Advertisement

Efficient Fuzzy Goal Programming Model for Multi-objective Production Distribution Problem

  • Srikant Gupta
  • Irfan Ali
  • Aquil Ahmed
Original Paper
  • 28 Downloads

Abstract

This paper comprises of modelling and optimization of a production–distribution problem with the multi-product. The proposed model combined three well-known approaches, fuzzy programming, goal programming and interactive programming to develop an efficient fuzzy goal programming (EFGP) model for multi-objective production distribution problem (MOPDP). In this approach decision maker (DM) decide the goals and constructed membership functions for each objective, and they changed according to the iterative decision taken by the DM. The proposed EFGP model for MOPDP attempts to simultaneously minimize total transportation costs and total delivery time concerning inventory levels, available initial stock at each source, as well as market demand and available warehouse space at each destination, and the constraint on the total budget. The main aid of the proposed model is that its offerings an organized outline that enables fuzzy goal decision-making for solving the MOPDP under an uncertain environment.

Keywords

Multi-objective programming Production–distribution problem Fuzzy goal programming Interactive programming 

Notes

Funding

Funding was provided by University Grant Commission (UGC), INDIA [UGC start-up Grant No. F.30-90/2015 (BSR)].

References

  1. 1.
    Sarrafha, K., Rahmati, S.H.A., Niaki, S.T.A., Zaretalab, A.: A bi-objective integrated procurement, production, and distribution problem of a multi-echelon supply chain network design: a new tuned MOEA. Comput. Oper. Res. 54, 35–51 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Gen, M., Syarif, A.: Hybrid genetic algorithm for multi-time period production distribution planning. Int. J. Comput. Ind. Eng. 48, 799–809 (2005)CrossRefGoogle Scholar
  3. 3.
    Martin, C.H., Dent, D.C., Eckhart, J.C.: Integrated production, distribution, and inventory planning at Libbey–Owens–Ford. Interfaces 23, 78–86 (1993)CrossRefGoogle Scholar
  4. 4.
    Chen, M., Wang, W.: A linear programming model for integrated steel production and distribution planning. Int. J. Oper. Prod. Manag. 17, 592–610 (1997)CrossRefGoogle Scholar
  5. 5.
    Oh, H.C., Karimi, I.A.: Global multiproduct production–distribution planning with duty drawbacks. AIChE J. 52, 595–610 (2006)CrossRefGoogle Scholar
  6. 6.
    Kanyalkar, A.P., Adil, G.K.: An integrated aggregate and detailed planning in a multi-site production environment using linear programming. Int. J. Prod. Res. 43, 4431–4454 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Ryu, J.H., Dua, V., Pistikopoulos, E.N.: A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput. Chem. Eng. 28, 1121–1129 (2004)CrossRefGoogle Scholar
  8. 8.
    Bredstrom, D., Ronnqvist, M.: Integrated production planning and route scheduling in pulp mill industry. In: Proceedings of the 35th Annual Hawaii International Conference on System Sciences, HICSS (2002)Google Scholar
  9. 9.
    Goetschalckx, M., Vidal, C.J., Dogan, K.: Modeling and design of global logistics systems: a review of integrated strategic and tactical models and design algorithms. Eur. J. Oper. Res. 143, 1–18 (2002)CrossRefzbMATHGoogle Scholar
  10. 10.
    Sabri, E., Beamon, B.M.: A Multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega 28, 581–598 (2000)CrossRefGoogle Scholar
  11. 11.
    Rizk, N., Martel, A., D’amours, S.: Synchronized production-distribution planning in a single-plant multi-destination network. J. Oper. Res. Soc. 59, 90–104 (2008)CrossRefzbMATHGoogle Scholar
  12. 12.
    Jung, H., Jeong, B., Lee, C.G.: An order quantity negotiation model for distributor-driven supply chains. Int. J. Prod. Econ. 111, 147–158 (2008)CrossRefGoogle Scholar
  13. 13.
    Park, Y.B.: An integrated approach for production and distribution planning in supply chain management. Int. J. Prod. Res. 43, 1205–1224 (2005)CrossRefzbMATHGoogle Scholar
  14. 14.
    Huang, G.Q., Lau, J.S.K., Mak, K.L.: The impacts of sharing production information on supply chain dynamics: a review of the literature. Int. J. Prod. Res. 41, 1483–1517 (2003)CrossRefGoogle Scholar
  15. 15.
    Haq, A.N., Vrat, P., Kanda, A.: An integrated production-inventory-distribution model for manufacture of urea: a case. Int. J. Prod. Econ. 25(1), 39–49 (1991)CrossRefGoogle Scholar
  16. 16.
    Gupta, S., Ali, I., & Ahmed, A.: Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment. OPSEARCH (2018).  https://doi.org/10.1007/s12597-018-0330-4
