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Combining Mathematical Programming and Monte Carlo Simulation to Deal with Uncertainty in Energy Project Portfolio Selection

Chapter
Part of the Green Energy and Technology book series (GREEN, volume 129)

Abstract

Mathematical programming (MP) is the most common methodology for modeling and optimization of energy systems. Energy systems’ planning and optimization assume the knowledge of future situation, which is usually known with limited certainty. Therefore, the parameters of the model (data which assumed to be known during the modeling process) have usually a degree of uncertainty. Various methods have been proposed for dealing with this uncertainty, the most common ones being fuzzy programming, chance constrained programming, robust programming, and stochastic programming. In this work, we consider the implied uncertainty in the parameters as being of stochastic nature. Each uncertain parameter is characterized by a probability distribution. Subsequently, a Monte Carlo simulation samples the values from these distributions, and the MP models with the sampled values are solved. This process is repeated many times (1,000) in order to have an adequate sample for drawing robust conclusions. Relationships between the values of these parameters (i.e., interdependent parameters) can also be incorporated in the Monte Carlo process. The specific work is focused on the energy project portfolio selection problem where the output of each project as well as other parameters may be uncertain. In the current work, we introduce the iterative trichotomic approach (ITA) that gradually separates projects into green (selected under all circumstances), red (rejected under all circumstances), and gray sets (need further elaboration), combining Monte Carlo simulation and MP. The process output is not only the final portfolio, but also information about the certainty of participation or exclusion of every project in the final portfolio. A case study with real data from clean development mechanism (CDM) projects’ database is elaborated in order to illustrate the method.

Keywords

Clean Development Mechanism Optimal Portfolio Clean Development Mechanism Project Multiple Criterion Decision Analysis Hydro Power Plant 
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.

Notes

Acknowledgments

Olena Pechak would like to thank the Hellenic State Scholarship Foundation (IKY) for financial support of her Ph.D. studies. The authors would like to thank the anonymous reviewers for their comments that helped to improve the manuscript.

