OR/MS and Environmental Decision Making under Uncertainty

  • Jerzy A. Filar
  • Alain B. Haurie
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 138)


In this chapter we present a broad overview of Operations Research and Management Science (OR/MS) methods and models used to support Environmental Decision Making (EDM) under uncertainty. We first survey the challenges and pitfalls frequently accompanying OR/MS applications to problems involving environmental issues. We consider and classify generic sources of uncertainty in quantitative models involving life support systems. We show how stochastic reasoning pervades some fundamental issues affecting decision making pertaining to the natural environment and environmental economics, in particular those related to discounting and intergenerational equity. We then discuss a selection of concepts and techniques that enable us to better understand and manage uncertainty in EDM. Finally, we indicate how the methods of stochastic control, stochastic programming, robust optimization and statistical emulation in meta-modeling can be used to shed light on some difficult issues arising in environmental decision making under uncertainty. This general discussion constitutes a preparation for the forthcoming chapters of this book.


Discount Rate Optimal Trajectory Markov Decision Process Robust Optimization Environmental Decision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abilock H., Bergstrom, C., Brady, J., Doernberg, A., Ek A., Fishbone L., Hill D., Hirano M., Karvanagh, R., Koyama, S., Larsson, K., Leman, G., Moy, M., Sailor, V., Sato, O., Shore, F., Sira, T., Teichman and Wene, C.-O., MARKAL: A multiperiod linear programming model for energy system analysis, in Kavanagh, R. (Editor), Proc. Int. Conf. On Energy System Analysis, 9–11 October 1979, Dublin, Ireland, p482, Reidel, Dordrecht, 1980.Google Scholar
  2. [2]
    Ainslie, G. and Haslam, N., Hyperbolic discounting, in Loewenstein & Elster (eds) Choice Over Time, Russell Sage Foundation, New York, (1992).Google Scholar
  3. [3]
    Altman A., Feinberg E. and Schwartz A., Weighted discounted stochastic games with perfect information, in J.A. Filar, V. Gaitsgory and K. Mizukami eds., Advances in Dynamic Games and Applications, Annals of the International Socity of Dynamic Games, 2000.Google Scholar
  4. [4]
    Arndt, H. W. The rise and fall of economic growth: a study in contemporary thought, Longman Cheshire, Sydney, 1978.Google Scholar
  5. [5]
    Arrow K. and M. Kurz, Public investment, the rate of return, and optimal investment policies, John Hopkins Press, Baltimore, 1970.Google Scholar
  6. [6]
    Arrow, K, Bolin, B., Costanza, R., Dasgupta, P., Folke, C., Holling, C., Jansson, B-O., Levin, S., Maler, K-G., Perrings, C., and Pimental, D., Economic growth carrying capacity and the environment., Science, 1995: 268, 520–21.Google Scholar
  7. [7]
    Arrow, K.J., W.R. Cline, K.G. Maeler, M. Munasinghe, R. Squitieri and J.E. Stiglitz Intertemporal Equity, Discounting, and Economic Efficiency, in J.P. Bruce, H. Lee and E.F. Haites (eds.), Climate Change 1995: Economic and Social Dimensions - Contribution of Working Group III to the Second Assessment Report of the Intergovernmental Panel on Climate Change, pp. 125–144, Cambridge University Press, Cambridge, 1996.Google Scholar
  8. [8]
    Asheim G.B., W. Buchholz and B. Tungodden, Justifying sustainability, J ournal of Environmental Economics and Management, Vol. 41, 2001, pp. 252–268.CrossRefGoogle Scholar
  9. [9]
