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On the convex hull of the simple integer recourse objective function

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Abstract

We consider the objective function of a simple integer recourse problem with fixed technology matrix.

Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program.

We present an algorithm to compute the convex hull of the expected value function in case of discrete right-hand side random variables. Allowing for restrictions on the first stage decision variables, this result is then extended to the convex hull of the objective function.

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References

  1. P. Kall,Stochastic Linear Programming (Springer, 1976).

  2. W.K. Klein Haneveld, L. Stougie and M.H. van der Vlerk, Stochastic integer programming with simple recourse, Research Memorandum 455, Institute of Economic Research, University of Groningen (1991).

  3. W.K. Klein Haneveld, L. Stougie and M.H. van der Vlerk, An algorithm for the construction of convex hulls in simple integer recourse programming, Ann. Oper. Res., to appear.

  4. F.V. Louveaux and M.H. van der Vlerk, Stochastic programming with simple integer recourse, Math. Progr. 61 (1993) 301–325.

    Article  Google Scholar 

  5. R.T. Rockafellar,Convex Analysis (Princeton University Press, 1970).

  6. R. Schultz, Continuity and stability in two-stage stochastic integer programming, in:Stochastic Optimization; Numerical Methods and Technical Applications, ed. K. Marti, GAMM/IFIP Workshop, Berlin (Springer, 1992) pp. 81–92.

  7. R.J-B. Wets, Solving stochastic programs with simple recourse, Stochastics 10 (1984) 219–242.

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Authors and Affiliations

  1. Rijksuniversiteit Groningen, Groningen, The Netherlands

    Willem K. Klein Haneveld & Maarten H. van der Vlerk

  2. Universiteit van Amsterdam, Amsterdam, The Netherlands

    Leen Stougie

Authors
  1. Willem K. Klein Haneveld
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  2. Leen Stougie
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  3. Maarten H. van der Vlerk
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Additional information

Supported by the National Operations Research Network in the Netherlands (LNMB).

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Klein Haneveld, W.K., Stougie, L. & van der Vlerk, M.H. On the convex hull of the simple integer recourse objective function. Ann Oper Res 56, 209–224 (1995). https://doi.org/10.1007/BF02031708

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  • DOI: https://doi.org/10.1007/BF02031708

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