Skip to main content
SpringerLink
Log in

Stochastic programming: Potential hazards when random variables reflect market interaction

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

There are two types of random phenomena modeled in stochastic programs. One type is what we may term “external” or “natural” random variables, such as temperature or the roll of a dice. But in many other cases, random variables are used to reflect the behavior of other market participants. This is the case for such as price and demand of a product. Using simple game theoretic models, we demonstrate that stochastic programming may not be appropriate in these cases, as there may be no feasible way to replace the decisions of others by a random variable, and arrive at the correct decision. Hence, this simple note is a warning against certain types of stochastic programming models. Stochastic programming is unproblematic in pure forms of monopoly and perfect competition, and also with respect to external random phenomena. But if market power is involved, such as in oligopolies, the modeling may not be appropriate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Binmore, K. (1992). Fun and Games. D.C. Heath and Company, Lexington, Massachusetts, Toronto.

  • Birge, J. and F. Louveaux. (1997). Introduction to Stochastic Programming. Springer-Verlag, New York, NY.

    Google Scholar 

  • Escudero, L.F., F.J. Quintana, and J. Samerøn. (1999). “CORO, A Modeling and An Algorithmic Framework for Oil Supply, Transformation and Distribution Optimization Under Uncertainty.” European Journal of Operational Research 114, 638–656.

    Article  Google Scholar 

  • Fleten, S.-E., S.W. Wallace, and W.T. Ziemba. (2002). “Hedging Electricity Portfolios via Stochastic Programming.” In C. Greengard and A. Ruszczynski (eds.), Decision Making under Uncertainty: Energy and Power, Springer-Verlag, New York, pp. 71–94.

    Google Scholar 

  • Fragnière, E. and A. Haurie. (1996). “A Stochastic Programming Model for Energy/Environment Choices Under Uncertainty.” Int. J. Environment and Pollution 6, 587–603.

    Google Scholar 

  • Gröwe-Kuska, N., K.C. Kiwiel, M.P. Nowak, W. Römisch, and I. Wegner. (2002). “Power Management in a Hydro-thermal System Under Uncertainty by Lagrangian Relaxation.” In C. Greengard and A. Ruszczynski (eds.), Decision Making under Uncertainty: Energy and Power, Springer-Verlag, New York, pp. 39–70.

    Google Scholar 

  • Hobbs, B.F. (1995). “Optimization Methods for Electric Utility Resource Planning.” European Journal of Operational Research 83, 1–20.

    Article  Google Scholar 

  • Jacobs, J.M. and G.L. Schultz. (2002). “Opportunities for Stochastic and Probabilistic Modeling in the Deregulated Electricity Industry.” In C. Greengard and A. Ruszczynski (eds.), Decision Making under Uncertainty: Energy and Power, Springer-Verlag, New York, pp. 95–114.

  • Jonsbråten, T.W. (1998). “Oil Field Optimization Under Price Uncertainty.” Journal of the Operational Research Society 49(8), 811–818.

    Article  Google Scholar 

  • Jørnsten, K. (1992). “Sequencing Offshore Oil and Gas Fields under Uncertainty.” European Journal of Operational Research 58, 191–201.

    Article  Google Scholar 

  • Kahneman, D., P. Slovic, and A. Tversky (eds.), (1982). Judgment under uncertainty: Heuristics and biases. Cambridge University Press.

  • Kall, P. and S.W. Wallace. (1994). Stochastic Programming. Wiley, Chichester.

    Google Scholar 

  • Kanudia, A. and Shukla, P.R. (1998). “Modelling of Uncertainties and Price Elastic Demands in Energy-Environment Planning for India.” Omega-International Journal of Management Science 26(3), 409–423.

    Article  Google Scholar 

  • Modiano, E.M. (1987). “Derived Demand and Capacity Planning Under Uncertainty.” Operations Research 35(2), 185–197.

    Article  Google Scholar 

  • Nowak, M.P., R. Nürnberg, W. Römisch, R. Schultz, and W. Westphalen. (2000). “Stochastic Programming for Power Production and Trading Under Uncertainty.” Working Paper SM-DU-471, Gerhard Mercator Universität Duisburg.

  • Rasmusen, E. (2001). Games and Information. Blackwell, Oxford, UK.

  • Takriti, S., B. Krasenbrink, and L.S.Y. Wu. (2000). “Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem.” Operations Research 48(2), 268–280.

    Article  Google Scholar 

  • Wallace, S.W. (2000). “Decision Making Under Uncertainty: Is Sensitivity Analysis of Any Use?” Operations Research 48(1), 20–25.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Molde University College, P.O. Box 2110, NO-6402, Molde, Norway

    Kjetil K. Haugen & Stein W. Wallace

Authors
  1. Kjetil K. Haugen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stein W. Wallace
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stein W. Wallace.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haugen, K.K., Wallace, S.W. Stochastic programming: Potential hazards when random variables reflect market interaction. Ann Oper Res 142, 119–127 (2006). https://doi.org/10.1007/s10479-006-6164-0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-006-6164-0

Keywords

Search

Navigation