6):1477–1494CrossRefzbMATHGoogle Scholar
  39. 39.
    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):2640–2657MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    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):5475–5499CrossRefzbMATHGoogle Scholar
  41. 41.
    Liang TF (2011) Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains. Inf Sci 181(4):842–854CrossRefzbMATHGoogle Scholar
  42. 42.
    Peidro D, Mula J, Alemany MM, Lario FC (2012) Fuzzy multi-objective optimisation for master planning in a ceramic supply chain. Int J Prod Res 50(11):3011–3020CrossRefGoogle Scholar
  43. 43.
    Sahebjamnia N, Jolai F, Torabi SA, Aghabeiglo M (2016) A novel fuzzy stochastic multi-objective linear programming for multi-level capacitated lot-sizing problem: a real case study of a furniture company. Int J Adv Manuf Technol 84(1–4):749–767CrossRefGoogle Scholar
  44. 44.
    Mohammed A, Wang Q (2017) The fuzzy multi-objective distribution planner for a green meat supply chain. Int J Prod Econ 184:47–58CrossRefGoogle Scholar
  45. 45.
    Mokhtari H, Hasani A (2017) A multi-objective model for cleaner production-transportation planning in manufacturing plants via fuzzy goal programming. J Manuf Syst 44:230–242CrossRefGoogle Scholar
  46. 46.
    Selim H, Araz C, Ozkarahan I (2008) Collaborative production–distribution planning in supply chain: a fuzzy goal programming approach. Transport Res E-Log 44(3):396–419CrossRefGoogle Scholar
  47. 47.
    Gholamian N, Mahdavi I, Tavakkoli-Moghaddam R, Mahdavi-Amiri N (2015) Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty. Appl Soft Comput 37:585–607CrossRefGoogle Scholar
  48. 48.
    Jolai F, Razmi J, Rostami NK (2011) A fuzzy goal programming and meta heuristic algorithms for solving integrated production: distribution planning problem. Cent Eur J Oper Res 19(4):547–569MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Sharma P, Singhal S (2017) Implementation of fuzzy TOPSIS methodology in selection of procedural approach for facility layout planning. Int J Adv Manuf Technol 88(5–8):1485–1493CrossRefGoogle Scholar
  50. 50.
    Khalili-Damghani K, Tavana M, Amirkhan M (2014) 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(9–12):1567–1595CrossRefGoogle Scholar
  51. 51.
    Lai YJ, Hwang CL (1992) Fuzzy mathematical programming. In: Fuzzy mathematical programming. Springer, Berlin, pp 74–186CrossRefGoogle Scholar
  52. 52.
    Sadeghi M, Hajiagha SH, Hashemi SS (2013) A fuzzy grey goal programming approach for aggregate production planning. Int J Adv Manuf Technol 64(9–12):1715–1727CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Gaurav Kumar Badhotiya
    • 1
  • Gunjan Soni
    • 1
    Email author
  • M. L. Mittal
    • 1
  1. 1.Department of Mechanical EngineeringMalaviya National Institute of Technology JaipurJaipurIndia

Personalised recommendations