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Use of Sample Information in Stochastic Recourse and Chance-Constrained Programming Models

Author

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  • R. Jagannathan

    (College of Business Administration, The University of Iowa, Iowa City, Iowa 52242)

Abstract

In probabilistic linear programming models the decision maker is typically assumed to know the probability distribution of the random parameters. Here it is assumed that the distribution functions of the parameters have a specified functional form F(t, \theta ), where \theta is an unknown (real) vector parameter. We suppose that the decision maker has the opportunity of observing a random sample drawn from F(t, \theta ). For a two-stage stochastic programming with recourse model the deterministic equivalent model is found using a Bayesian approach. Properties are presented for the deterministic equivalents in general and in the special case of the simple recourse model. Expressions for Expected Value of Sample Information (EVSI) and Expected Net Gain from Sampling (ENGS) are also derived. In the final section similar results are obtained for chance constrained programming models.

Suggested Citation

  • R. Jagannathan, 1985. "Use of Sample Information in Stochastic Recourse and Chance-Constrained Programming Models," Management Science, INFORMS, vol. 31(1), pages 96-108, January.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:1:p:96-108
    DOI: 10.1287/mnsc.31.1.96
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    Cited by:

    1. Robert F. Bordley & Stephen M. Pollock, 2009. "A Decision-Analytic Approach to Reliability-Based Design Optimization," Operations Research, INFORMS, vol. 57(5), pages 1262-1270, October.
    2. Hermann Held, 2019. "Cost Risk Analysis: Dynamically Consistent Decision-Making under Climate Targets," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 247-261, January.
    3. Lars M. Hvattum & Arne Løkketangen & Gilbert Laporte, 2006. "Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic," Transportation Science, INFORMS, vol. 40(4), pages 421-438, November.
    4. Matthias Schmidt & Alexander Lorenz & Hermann Held & Elmar Kriegler, 2011. "Climate targets under uncertainty: challenges and remedies," Climatic Change, Springer, vol. 104(3), pages 783-791, February.
    5. Mehrez, A. & Yuan, Y. & Gafni, A., 1995. "The search for information -- A patient perspective on multiple opinions," European Journal of Operational Research, Elsevier, vol. 85(2), pages 244-262, September.
    6. Held, Hermann, 2020. "Cost Risk Analysisː How Robust Is It in View of Weitzman's Dismal Theorem and Undetermined Risk Functions?," WiSo-HH Working Paper Series 55, University of Hamburg, Faculty of Business, Economics and Social Sciences, WISO Research Laboratory.
    7. Cooper, W. W. & Hemphill, H. & Huang, Z. & Li, S. & Lelas, V. & Sullivan, D. W., 1997. "Survey of mathematical programming models in air pollution management," European Journal of Operational Research, Elsevier, vol. 96(1), pages 1-35, January.

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