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Multi-objective stochastic linear programming problem when b i ’s follow Weibull distribution

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Abstract

Probabilistic or stochastic programming is concerned with optimization problem in which some or all parameters are treated as random variable. A general approach to deal with uncertainty is to assign a probability distribution to the unknown parameter. In this paper a multi-objective probabilistic programming problem has been considered when right hand side vector follows Weibull distribution. The probabilistic problem is converted into an equivalent deterministic model, and is solved using LINGO software. A numerical is presented to illustrate the methodology.

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References

  1. Charnes, A., Cooper, W.W.: Chance-constrained programming. Manag. Sci. 6, 73–79 (1959)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Contini, B.: A stochastic approach to goal programming. Oper. Res. 16, 576–586 (1978)

    Article  Google Scholar 

  4. Dantzig, G.B.: Linear programming under uncertainty. Manag. Sci. 1, 197–206 (1955)

    Article  Google Scholar 

  5. Goicoechea, A., Hansen, D.R., Duckstein, L.: Multi-Objective Decision Analysis with Engineering and Business Application. John Wiley, New York (1982)

    Google Scholar 

  6. Kall, P., Wallace, S.W.: Stochastic Programming. Wiley, New York (1994)

    Google Scholar 

  7. Kambo, N.S.: Mathematical Programming Techniques. Affiliated East–west Press, New Delhi (1984)

    Google Scholar 

  8. Leclercq, J.P.: Stochastic programming: an interactive multiple approach. Eur. J. Oper. Res. 10, 33–41 (1982)

    Article  Google Scholar 

  9. Stancu-Minasian, I.M.: Stochastic Programming with Multiple Objective Functions. Reidel, Dordrecht (1984)

    Google Scholar 

  10. Stancu-Minasian, I.M., Wets, M.J.: A research bibliography in stochastic programming (1955–1975). Oper. Res. 24, 1078–1119 (1976)

    Article  Google Scholar 

  11. Vajda, S.: Probabilistic Programming. Academic, New York (1972)

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, UP, India

    S. Javaid, S. I. Ansari & Zaki Anwar

Authors
  1. S. Javaid
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  2. S. I. Ansari
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  3. Zaki Anwar
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Correspondence to S. Javaid.

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Remark

If we change the value of any parameter for the same problem, then RHS of the constraints of the deterministic model of the problem and hence its value of the objective function will be changed. Moreover, if c i ’s approached to zero, then the RHS of the deterministic model of the problem depends only on μ i and hence the value of the objective function will depend on μ i .

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Javaid, S., Ansari, S.I. & Anwar, Z. Multi-objective stochastic linear programming problem when b i ’s follow Weibull distribution. OPSEARCH 50, 250–259 (2013). https://doi.org/10.1007/s12597-012-0101-6

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  • DOI: https://doi.org/10.1007/s12597-012-0101-6

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