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, Volume 15, Issue 1, pp 48–64 | Cite as

The value of the stochastic solution in multistage problems

  • Laureano F. Escudero
  • Araceli Garín
  • María Merino
  • Gloria Pérez
Original Paper

Abstract

We generalize the definition of the bounds for the optimal value of the objective function for various deterministic equivalent models in multistage stochastic programs. The parameters EVPI and VSS were introduced for two-stage models. The parameter EVPI, the expected value of perfect information, measures how much it is reasonable to pay to obtain perfect information about the future. The parameter VSS, the value of the stochastic solution, allows us to obtain the goodness of the expected solution value when the expected values are replaced by the random values for the input variables. We extend the definition of these parameters to the multistage stochastic model and prove a similar chain of inequalities with the lower and upper bounds depending substantially on the structure of the problem.

Keywords

Stochastic programming Scenario tree Complete recourse Deterministic equivalent model 

Mathematics Subject Classification (2000)

60H35 65C20 68Q25 

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Copyright information

© Sociedad de Estadistica e Investigación Operativa 2007

Authors and Affiliations

  • Laureano F. Escudero
    • 1
  • Araceli Garín
    • 2
  • María Merino
    • 3
  • Gloria Pérez
    • 4
  1. 1.Centro de Investigación OperativaUniversidad Miguel HernándezElche (Alicante)Spain
  2. 2.Dpto. de Economía Aplicada IIIUniversidad del País VascoBilbao (Vizcaya)Spain
  3. 3.Dpto. de Matemática Aplicada, Estadística e I.O.Universidad del País VascoLeioa (Vizcaya)Spain
  4. 4.Dpto. de Matemática Aplicada, Estadística e I.O.Universidad del País VascoLeioa (Vizcaya)Spain

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