# Mathematical Programming Basis for Decision Making Using Weather and Climate Information for the Energy Sector

## Abstract

Decision making (DM) problem is of great practical value in many areas of human activities. Most widely used DM methods are based on probabilistic approaches. Well-known Bayesian theorem for conditional probability density function (PDF) is a background for such techniques. It is due to some uncertainty in many parameters entered in any model described functioning of many real systems or objects. Uncertainty in our knowledge might be expressed in alternative form. I offer to employ appropriate confidential intervals for model parameters instead of relevant PDF. Thus one can formulate a prior uncertainty in model parameters by means of a set of linear constraints. Related cost or goal function should be defined at corresponding set of parameters. That leads us to statement of problem in terms of operational research or mathematical linear programming. It is more convenient to formulate such optimization problem for discreet or Boolean variables. Review of relevant problem statements and numerical techniques will be presented as well as several examples. The house heating and air condition optimal strategies responded to different IPCC climate change scenarios for some domains of Russia are considered. Evolving of climate and energy costs should be taken into account in building construction design. Optimal relationship between future expenses for house heating and costs of new house constructions including material costs and its amounts is a subject of discussion. In both considered tasks DM might be performed by means of the discreet optimization algorithms. If the DM variables are all required to be integers, then the problem is called an integer programming (IP). The “0-1” IP is the special case of integer programming where variables are required to be 0 or 1 (rather than arbitrary integers). The IP is a most convenient form for decision maker use. The “1” value means that a given scenarios is accepted, the “0” value means that a given scenarios is rejected. To illustrate suggested approach the “branch and bound” technique was implemented to seasonal surface atmosphere temperature ensemble predictions system (EPS) for northern parts of Russia. Aim of this illustrative research was to link the EPS output facility to requirements of particular users.

## Keywords

Climate change energy sector decision making operational research techniques integer programming branch and bound method## Preview

Unable to display preview. Download preview PDF.

## References

- BP (British Petrolium), 2003, Statistical Review of World Energy, 487 p.Google Scholar
- Ben-Tal A., Ghaoui L. Al., and Nemirovski A., 2006, Mathematical programming. Special Issue on Robust Optimization, 107(1–2), 1–37.Google Scholar
- Dantzig G.B., 1949, Programming of interdependent activities. Math. Model. Econometrica, 17(3), 200–211.Google Scholar
- Ecker J.G., and Kupferschmid M., 1988, Introduction to Operations Research. Wiley, NY.Google Scholar
- Gass S.I., 1958, Linear Programming (Methods and Applications). McGraw Hill, NY/ Toronto/London, 249 p.Google Scholar
- Gomory R.E., 1963, An Algorithm for Integer Solution to Linear Programming. McGraw Hill, NY/Toronto/London, 289 p.Google Scholar
- IEA (International Energy Agency), 2003, Cool Appliances: Policy Strategies for Energy Efficient Homes. OECD Publications, Paris, 215 p.Google Scholar
- IEA (International Energy Agency), 2004, World Energy Outlook 2004. IEA, Paris, 503 p.Google Scholar
- IEA (International Energy Agency), 2005, Renewables Information- 2005. IEA, Paris, 157 p.Google Scholar
- IPCC (Intergovernmental Panel for Climate Change), 2007, The Forth Assessment Report, 2007.Google Scholar
- Kantorovich L.V., 1939, Mathematical Methods in Industry Management and Planning. Publ. by Leningrad State University, 66 p. (in Russian).Google Scholar
- Kantorovich L.V. (ed.), 1966, Mathematical Models and Methods of Optimal Economical Planning. “Nauka”, Novosibirsk, 256 p. (in Russian).Google Scholar
- Korbut A.A., and Finkelstein Y.Y., 1969, Discreet Programming. “Nauka”, Moscow, 302 p. (in Russian).Google Scholar
- Kouvelis P., and Yu G., 1997, Robust Discrete Optimization and Its Applications. Kluwer, The Netherlands, 347 p.Google Scholar
- Meier A., 2001, Energy testing for appliances. In Energy-Efficiency Labels and Standards: A Guidebook for Appliances, Equipment, and Lighting, Collaborative Labeling and Appliance Standards Program (S. Wiel and J. E. McMahon, eds.). Washington, DC, pp. 55–70.Google Scholar
- Pokrovsky O.M., 2005, Development of integrated “climate forecast-multi-user” model to provide the optimal solutions for environment decision makers. Proceedings of the Seventh International Conference for Oil and Gas Resources Development of the Russian Arctic and CIS Continental Shelf, St. Petersburg, 13–15 September 2005, Publ. by AMAP, Oslo, Norway, pp. 661–663.Google Scholar
- Pokrovsky O.M., 2006, Multi-user consortium approach to multi-model weather forecasting system based on integer programming techniques. Proceedings of the Second THORPEX International Scientific Symposium (Landshut, 3–8 December, 2006), WMO/TD, No. 1355, pp. 234–235.Google Scholar
- Pokrovsky O.M., 2009, Operational research approach to decision making. In A Book “Unexploded Ordnance Detection and Mitigation” (J. Byrnes, ed.). Springer, Berlin, pp. 249–273.Google Scholar
- Raftery A.E., 1996a, Approximate Bayes factors and accounting from model uncertainty in generalised linear models. Biometrika, 83, 251–266.CrossRefGoogle Scholar
- Raftery A.E., 1996b, Hypothesis testing and model selection. In Markov Chain Monte Carlo in Practice (W. R. Gilks and D. Spiegelhalter, eds.) pp. 163–188. Chapman and Hall, London.Google Scholar
- Richardson R., 2000, Skill and relative economic value of the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc., 126, 649–668.CrossRefGoogle Scholar
- Thie P., 1988, An Introduction to Linear Programming and Game Theory. Wiley, NY, 378 p.Google Scholar
- Von Moltke A., McKee C., and Morgan T., 2004, Energy Subsidies: Lessons Learned in Assessing their Impact and Designing Policy Reforms. United Nations Environment Programme and Greenleaf Publishing, United Kingdom, pp. 231–247.Google Scholar
- WBCSD (World Business Council for Sustainable Development), 2004a, Facts and Trends to 2050: Energy and Climate Change, 547 p.Google Scholar
- WBCSD (World Business Council for Sustainable Development), 2004b, Mobility to 2030: Meeting the Challenges to Sustainability, 374 p.Google Scholar
- WBCSD (World Business Council for Sustainable Development), 2006, Pathways to 2050: Energy and Climate Change, 127 p.Google Scholar
- Weakliem D.L., 1999, A critique of the Bayesian information criterion for model selection. Sociol. Methods and Res., 27, 359–297.CrossRefGoogle Scholar