    Ayong Le Kama, A., Sustainable growth, renewable resources and pollution, Journal of Economic Dynamics and Control, 2001: 25, pp. 1911–1918.CrossRefGoogle Scholar
  10. [10]
    Babonneau, F. and Beltran, C. and Haurie, A. and Tadonki, C. and Vial, J.-P., Proximal-ACCPM: a versatile oracle based optimization method, In Optimisation, Econometric and Financial Analysis, E. J. Kontoghiorghes editor, vol. 9 of Advances in Computational Management Science, 2006.Google Scholar
  11. [11]
    Bahn, O. and Drouet, L., Edwards, N.R., Haurie, A., Knutti, R., Kypreos, S., Stocker, T.F., and Vial, J.-P., (2006), The coupling of optimal economic growth and climate dynamics, Climatic Change, Volume 79, Numbers 1–2 /, pp. 103–119.Google Scholar
  12. [12]
    Baumol, W., and Oates, W., Economics, environmental policy and the quality of life, Prentice Hall, Englewood Cliffs, 1979.Google Scholar
  13. [13]
    Beltran C., L. Drouet, N. R. Edwards, A. Haurie, J.-P. Vial and D. S. Zachary, An Oracle Method to Couple Climate and Economic Dynamics, Chap. 3 in A. Haurie and L. Viguier (eds.), The Coupling of Climate and Economic Dynamics, Springer, 2005.Google Scholar
  14. [14]
    Beltratti A., Chichilnisky G. and Heal G., The green golden rule, Economic Letters Vol. 49, 1995, pp. 175–179.CrossRefGoogle Scholar
  15. [15]
    Ben-Tal, A., A. Nemirovski. Robust optimization methodology and applications. Mathematical Programming 92(3) 453–480, 2003.CrossRefGoogle Scholar
  16. [21]
    Berger, C., Dubois, R., Haurie, A., Lessard, E., Loulou R. and Waaub, J.-P., Canadian Markal: An advanced linear Programming system for Energy and Environmental modelling, INFOR., 1993. CLAPPIER, A., A correction Method for use in Multidimensionnal Time Splitting Advection Algorithms: Application to Two- and Three- Dimensional Transport, Mon. Wea. Rev, 126, 232–242, 1998.Google Scholar
  17. [17]
    D. Bertsimas, O. Nohadani, and K. M. Teo. Robust nonconvex optimization for simulation-based prob- lems. To appear in Operations Research.Google Scholar
  18. [18]
    Box, G.E.P. and Jenkins G.M., Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco, 1970.Google Scholar
  19. [19]
    Braddock, R.D. Filar, J.A., Zapert R, Den Elzen M.G. Rotmans J, Mathematical forumulation of the IMAGE greenhouse effect model, Appl Mathematical Modelling 18: 234–254, 1994.CrossRefGoogle Scholar
  20. [20]
    Carlson D., A. Haurie and A. Leizarowitz, Infinite Horizon Optimal Control: Deterministic and stochastic Systems, Springer Verlag, 1994.Google Scholar
  21. [21]
    Carlson D., Haurie A., J.-P. Vial and Zachary D.S., Large scale convex optimization methods for air quality policy, Automatica, pp. 385395, January 2004.Google Scholar
  22. [22]
    Challenor, P.. The probability of rapid climate change. Significance, 1, (4), 155–158. 2004.CrossRefGoogle Scholar
  23. [23]
    Challenor, P.. The probability of rapid climate change: II. Significance, 4, (2), 60–62. 2007.CrossRefGoogle Scholar
  24. [24]
    Challenor, P.G., R.K.S. Hankin and R. Marsh Towards the Probability of rapid Climate Change. pp 55–63 in Avoiding Dangerous Climate Change Ed Schellnhuber, H.J., W. Cramer, N. Nakicenovic, T. Wigley amd G Yohe. Cambridge University Press, 2006.Google Scholar
  25. [25]
    Chichilnisky G., An axiomatic approach to sustainable development, Soc. Choice Welf. Vol. 13, 1996, pp. 231–257.CrossRefGoogle Scholar
  26. [26]
    Chichilnisky, G., What is sustainable development, Land Economy Vol. 73, 1997, pp. 467–491.CrossRefGoogle Scholar
  27. [27]
