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Multi-choice probabilistic linear programming problem

Author

Listed:
  • Avik Pradhan

    (Indian Institute of Technology Kharagpur)

  • M. P. Biswal

    (Indian Institute of Technology Kharagpur)

Abstract

In this paper, we present a linear programming model where the parameter space contains some multi-choice parameters. Alternative choices of multi-choice parameter are considered as random variables. Using interpolating polynomial for each multi-choice parameter, the model has been transformed into a non-linear mixed integer probabilistic programming problem. Then chance constrained programming technique is used to obtain an equivalent deterministic model of the transformed problem. To find the deterministic form of the objective function four different models namely, E-model, V-model, probability maximization model and fractile criterion model are used. Assuming the values of the multi-choice parameters as independent normal random variables, the methodology is presented. A numerical example is also presented to illustrate the methodology.

Suggested Citation

  • Avik Pradhan & M. P. Biswal, 2017. "Multi-choice probabilistic linear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 122-142, March.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:1:d:10.1007_s12597-016-0272-7
    DOI: 10.1007/s12597-016-0272-7
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    References listed on IDEAS

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    1. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Stochastic Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 149-196, Springer.
    2. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Multiobjective Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 73-103, Springer.
    3. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, April.
    4. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    5. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Linear and Multiobjective Programming with Fuzzy Stochastic Extensions," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4614-9399-0, April.
    6. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Fuzzy Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 105-148, Springer.
    7. C. van de Panne & W. Popp, 1963. "Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints," Management Science, INFORMS, vol. 9(3), pages 405-430, April.
    8. Arthur M. Geoffrion, 1967. "Stochastic Programming with Aspiration or Fractile Criteria," Management Science, INFORMS, vol. 13(9), pages 672-679, May.
    9. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    10. Biswal, M. P. & Biswal, N. P. & Li, Duan, 1998. "Probabilistic linear programming problems with exponential random variables: A technical note," European Journal of Operational Research, Elsevier, vol. 111(3), pages 589-597, December.
    11. Chang, Ching-Ter, 2007. "Multi-choice goal programming," Omega, Elsevier, vol. 35(4), pages 389-396, August.
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    Cited by:

    1. D. K. Mohanty & Avik Pradhan & M. P. Biswal, 2020. "Chance constrained programming with some non-normal continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1281-1298, December.

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