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Solution of multi-item interval valued solid transportation problem with safety measure using different methods

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Abstract

The goal of this work is to solve an interval valued multi-item solid transportation problem (MIIVSTP) with safety measure. In this paper we introduce a new concept “safety factor” in transportation problem. When items are transported from origins to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency etc. in some routes specially in developing countries. Due to this reason desired total safety factor is being introduced and depending upon the nature of safety factor, we formulate five models without and with safety factor where this factor may be crisp, fuzzy, interval, stochastic in nature. Here the transportation costs are intervals, the corresponding multi-objective transportation problem is formulated using “mean and width” technique. Then the problem is converted to a single objective transportation problem taking convex combination of the objectives according to their weights. Finally all the models are solved by Generalized Reduced Gradient (GRG) method using LINGO software. Numerical examples are used to illustrate the model and methodologies.

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References

  1. Azadeh, A., Saberi, M., Ghaderi, S.F., Gitiforou, A.: Estimating and improving electricity demand function in residential sector with imprecise data by fuzzy regression. Int. J. Math. Oper. Res. 2(4), 405–423 (2010)

    Article  Google Scholar 

  2. Bera, U.K., Mahapatra, N.K., Maity, M.: An imperfect fuzzy production-inventory model over a finite time horizon under the effect of learning. Int. J. Math. Oper. Res. 1(3), 351–371 (2009)

    Article  Google Scholar 

  3. Bit, A.K., Biswal, M.P., Alam, S.S.: Fuzzy programming approach to multi-objective solid transportation problem. Fuzzy Set Syst. 57, 183–194 (1993)

    Article  Google Scholar 

  4. Charnes, A., Cooper, W.W.: Chance-constrained and normal deviates. J. Am. Stat. Assoc. 57, 134–118 (1952)

    Article  Google Scholar 

  5. Charnes, A., Cooper, W.W.: Deterministic equivalents for optimizing and satisfying under chance constraints. Oper. Res. 11, 18–39 (1963)

    Article  Google Scholar 

  6. Das, S.K., Goswami, A., Alam, S.S.: Multi-objective transportation problem with interval cost, source and destination parameters. Eur. J. Oper. Res. 117, 100–112 (1999)

    Article  Google Scholar 

  7. Das, B., Maity, K., Maiti, M.: A warehouse supply-chain model under possibility/necessity/credibility measure. Math. Comput. Model. 46, 398–409 (2007)

    Article  Google Scholar 

  8. Dubois, D., Prade, H.: Fuzzy sets and system—Theory and application. Academic, New York (1980)

    Google Scholar 

  9. Dubois, D., Prade, H.: Fuzzy sets and systems: Theory and Applications. Academic, New York (1988)

    Google Scholar 

  10. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized processing of Uncertain. Plenum Press, New York (1988)

    Book  Google Scholar 

  11. Dubois, D., Prade, H.: Fuzzy sets and probability: Misunderstanding, bridges and gaps, Proceedings of the 2nd IEEE International Conference on Furry Systems, San Francisco, pp. 1059–1068, (1993)

  12. Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)

    Google Scholar 

  13. Jimenez, F., Verdegay, J.L.: Uncertain solid transportation problem. Fuzzy Sets and Syst. Elsevier 100(1–3), 45–57 (1998)

    Article  Google Scholar 

  14. Liu, B., Iwamura, K.: Chance constrained programming with fuzzy parameters. Fuzzy Set Syst. 94(2), 227–237 (1998)

    Article  Google Scholar 

  15. Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value model. IEEE Trans. Fuzzy Syst. 10(4), 445–450 (2002)

    Article  Google Scholar 

  16. Nagarajan, A., Jeyaraman, K.: Solution of chance constrained programming problem for multi-objective interval solid transportation problem under stochastic environment using fuzzy approach. Int. J. Comput. Appl. 10(9) (2010). 0975 – 8887

    Google Scholar 

  17. Rong, M., Maiti, M.: A two-warehouse inventory model with stochastic demand controllable lead time and fuzzy present value: a technique to deal with arbitrary fuzzy number. Int. J. Oper. Res. 8(2), 208–229 (2010)

    Article  Google Scholar 

  18. Sengupta, A., Pal, T.K.: On comparing interval numbers. Eur. J. Oper. Res. 127, 28–43 (2000)

    Article  Google Scholar 

  19. Sengupta, A., Pal, T.K., Chakraborty, D.: Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Set Syst. 119, 129–138 (2001)

    Article  Google Scholar 

  20. Sengupta, A., Pal, T. K.: Interval-valued transportation problem with multiple penalty factors, Vidyasagar University Journal of Physical Science, pp. 71–81, (2004)

  21. Shell, E.: Distribution of a product by several properties, Directorate of management analysis, Proceedings of the Second Symposium in Linear Programming, vol. 2, pp. 615–642. DCS/Comptroller H.Q. U.S.A.F, Washington, D.C (1955)

    Google Scholar 

  22. Yadeb, D., Pundir, S., Kumari, R.: A fuzzy multi-item production model with reliability and flexibility under limited storage capacity with deterioration via geometric programming. Int. J. Math. Oper. Res. 3(1), 78–98 (2011)

    Article  Google Scholar 

  23. Zadeh, L.A.: Fuzzy sets. Information Control 8, 338–353 (1965)

    Google Scholar 

  24. Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning. Technical Report ERL-M 411, University of California-Berkely, (1973)

  25. Zadeh, L.A.: Fuzzy set as a basis for a theory of possibility. Fuzzy Set Syst. 1, 3–28 (1978)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Agartala, Jirania, 799055, West Tripura, India

    A. Baidya & U. K. Bera

  2. Department of Applied Mathematics, Vidyasagar University, Midnapore, 721102, WB, India

    M. Maiti

Authors
  1. A. Baidya
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  2. U. K. Bera
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  3. M. Maiti
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Correspondence to U. K. Bera.

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Baidya, A., Bera, U.K. & Maiti, M. Solution of multi-item interval valued solid transportation problem with safety measure using different methods. OPSEARCH 51, 1–22 (2014). https://doi.org/10.1007/s12597-013-0129-2

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