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Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply

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Abstract

This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice parameters. Assume that the supply parameters of the constraints in a transportation problem (TP) follow logistic distribution. The main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required demand. Using stochastic programming, the stochastic supply constraints of the TP are transformed into deterministic constraints. Finally, a non-linear deterministic model is formulated. Using Lingo software, the optimal solution of the proposed problem is derived. To illustrate the methodology, a real-life problem on the TP is considered.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Tao, Z., Xu, J.: A class of rough multiple objective programming and its application to solid transportation problem. Inform. Sci. 188, 215–235 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kantorovich, L.V.: Mathematical methods of organizing and planning production. Manag. Sci. 6, 336–422 (1960)

    Article  MathSciNet  Google Scholar 

  4. Mahapatra, D.R., Roy, S.K., Biswal, M.P.: Multi-choice stochastic transportation problem involving extreme value distribution. Appl. Math. Model. 37, 2230–2240 (2013)

    Article  MathSciNet  Google Scholar 

  5. Healy, W.C.: Multiple choice programming: (a procedure for linear programming with zero-one variables). Oper. Res. 12(1), 122–138 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chang, C.T.: Multi-choice goal programming OMEGA. Int. J. Manag. Sci. 35, 389–396 (2007)

    Google Scholar 

  7. Chang, C.T.: Revised multi-choice goal programming. Appl. Math. Model. 32, 2587–2595 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Biswal, M.P., Acharya, S.: Solving multi-choice linear programming problems by interpolating polynomials. Math. Comput. Model. 54, 1405–1412 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Roy, S.K., Mahapatra, D.R., Biswal, M.P.: Multi-choice stochastic transportation problem with exponential distribution. J. Uncertain. Syst. 6(3), 200–213 (2013)

    Google Scholar 

  10. Maity, G., Roy, S.K.: Solving multi-choice multi-objective transportation problem: a utility function approach. J. Uncertain. Anal. Appl. 2(1), 1 (2014)

    Article  Google Scholar 

  11. Scarborough, J.B.: Numerical Mathematical Analysis. John Hopkins University Press, Baltimore (1950)

    MATH  Google Scholar 

  12. Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, 2nd edn. Springer, New York (2011)

    Book  MATH  Google Scholar 

Download references

Acknowledgments

The author is very much thankful to the referee for his valuable comments to revise the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Sankar Kumar Roy

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  1. Sankar Kumar Roy
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Correspondence to Sankar Kumar Roy.

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Roy, S.K. Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply. J. Oper. Res. Soc. China 4, 193–204 (2016). https://doi.org/10.1007/s40305-016-0125-3

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