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A multi-stage stochastic supply network design problem with financial decisions and risk management


  • Nickel, Stefan
  • Saldanha-da-Gama, Francisco
  • Ziegler, Hans-Peter


In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.

Suggested Citation

  • Nickel, Stefan & Saldanha-da-Gama, Francisco & Ziegler, Hans-Peter, 2012. "A multi-stage stochastic supply network design problem with financial decisions and risk management," Omega, Elsevier, vol. 40(5), pages 511-524.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:5:p:511-524
    DOI: 10.1016/

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    References listed on IDEAS

    1. Schütz, Peter & Tomasgard, Asgeir & Ahmed, Shabbir, 2009. "Supply chain design under uncertainty using sample average approximation and dual decomposition," European Journal of Operational Research, Elsevier, vol. 199(2), pages 409-419, December.
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    5. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
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    7. Hinojosa, Y. & Puerto, J. & Fernandez, F. R., 2000. "A multiperiod two-echelon multicommodity capacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 271-291, June.
    8. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
    9. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
    10. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
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