IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v320y2025i1p160-174.html
   My bibliography  Save this article

Generating sets of diverse and plausible scenarios through approximated multivariate normal distributions

Author

Listed:
  • Aalto, Eljas
  • Kuosa, Tuomo
  • Stucki, Max

Abstract

This article presents a novel and broadly generalizable framework for generating diverse and plausible sets of scenarios. Potential future outcomes are decomposed using a set of uncertainties which are assumed to be multivariate normally distributed, regardless of whether the uncertainties actually present numerically quantifiable phenomena. The optimal scenarios are then chosen along the principal components of the distribution, and the results can be easily interpreted and visualized. Notably, our approach requires a relatively small number of numerical assessments, offering an efficient and practical solution for decision-makers. The framework also provides a testable setting for evaluating its performance and allows users to iteratively improve future-related assumptions and predictions. These findings are relevant for all fields that aim to understand potential future developments, such as, but not limited to, foresight, economics, business strategy and strategic intelligence analysis.

Suggested Citation

  • Aalto, Eljas & Kuosa, Tuomo & Stucki, Max, 2025. "Generating sets of diverse and plausible scenarios through approximated multivariate normal distributions," European Journal of Operational Research, Elsevier, vol. 320(1), pages 160-174.
  • Handle: RePEc:eee:ejores:v:320:y:2025:i:1:p:160-174
    DOI: 10.1016/j.ejor.2024.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724006039
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2024.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ahti Salo & Edoardo Tosoni & Juho Roponen & Derek W. Bunn, 2022. "Using cross‐impact analysis for probabilistic risk assessment," Futures & Foresight Science, John Wiley & Sons, vol. 4(2), June.
    2. Kowalski, Katharina & Stagl, Sigrid & Madlener, Reinhard & Omann, Ines, 2009. "Sustainable energy futures: Methodological challenges in combining scenarios and participatory multi-criteria analysis," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1063-1074, September.
    3. Barrios, Maite & Guilera, Georgina & Nuño, Laura & Gómez-Benito, Juana, 2021. "Consensus in the delphi method: What makes a decision change?," Technological Forecasting and Social Change, Elsevier, vol. 163(C).
    4. T Ritchey, 2006. "Problem structuring using computer-aided morphological analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(7), pages 792-801, July.
    5. Fildes, Robert & Goodwin, Paul & Lawrence, Michael & Nikolopoulos, Konstantinos, 2009. "Effective forecasting and judgmental adjustments: an empirical evaluation and strategies for improvement in supply-chain planning," International Journal of Forecasting, Elsevier, vol. 25(1), pages 3-23.
    6. A. W. Phillips, 1958. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica, London School of Economics and Political Science, vol. 25(100), pages 283-299, November.
    7. Philippe Aghion & Nick Bloom & Richard Blundell & Rachel Griffith & Peter Howitt, 2005. "Competition and Innovation: an Inverted-U Relationship," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 701-728.
    8. Rowe, Gene & Wright, George, 1999. "The Delphi technique as a forecasting tool: issues and analysis," International Journal of Forecasting, Elsevier, vol. 15(4), pages 353-375, October.
    9. Arcady Novosyolov & Daniel Satchkov, 2008. "Global term structure modelling using principal component analysis," Journal of Asset Management, Palgrave Macmillan, vol. 9(1), pages 49-60, May.
    10. Alessandro Fergnani & Thomas J. Chermack, 2021. "The resistance to scientific theory in futures and foresight, and what to do about it," Futures & Foresight Science, John Wiley & Sons, vol. 3(3-4), September.
    11. Gertler, Pavel & Hofmann, Boris, 2018. "Monetary facts revisited," Journal of International Money and Finance, Elsevier, vol. 86(C), pages 154-170.
    12. Tietje, Olaf, 2005. "Identification of a small reliable and efficient set of consistent scenarios," European Journal of Operational Research, Elsevier, vol. 162(2), pages 418-432, April.
    13. Lawrence, Michael & O'Connor, Marcus & Edmundson, Bob, 2000. "A field study of sales forecasting accuracy and processes," European Journal of Operational Research, Elsevier, vol. 122(1), pages 151-160, April.
    14. Bunn, Derek W. & Salo, Ahti A., 1993. "Forecasting with scenarios," European Journal of Operational Research, Elsevier, vol. 68(3), pages 291-303, August.
    15. Wheatcroft, Edward, 2019. "Interpreting the skill score form of forecast performance metrics," International Journal of Forecasting, Elsevier, vol. 35(2), pages 573-579.
