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The Value of Information and Stochastic Programming

Author

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  • M. Avriel

    (Mobil Research and Development Corporation, Princeton, New Jersey)

  • A. C. Williams

    (Mobil Research and Development Corporation, Princeton, New Jersey)

Abstract

The problem of planning under uncertainty has many aspects; in this paper we consider the aspect that has to do with evaluating the state of information. We address ourselves to the question of how much better (i.e., how much more profitable) we could expect our plans to be if somehow we could know at planning time what the outcomes of the uncertain events will turn out to be. This expected increase in profitability is the “expected value of perfect information” and represents an upper bound to the amount of money that it would be worthwhile to spend in any survey or other investigation designed to provide that information beforehand. In many cases, the amount of calculation to compute an exact value is prohibitive. However, we derive bounds (estimates) for the value. Moreover, in the case of operations planning by linear or convex programming, we show how to evaluate these bounds as part of a post-optimal analysis.

Suggested Citation

  • M. Avriel & A. C. Williams, 1970. "The Value of Information and Stochastic Programming," Operations Research, INFORMS, vol. 18(5), pages 947-954, October.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:5:p:947-954
    DOI: 10.1287/opre.18.5.947
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    Cited by:

    1. Renaud Chicoisne & Fernando Ordóñez & Daniel Espinoza, 2018. "Risk Averse Shortest Paths: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 539-553, August.
    2. Douglas Alem & Pedro Munari & Marcos Arenales & Paulo Ferreira, 2010. "On the cutting stock problem under stochastic demand," Annals of Operations Research, Springer, vol. 179(1), pages 169-186, September.
    3. Alysson Costa & Lana Santos & Douglas Alem & Ricardo Santos, 2014. "Sustainable vegetable crop supply problem with perishable stocks," Annals of Operations Research, Springer, vol. 219(1), pages 265-283, August.
    4. Borgonovo, Emanuele & Hazen, Gordon B. & Jose, Victor Richmond R. & Plischke, Elmar, 2021. "Probabilistic sensitivity measures as information value," European Journal of Operational Research, Elsevier, vol. 289(2), pages 595-610.
    5. Erfan Hassannayebi & Seyed Hessameddin Zegordi & Mohammad Reza Amin-Naseri & Masoud Yaghini, 2017. "Train timetabling at rapid rail transit lines: a robust multi-objective stochastic programming approach," Operational Research, Springer, vol. 17(2), pages 435-477, July.
    6. Zhen, Lu, 2014. "Container yard template planning under uncertain maritime market," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 199-217.
    7. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    8. Daniel Espinoza & Eduardo Moreno, 2014. "A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs," Computational Optimization and Applications, Springer, vol. 59(3), pages 617-638, December.
    9. Mehrez, Abraham, 1997. "The interface between OR/MS and decision theory," European Journal of Operational Research, Elsevier, vol. 99(1), pages 38-47, May.
    10. Arielle Anderer & Hamsa Bastani & John Silberholz, 2022. "Adaptive Clinical Trial Designs with Surrogates: When Should We Bother?," Management Science, INFORMS, vol. 68(3), pages 1982-2002, March.
    11. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    12. Emanuele Borgonovo & Alessandra Cillo, 2017. "Deciding with Thresholds: Importance Measures and Value of Information," Risk Analysis, John Wiley & Sons, vol. 37(10), pages 1828-1848, October.
    13. Marcus Ritt & Alysson M. Costa & Cristóbal Miralles, 2016. "The assembly line worker assignment and balancing problem with stochastic worker availability," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 907-922, February.
    14. P V Schaeffer & L D Hopkins, 1987. "Behavior of Land Developers: Planning and the Economics of Information," Environment and Planning A, , vol. 19(9), pages 1221-1232, September.
    15. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2014. "Bounds in Multistage Linear Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 200-229, October.
    16. Zhen, Lu & Lee, Loo Hay & Chew, Ek Peng, 2011. "A decision model for berth allocation under uncertainty," European Journal of Operational Research, Elsevier, vol. 212(1), pages 54-68, July.
    17. Zhen, Lu & Zhuge, Dan & Wang, Shuaian & Wang, Kai, 2022. "Integrated berth and yard space allocation under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 1-27.
    18. Zhen, Lu & Wang, Shuaian & Zhuge, Dan, 2017. "Analysis of three container routing strategies," International Journal of Production Economics, Elsevier, vol. 193(C), pages 259-271.
    19. Zhen, Lu, 2015. "Tactical berth allocation under uncertainty," European Journal of Operational Research, Elsevier, vol. 247(3), pages 928-944.
    20. Reinol Josef Compañero & Andreas Feldmann & Peter Samuelsson & Anders Tilliander & Pär Göran Jönsson & Rutger Gyllenram, 2023. "Appraising the value of compositional information and its implications to scrap-based production of steel," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 36(3), pages 463-480, September.
    21. Marcio Costa Santos & Michael Poss & Dritan Nace, 2018. "A perfect information lower bound for robust lot-sizing problems," Annals of Operations Research, Springer, vol. 271(2), pages 887-913, December.
    22. Zhen, Lu & Zhuge, Dan & Zhu, Sheng-Lei, 2017. "Production stage allocation problem in large corporations," Omega, Elsevier, vol. 73(C), pages 60-78.
    23. Rui Chen & James Luedtke, 2022. "On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2332-2349, July.
    24. Meersman, Tine & Maenhout, Broos & Van Herck, Koen, 2023. "A nested Benders decomposition-based algorithm to solve the three-stage stochastic optimisation problem modeling population-based breast cancer screening," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1273-1293.
    25. Mor Armony & Rami Atar & Harsha Honnappa, 2019. "Asymptotically Optimal Appointment Schedules," Management Science, INFORMS, vol. 44(4), pages 1345-1380, November.

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