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Capacitated two-stage facility location problem with fuzzy costs and demands

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Abstract

In this study, we develop a two-stage capacitated facility location model with fuzzy costs and demands. The proposed model is a task of 0–1 integer two-stage fuzzy programming problem. In order to solve the problem, we first apply an approximation approach to estimate the objective function (with fuzzy random parameters) and prove the convergence of the approach. Then, we design a hybrid algorithm which integrates the approximation approach, neural network and particle swarm optimization, to solve the proposed facility location problem. Finally, a numerical example is provided to test the hybrid algorithm.

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References

  1. Badri MA (1999) Combining the analytic hierarchy process and goal programming for global facility location–allocation problem. Int J Prod Econ 62(3):237–248

    Article  Google Scholar 

  2. Bhattacharya U, Rao JR, Tiwari RN (1992) Fuzzy multi-criteria facility location problem. Fuzzy Sets Syst 51(3):277–287

    Article  MathSciNet  MATH  Google Scholar 

  3. Boehm O, Hardoon DR, Manevitz LM (2011) Classifying cognitive states of brain activity via one-class neural networks with feature selection by genetic algorithms. Int J Mach Learn Cybern 2(3):125–134

    Article  Google Scholar 

  4. Bongartz I, Calamai PH, Conn AR (1994) A projection method for lp norm location–allocation problems. Math Program 66(1–3):283–312

    Article  MathSciNet  MATH  Google Scholar 

  5. Carrizosa E, Conde E, Munoz-Marquez M, Puerto J (1995) The generalized Weber problem with expected distances. Rairo-Recherche Operationnelle Oper Res 29(1):35–57

    MathSciNet  MATH  Google Scholar 

  6. Castellano G, Fanelli AM, Pelillo M (1997) An iterative pruning algorithm for feedforward neural networks. IEEE Trans Neural Netw 8:519–537

    Article  Google Scholar 

  7. Chen C-J (2011) Structural vibration suppression by using neural classifier with genetic algorithm. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0053-9

  8. Chvatal V (1983) Linear Programming. W. H. Freeman and Company, New York

    MATH  Google Scholar 

  9. Cooper L (1963) Location–allocation problems. Oper Res 11(3):331–344

    Article  MATH  Google Scholar 

  10. Dantzig GB (1963) Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey

    MATH  Google Scholar 

  11. Darzentas J (1987) A discrete location model with fuzzy accessibility measures. Fuzzy Sets Syst 23(1):149–154

    Article  Google Scholar 

  12. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  13. Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York

    Book  MATH  Google Scholar 

  14. Ernst AT, Krishnamoorthy M (1999) Solution algorithms for the capacitated single allocation hub location problem. Ann Oper Res 86(1–4):141–159

    Article  MathSciNet  MATH  Google Scholar 

  15. Gong D, Gen M, Xu W, Yamazaki G (1995) Hybrid evolutionary method for obstacle location–allocation problem. Comput Ind Eng 29(1–4):525–530

    Article  Google Scholar 

  16. Ishii H, Lee YL, Yeh KY (2007) Fuzzy facility location problem with preference of candidate sites. Fuzzy Sets Syst 158(17):1922–1930

    Article  MathSciNet  MATH  Google Scholar 

  17. Jarboui B, Damak N, Siarry P, Rebai A (2008) A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Appl Math Comput 195(1):299–308

    Article  MathSciNet  MATH  Google Scholar 

  18. Karayiannis NB, Venetsanopoulos AN (1992) Fast learning algorithms for neural networks. IEEE Trans Circuits Syst II Analog Digital Signal Process 39:453–474

    Article  MATH  Google Scholar 

  19. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks, vol IV, pp 1942–1948

  20. Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Morgan Kaufmann Publishers, San Francisco

    Google Scholar 

  21. Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10:445–450

    Article  Google Scholar 

  22. Liu YK (2005) Fuzzy programming with recourse. Int J Uncertain Fuzziness Knowl Based Syst 13(4):381–413

    Article  MATH  Google Scholar 

  23. Liu YK (2006) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Trans Fuzzy Syst 14(2):295–304

    Article  Google Scholar 

  24. Logendran R, Terrell MP (1988) Uncapacitated plant location–allocation problems with price sensitive stochastic demands. Comput Oper Res 15(2):189–198