    16. Seeve, Teemu & Vilkkumaa, Eeva, 2022. "Identifying and visualizing a diverse set of plausible scenarios for strategic planning," European Journal of Operational Research, Elsevier, vol. 298(2), pages 596-610.
    17. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    18. Cornelis A. De Kluyver & Herbert Moskowitz, 1984. "Assessing Scenario Probabilities Via Interactive Goal Programming," Management Science, INFORMS, vol. 30(3), pages 273-278, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    2. Seeve, Teemu & Vilkkumaa, Eeva, 2022. "Identifying and visualizing a diverse set of plausible scenarios for strategic planning," European Journal of Operational Research, Elsevier, vol. 298(2), pages 596-610.
    3. Leitner, Johannes & Leopold-Wildburger, Ulrike, 2011. "Experiments on forecasting behavior with several sources of information - A review of the literature," European Journal of Operational Research, Elsevier, vol. 213(3), pages 459-469, September.
    4. Perera, H. Niles & Hurley, Jason & Fahimnia, Behnam & Reisi, Mohsen, 2019. "The human factor in supply chain forecasting: A systematic review," European Journal of Operational Research, Elsevier, vol. 274(2), pages 574-600.
    5. Lin, Vera Shanshan & Goodwin, Paul & Song, Haiyan, 2014. "Accuracy and bias of experts’ adjusted forecasts," Annals of Tourism Research, Elsevier, vol. 48(C), pages 156-174.
    6. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti & Ilmola-Sheppard, Leena, 2018. "Scenario-based portfolio model for building robust and proactive strategies," European Journal of Operational Research, Elsevier, vol. 266(1), pages 205-220.
    7. Trutnevyte, Evelina & Stauffacher, Michael & Scholz, Roland W., 2012. "Linking stakeholder visions with resource allocation scenarios and multi-criteria assessment," European Journal of Operational Research, Elsevier, vol. 219(3), pages 762-772.
    8. Pennings, Clint L.P. & van Dalen, Jan & Rook, Laurens, 2019. "Coordinating judgmental forecasting: Coping with intentional biases," Omega, Elsevier, vol. 87(C), pages 46-56.
    9. Sroginis, Anna & Fildes, Robert & Kourentzes, Nikolaos, 2023. "Use of contextual and model-based information in adjusting promotional forecasts," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1177-1191.
    10. Makridakis, Spyros & Hyndman, Rob J. & Petropoulos, Fotios, 2020. "Forecasting in social settings: The state of the art," International Journal of Forecasting, Elsevier, vol. 36(1), pages 15-28.
    11. Arvan, Meysam & Fahimnia, Behnam & Reisi, Mohsen & Siemsen, Enno, 2019. "Integrating human judgement into quantitative forecasting methods: A review," Omega, Elsevier, vol. 86(C), pages 237-252.
    12. Bolger, Fergus & Wright, George, 2017. "Use of expert knowledge to anticipate the future: Issues, analysis and directions," International Journal of Forecasting, Elsevier, vol. 33(1), pages 230-243.
    13. Sagaert, Yves R. & Aghezzaf, El-Houssaine & Kourentzes, Nikolaos & Desmet, Bram, 2018. "Tactical sales forecasting using a very large set of macroeconomic indicators," European Journal of Operational Research, Elsevier, vol. 264(2), pages 558-569.
    14. Ahti Salo, 2021. "Developing the needed scientific theory will not be easy: A commentary on Fergnani and Chermack 2021," Futures & Foresight Science, John Wiley & Sons, vol. 3(3-4), September.
    15. Wiek, Arnim & Walter, Alexander I., 2009. "A transdisciplinary approach for formalized integrated planning and decision-making in complex systems," European Journal of Operational Research, Elsevier, vol. 197(1), pages 360-370, August.
    16. Önkal, Dilek & Zeynep Sayım, K. & Lawrence, Michael, 2012. "Wisdom of group forecasts: Does role-playing play a role?," Omega, Elsevier, vol. 40(6), pages 693-702.
    17. Song, Haiyan & Gao, Bastian Z. & Lin, Vera S., 2013. "Combining statistical and judgmental forecasts via a web-based tourism demand forecasting system," International Journal of Forecasting, Elsevier, vol. 29(2), pages 295-310.
    18. Xu, Jinou & Pero, Margherita & Fabbri, Margherita, 2023. "Unfolding the link between big data analytics and supply chain planning," Technological Forecasting and Social Change, Elsevier, vol. 196(C).
    19. Beiderbeck, Daniel & Evans, Nicolas & Frevel, Nicolas & Schmidt, Sascha L., 2023. "The impact of technology on the future of football – A global Delphi study," Technological Forecasting and Social Change, Elsevier, vol. 187(C).
    20. Klerkx, Rik & Pelsser, Antoon, 2022. "Narrative-based robust stochastic optimization," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 266-277.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:320:y:2025:i:1:p:160-174. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.