    Clappier, A., Kübler, J., Sathya, V., Martilli, A., Perego, S., Krüger, B.C., Simeonov, V., Jeanneret, F., Calpini, B. and Van den Bergh, H., Modélisation du smog photochimique en territoire genevois et Analyse de scénarios de réduction des émissions de polluants, Technical Report for the COST-615 CITAIR program, Swiss NSF, LPAS-DGR/EPFL, CH-1015 Lausanne, 1997.Google Scholar
  28. [28]
    Cline, W.R.. Discounting for the Very Long Term, in Portney & Weyant (eds): Discounting and Intergenerational Equity, Resources for the Future, Washington DC, 1999.Google Scholar
  29. [29]
    Cohn, R.D., Eder, B.K. and Leduc, S.K., An Aggregation and Episode Selection Scheme designed to Support MODELS-3 CMAQ, EPA/600/R-99/030, 1998.Google Scholar
  30. [30]
    Drouet L., N.R. Edwards and A.Haurie, Coupling Climate and Economic Models: A Convex Optimization Approach, Environmental Modeling and Assessment, Vol.11, pp.101–114, 2006.CrossRefGoogle Scholar
  31. [31]
    Dillon, W.R. and Goldstein M., Multivariate Analysis, Wiley, New York, 1984.Google Scholar
  32. [32]
    Embrechts P., Klüppelberg C. and Mikosch T., Modelling Extremal Events, Applications of Mathematics: Stochastic Modelling and Applied Probability, Springer, Berlin, 1997.Google Scholar
  33. [33]
    Feinberg E.A. and Schwartz A., Constrained Dynamic Programming with Two Discount Factors: Applications and an Algorithm, IEEE Transactions on Automatic Control, 44, 1999, pp. 628–631.CrossRefGoogle Scholar
  34. [34]
    Feinberg E.A. and Schwartz A., Mixed Criteria, Handbook of Markov Decision Processes: Methods and Applications, Kluwer, pp 209–230, 2002.Google Scholar
  35. [35]
    Feinstein C.D and D.G. Luenberger, Analysis of the asymptotic behavior of optimal control trajectories, SIAM Journal on Control and Optimization, Vol. 19, 1981, pp. 561–585.CrossRefGoogle Scholar
  36. [36]
    Filar, J.A., “Mathematical Models”, In: Knowledge For Sustainable Systems. An Insight Into the Encyclopedia ofLife Support Systems, Vol 1., pp. 339–354. UNESCO Publishing-Eolss Publishers, Paris, France, Oxford, UK. 2002.Google Scholar
  37. [37]
    Filar, J.A. and Haurie A. (1998), Uncertainty in Environmental Models: Dynamic Systems Perspective, in H. Greppin, R. Degli Agosti and C. Penel, eds. The Co-action between Living Systems and the Planet, University of Geneva, 1998.Google Scholar
  38. [38]
    Filar, J.A. and Vrieze, O.J., Weighted Reward Criteria in Competitive Markov Decision Processes, Zeitschrift für O.R., Vol.36, 1992, pp.343–358.Google Scholar
  39. [39]
    Filar, J. A. and Zapert R., Uncertainty Analysis of a Greenhouse Effect Model, in: C. Carraro and A. Haurie, eds., Operations Research and Environmental Management, Kluwer Academic Press, Dordrecht, 1996.Google Scholar
  40. [40]
    Filar, J.A., Krawczyk, J.B. and Agrawal,M., On production and abatement time scales in sustainable development. Can we loosen the sustainability screw?, CORE Discussion Paper, forthcoming, 2009.Google Scholar
  41. [41]
    Fisher R.A. and Tippett T.H.C., Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Cambridge Philos. Soc., 24, pp180–190, 1928.CrossRefGoogle Scholar
  42. [42]
    Fragnière, E. and Haurie, A., A stochastic programming model for energy/environnement choices under uncertainty, in Gheorghe, A. V. (Editor) Integrated regional health and environmental risk assessement and safety management, Published in J. Environment and Pollution, 4–6, 587–603, 1996.Google Scholar
  43. [43]
    Goffin J.-L., Haurie, A. and Vial, J.-P., Decomposition and nondifferentiable optimization with the projective algorithm, Management Science, 38, 2, 284–302, 1992.CrossRefGoogle Scholar
  44. [44]