  17. 17.
    Jindal, A., Sangwan, K.S., Saxena, S.: Network design and optimization for multi-product, multi-time, multi-echelon closed-loop supply chain under uncertainty. Procedia CIRP 29, 656–661 (2015)CrossRefGoogle Scholar
  18. 18.
    Selim, H., Araz, C., Ozkarahan, I.: Collaborative production–distribution planning in supply chain: a fuzzy goal programming approach. Transp. Res. Part E Logist. Transp. Rev. 44(3), 396–419 (2008)CrossRefGoogle Scholar
  19. 19.
    Chen, C.L., Lee, W.C.: Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Comput. Chem. Eng. 28(6), 1131–1144 (2004)CrossRefGoogle Scholar
  20. 20.
    Aliev, R.A., Fazlollahi, B., Guirimov, B.G., Aliev, R.R.: Fuzzy-genetic approach to aggregate production–distribution planning in supply chain management. Inf. Sci. 177, 4241–4255 (2007)CrossRefzbMATHGoogle Scholar
  21. 21.
    Tang, J., Wang, D., Fung, R.Y.: Fuzzy formulation for multi-product aggregate production planning. Prod. Plan. Control 11(7), 670–676 (2000)CrossRefGoogle Scholar
  22. 22.
    Bilgen, B.: Application of fuzzy mathematical programming approach to the production allocation and distribution supply chain network problem. Expert Syst. Appl. 37(6), 4488–4495 (2010)CrossRefGoogle Scholar
  23. 23.
    Sel, Ç., Bilgen, B.: Hybrid simulation and MIP based heuristic algorithm for the production and distribution planning in the soft drink industry. J. Manuf. Syst. 33(3), 385–399 (2014)CrossRefGoogle Scholar
  24. 24.
    Jamalnia, A., Soukhakian, M.A.: A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning. Comput. Ind. Eng. 56(4), 1474–1486 (2009)CrossRefGoogle Scholar
  25. 25.
    Roghanian, E., Sadjadi, S.J., Aryanezhad, M.B.: A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl. Math. Comput. 188, 786–800 (2007)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Liang, T.F.: Integrating production-transportation planning decision with fuzzy multiple goals in supply chains. Int. J. Prod. Res. 46(6), 1477–1494 (2008)CrossRefzbMATHGoogle Scholar
  27. 27.
    Liang, T.F., Cheng, H.W.: Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains. Expert Syst. Appl. 36(2), 3367–3377 (2009)CrossRefGoogle Scholar
  28. 28.
    Hannan, E.L.: Linear programming with multiple fuzzy goals. Fuzzy Sets Syst. 6(3), 235–248 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Gholamian, N., Mahdavi, I., Tavakkoli-Moghaddam, R., Mahdavi-Amiri, N.: Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty. Appl. Soft Comput. 37, 585–607 (2015)CrossRefGoogle Scholar
  30. 30.
    Garai, A., Mandal, P., Roy, T.K.: Intuitionistic fuzzy T-sets based optimization technique for production distribution planning in supply chain management. OPSEARCH 53(4), 950–975 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Peidro, D., Mula, J., Poler, R., Verdegay, J.L.: Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets Syst. 160(18), 2640–2657 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Latpate, R. V., Bajaj, V.H.: Fuzzy multi-objective, multi-product, production distribution problem with manufacturer storage. In: Proceedings of International Congress on PQROM, pp. 340–355 (2011)Google Scholar
  33. 33.
    Vahidi, J., Rezvani, S.: Arithmetic operations on trapezoidal fuzzy numbers. J. Nonlinear Anal. Appl. 2013, 1–8 (2013)Google Scholar
  34. 34.
    Bit, A.K., Biswas, M.P., Alam, S.S.: An additive fuzzy programming model for multiobjective transportation problem. Fuzzy Sets Syst. 57, 13–19 (1993)MathSciNetGoogle Scholar
  35. 35.
    Gupta, N., Ali, I., Bari, A.: Interactive fuzzy goal programming approach in multi-response stratified sample surveys. Yugosl. J. Oper. Res. 26(2), 241–258 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    El-Wahed, W.F.A., Lee, S.M.: Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34(2), 158–166 (2006)CrossRefGoogle Scholar
  37. 37.
    Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst. 89(2), 215–222 (1997)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Singh, P., Kumari, S., Singh, P.: Fuzzy efficient interactive goal programming approach for multi-objective transportation problems. Int. J. Appl. Comput. Math. 3(2), 505–525 (2017)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Waiel, F.A.E.W., Lee, S.M.: Interactive fuzzy goal programming for multiobjective transportation problems. Omega 34, 158–166 (2006)CrossRefGoogle Scholar
  40. 40.
    Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchAligarh Muslim UniversityAligarhIndia

Personalised recommendations