    Article  Google Scholar 

  25. Laporte G, Louveaux FV, Hamme LV (1994) Exact solution to a location problem with stochastic demands. Transport Sci 28(2):95–103

    Article  MATH  Google Scholar 

  26. Louveaux FV, Peeters D (1992) A dual-based procedure for stochastic facility location. Oper Res 40(3):564–573

    Article  MathSciNet  MATH  Google Scholar 

  27. Love RF (1976) One-dimensional facility location–allocation using dynamic programming. Manag Sci 24(5):224–229

    Google Scholar 

  28. Lozano S, Guerrero F, Onieva L, Larraneta J (1998) Kohonen maps for solving a class of location–allocation problems. Eur J Oper Res 108(1):106–117

    Article  MATH  Google Scholar 

  29. Megiddo N, Supowit KJ (1984) On the complexity of some common geometric location problems. SIAM J Comput 13(1):182–196

    Article  MathSciNet  MATH  Google Scholar 

  30. Murtagh BA, Niwattisyawong SR (1982) Efficient method for the muti-depot location em dash allocation problem. J Oper Res Soc 33(7):629–634

    MATH  Google Scholar 

  31. Nahmias S (1978) Fuzzy variable. Fuzzy Sets Syst 1(2):97–101

    Article  MathSciNet  MATH  Google Scholar 

  32. Shi Y, Eberhart RC (1998a) A modified particle swarm optimizer. In: Proceedings of the 1998 IEEE international conference on evolutionary computation, pp 69–73

  33. Shi Y, Eberhart RC (1998b) Parameter selection in particle swarm optimization. In: Proceedings of 7th annual conference on evolutionary programming, pp 591–600

  34. Tasgetiren MF, Liang YC, Sevkli M, Gencyilmaz G (2007) A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. Eur J Oper Res 177(3):1930–1947

    Article  MATH  Google Scholar 

  35. Tong DL, Mintram R (2010) Genetic Algorithm-Neural Network (GANN): a study of neural network activation functions and depth of genetic algorithm search applied to feature selection. Int J Mach Learn Cybern 1(1–4):75–87

    Article  Google Scholar 

  36. Wang S, Liu Y, Dai X (2007) On the continuity and absolute continuity of credibility functions. J Uncertain Syst 1(3):185–200

    MATH  Google Scholar 

  37. Wang X-Z, Li C-G (2008) A definition of partial derivative of random functions and its application to RBFNN sensitivity analysis. Neurocomputing 71(7–9):1515–1526

    Article  Google Scholar 

  38. Wang X-Z, He Y-L, Dong L-C, Zhao H-Y (2011) Particle swarm optimization for determining fuzzy measures from data. Inform Sci 181(19):4230–4252

    Article  MATH  Google Scholar 

  39. Wen M, Iwamura K (2008) Fuzzy facility location–allocation problem under the Hurwicz criterion. Eur J Oper Res 184(2):627–635

    Article  MathSciNet  MATH  Google Scholar 

  40. Zadeh LA (1965) Fuzzy sets. Inform Contr 8(3):338–353

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhou J, Liu B (2007) Modeling capacitated location–allocation problem with fuzzy demands. Comput Ind Eng 53(3):454–468

    Article  Google Scholar 

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Acknowledgments

The work was supported partially by “Ambient SoC Global COE Program of Waseda University” of Ministry of Education, Culture, Sports, Science and Technology, Japan, and by the Research Fellowships of the Japan Society for the Promotion of Science (JSPS) for Young Scientists.

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Correspondence to Shuming Wang.

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Wang, S., Watada, J. Capacitated two-stage facility location problem with fuzzy costs and demands. Int. J. Mach. Learn. & Cyber. 4, 65–74 (2013). https://doi.org/10.1007/s13042-012-0073-0

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  • DOI: https://doi.org/10.1007/s13042-012-0073-0

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