    Gondzio J., Du Merle, O., Sarkissian R. and Vial, J.-P., ACCPM - A Library for Convex Optimization Based on an Analytic Center Cutting Plane Method, European Journal of Operational Research, 94, 206–211, 1996.CrossRefGoogle Scholar
  45. [45]
    Hartwick, J. M., Intergenerational equity and the investing of rents from exhaustible resources, American Economic Review, 1977: 66, 972–4.Google Scholar
  46. [46]
    Harvey, C.M. The reasonableness of non-constant discounting, Journal of Public Economics, 1994:53, pp. 31–51.Google Scholar
  47. [47]
    Haurie A., Environmental Coordination in Dynamic Oligopolistic Markets, Group Decision and Negotiation, Vol. 4, 1995, pp. 39–57.Google Scholar
  48. [48]
    Haurie A., Turnpikes in Multidiscount Rate Environments and GCC Policy Evaluation, in G. Zaccour Ed., Optimal Control and Differential Games, Kluwer 2002Google Scholar
  49. [49]
    Haurie A., Time, Risk and Conflicts in Economics and Management Science: a Story about Turnpikes, in G. Zaccour Ed., Decision and Control in Management Science, Kluwer 2002.Google Scholar
  50. [50]
    Haurie A., J. Kübler, A. Clappier and H. vanden Bergh , A Meta-modeling Approach for Integrated Assessment of Air Quality Policies, Environmental Modeling and Assessment, Vol. 9, pp. 1–12, 2003.Google Scholar
  51. [51]
    Hawken, P., The Ecology of Commerce: A Declaration of Sustainability. HarperBusiness, New York, 1994.Google Scholar
  52. [52]
    Heal, G. M., Interpreting sustainability, mimeo Columbia Business School, New York, May 1996.Google Scholar
  53. [53]
    Heal, G. M., Optimality or sustainability ?, mimeo Columbia Business School, New York, June 2001.Google Scholar
  54. [54]
    Heal, G. M., Valuing the Future: Economic Theory and Sustainability, Columbia University Press, New York, 1998.Google Scholar
  55. [55]
    Holland, J.H (1998), Emergence: From Chaos to Order. Addison-Wesley, Reading, Mass.Google Scholar
  56. [56]
    Hosmer, D.W. and Lemeshow, S., Applied Logistic Regression, Wiley, New York, 1989.Google Scholar
  57. [57]
    Holland, J.H., Emergence: From Chaos to Order, Addison-Wesley, Reading, Mass., 1998.Google Scholar
  58. [58]
    IPCC, Climate Change 1995: Economic and Social Dimensions of Climate Change, NY. Cambridge University Pess, 1996.Google Scholar
  59. [59]
    Kirby, M. W., Operational Research in War and Peace, Imperial College Press, London, 2003Google Scholar
  60. [60]
    Kloeden, P.E., Platen, E. and Schurz, H., Numerical Solutions of SDE Through Computer Experiments, Springer, New York, 1993.Google Scholar
  61. [61]
    Kopp, R.J. and Portney, P.R. Mock Referenda for Intergenerational Decisionmaking in Portney P.R. and Weyant J., eds., Discounting and Intergenerational Effects, Resources for the Future, Washington, DC, 1999, pp. 87–98.Google Scholar
  62. [62]
    Krass, D., Filar, J.A. and Sinha, S. A Weighted Markov Decision Process. Operations Research, Vol.40, 1992, pp.1180–1187.CrossRefGoogle Scholar
  63. [63]
    Krige, D.G, A statistical approach to some mine valuations and allied problems at the Witwatersrand, Master's thesis of the University of Witwatersrand, 1951.Google Scholar
  64. [64]
    Kübler, J., A.G. Russel, Hakami, A. Clappier and Van den Bergh, H., Episode Selection for Ozone Modelling and Control Strategies Analysis on the Swiss Plateau. Submitted March 2001Google Scholar
  65. [65]
    Loewenstein, G.; Prelec, D., Anomalies in Intertemporal Choice: Evidence and an Interpretation, in Loewenstein & Elster (eds) Choice Over Time, Russell Sage Foundation, New York, 1992.Google Scholar
  66. [66]
    Li C.-Z. and K.-G. Löfgren, Justifying sustainability, Journal of Environmental Economics and Management, Vol. 41, 2001, pp. 135–165.CrossRefGoogle Scholar
  67. [67]
    Li C.-Z. and K.-G. Löfgren, Economic growth, environmental quality and hyperbolic discounting, Technical report, 1Dept. of Economics, Umea University, Sweden, 2001.Google Scholar
  68. [68]
    Matheron, G., “Principles of geostatistics”, Economic Geology, 58, pp 1246–1266, 1963CrossRefGoogle Scholar
  69. [69]
    Manne, A.S. and R. Richels, Buying Greenhouse Insurance, MIT Press, Cambridge Mass. 1992.Google Scholar
  70. [70]
    Meadows, D.H, D.L. Meadows, J. Randers and W.H. Beyrens, The Limits to Growth, A report for the Club of Rome, Earth Island Ltd, 1972Google Scholar
  71. [20]
    Nordhaus W.D. D. Managing the Global Commons: The Economics of Climate Change. Cambridge, MIT Press, 1994.Google Scholar
  72. [21]
    Nordhaus W.D., A market based discount rate, in Portney P.R. and Weyant J., eds., Discounting and Intergenerational Effects, Resources for the Future, Washington, DC, 1999, pp. 145–162.Google Scholar
  73. [73]
    Norgaard, R. and Howarth, R. , Sustainability and discounting the future, in R. Costanza (Ed) Ecological economics: the science and management of sustainability, Columbia University Press, New York, 1991.Google Scholar
  74. [74]
    Peleg B. and Yaari M.E., On the existence of consistent course of action when tastes are changing, Review of Economic Studies, 1973: 40, pp. 391–401.CrossRefGoogle Scholar
  75. [75]
    Phelps E.S. and Pollak R., On second best national saving and game-equilibrium growth, Review of Economic Studies, 1968: 35, pp. 185–199.CrossRefGoogle Scholar
  76. [76]
    Portney P.R. and Weyant J., eds., Discounting and Intergenerational Effects, Resources for the Future, Washington, DC, 1999.Google Scholar
  77. [77]
    Puterman M.L., (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley, New York.CrossRefGoogle Scholar
  78. [78]
    Rotmans J. IMAGE: An Integrated Model to Assess the Greenhouse Effect, Kluwer Acad Press, Dordrecht, The Netherlands, 1990.Google Scholar
  79. [79]
    Sacks, J. and Welch, W. J. and Mitchell, T. J. and Wynn, H. P., Design and Analysis of Computer Experiments. 4. Statistical Science. pp. 409435, 1989.Google Scholar
  80. [80]
    Seinfeld J.H. , Atmospheric chemistry and physics: from air pollution to climate change. New York: Wiley, 1998.Google Scholar
  81. [81]
    Stinstra E. and D. Den Hertog. Robust optimization using computer experiments. European Journal of Operational Research, 191(3):816837, 2008.CrossRefGoogle Scholar
  82. [82]
    STAR Program Final Report : Quantification of Uncertainty in Air Quality Models Used for Analysis of Ozone Control Strategies. National Center for Environmental Research, 1999.
  83. [83]
    TAPOM (Transport and Air Pollution Model)PAS, EPFL, 2004.
  84. [84]
    Weitzman, M.L., “Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate”, Journal of Environmental Economics and Management, 36, pp. 201–208, 1998.CrossRefGoogle Scholar
  85. [85]
    Wene, C.-O. and Ryden, B., A comprehensive energy model in the municipal energy planning process, European J. Operational Research, 33, 212–222, 1998.CrossRefGoogle Scholar
  86. [86]
    Zapert, R., Gaertner, P. S. and Filar, J. A., Uncertainty Propagation within an Integrated Model of Climate Change, Energy Economics, Vol. 20, No. 5–6, 571–598, 1998.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of South AustraliaAdelaideAustralia
  2. 2.GERAD-HEC Montréal, Canada and ORDECSYSChêne BougeriesSwitzerland

Personalised recommendations