References

  1. Abu-Taleb M, Mareschal B (1995) Water resources planning in the Middle East: application of the PROMETHEE V multicriteria method. Eur J Oper Res 81:500–511MATHCrossRefGoogle Scholar
  2. Albright SC (1975) Allocation of research grants to university research proposals. Socio-Econ Plann Sci 9:189–195CrossRefGoogle Scholar
  3. Badri MA, Davis D, Davis D (2001) A comprehensive 0–1 goal programming model for project selection. Int J Project Manage 19:243–252CrossRefGoogle Scholar
  4. Belton V, Stewart T (2002) Multiple criteria decision analysis. An integrated approach. Kluwer Academic Publishers, UKCrossRefGoogle Scholar
  5. Bernhard RH (1969) Mathematical programming models for capital budgeting–a survey, generalization, and critique. J Financ Quant Anal 4(2):111–158CrossRefGoogle Scholar
  6. Brooke A, Kendrick D, Meeraus A, Raman R (1998) GAMS. A user’s guide. GAMS development corporation, Washington. Available:www.gams.com
  7. Cavallaro F (2010) Fuzzy TOPSIS approach for assessing thermal-energy storage in concentrated solar power (CSP) systems. Appl Energ 87(2):496–503CrossRefGoogle Scholar
  8. UNEP Risø Centre (2012) Available: http://www.uneprisoe.org
  9. Cook WD, Green RH (2000) Project prioritisation: a resource-constrained data envelopment analysis approach. Socio-Econ PlanN Sci 34:85–99CrossRefGoogle Scholar
  10. Damghani KK, Sadi-Nezhad S, Aryanezhad MB (2011) A modular decision support system for optimum investment selection in presence of uncertainty: combination of fuzzy mathematical programming and fuzzy rule based system. Int J Expert Syst Appl 38:824–834CrossRefGoogle Scholar
  11. Fandel G, Gal T (2001) Redistribution of funds for teaching and research among universities: the case of North Rhine—Westphalia. Eur J Oper Res 130:111–120MATHCrossRefGoogle Scholar
  12. Georgopoulou E, Sarafidis Y, Diakoulaki D (1998) Design and implementation of a group DSS for sustaining renewable energies exploitation. Eur J Oper Res 109(2): 483–500 Google Scholar
  13. Golabi K, Kirkwood CW, Sicherman A (1981) Selecting a portfolio of solar energy projects using multi-attribute preference theory. Manage Sci 27:174–189CrossRefGoogle Scholar
  14. Gold Standard Foundation (2012) Available: http://www.cdmgoldstandard.org
  15. Hyde K, Maier HR, Colby C (2003) Incorporating uncertainty in the PROMETHEE MCDA method. J Multi-Criteria Decis Anal 12:245–259CrossRefGoogle Scholar
  16. Karakosta C, Doukas H, Psarras J (2010) Technology transfer through climate change: setting a sustainable energy pattern. Renew Sustain Energy Rev 14:1546–1557CrossRefGoogle Scholar
  17. Kwak NK, Lee C (1998) A multicriteria decision-making approach to university resource allocation and information infrastructure planning. Eur J Oper Res 110:234–242MATHCrossRefGoogle Scholar
  18. Lahdelma R, Hokkanen J, Salminen P (1998) SMAA: stochastic multiobjective acceptability analysis. Eur J Oper Res 106:137–143CrossRefGoogle Scholar
  19. Liesio J, Mild P, Salo A (2007) Preference programming for robust portfolio modeling and project selection. Eur J Oper Res 181(3):1488–1505MathSciNetCrossRefGoogle Scholar
  20. Liesio J, Mild P, Salo A (2008) Robust portfolio modeling with incomplete cost information and project interdependencies. Eur J Oper Res 190(3):679–695MathSciNetCrossRefGoogle Scholar
  21. Lorie JH, Savage LJ (1955) Three problems in rationing capital. J Bus 28(4):229–239CrossRefGoogle Scholar
  22. Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91Google Scholar
  23. Mavrotas G, Rozakis S (2009) Extensions of the PROMETHEE method to deal with segmentations constraints. J Decis Syst 18:203–229CrossRefGoogle Scholar
  24. Mavrotas G, Diakoulaki D, Capros P (2003) Combined MCDA: IP approach for project selection in the electricity market. Ann Oper Res 120:159–170MathSciNetMATHCrossRefGoogle Scholar
  25. Mavrotas G, Diakoulaki D, Caloghirou Y (2006) Project prioritization under policy restrictions. A combination of MCDA with 0–1 programming. Eur J Oper Res 171:296–308MathSciNetMATHCrossRefGoogle Scholar
  26. Mavrotas G, Diakoulaki D, Kourentzis A (2008) Selection among ranked projects under segmentation, policy and logical constraints. Eur J Oper Res 187:177–192MATHCrossRefGoogle Scholar
  27. Mukherjee K, Bera A (1995) Application of goal programming in project selection: a case study from the Indian Coal mining industry. Eur J Oper Res 82:18–25MATHCrossRefGoogle Scholar
  28. Oral M, Kettani O, Lang P (1991) A methodology for collective evaluation and selection of industrial R&D projects. Manage Sci 37:871–885MATHCrossRefGoogle Scholar
  29. Oral M, Kettani O, Cinar U (2001) Project evaluation and selection in a network of collaboration: a consensual disaggregation multi-criterion approach. Eur J Oper Res 130:332–346MATHCrossRefGoogle Scholar
  30. Pechak O, Mavrotas G, Diakoulaki D (2011) Role and contribution of clean development mechanism to the development of wind energy. Renew Sustain Energy Rev 15:3380–3387CrossRefGoogle Scholar
  31. Santhanam R, Kyparisis GJ (1996) A decision model for interdependent information system project selection. Eur J Oper Res 89:380–399MATHCrossRefGoogle Scholar
  32. Santhanam R, Muralidhar K, Scniederjans M (1989) A zero-one goal programming approach for information system project selection. Omega 17:583–593CrossRefGoogle Scholar
  33. Shakhsi-Niaei M, Torabi SA, Iranmanesh SH (2011) A comprehensive framework for project selection problem under uncertainty and real-world constraints. Comp Ind Eng 61:226–237CrossRefGoogle Scholar
  34. Tervonen T, Lahdelma R (2007) Implementing stochastic multicriteria acceptability analysis. Eur J Oper Res 178:500–513MATHCrossRefGoogle Scholar
  35. UN Framework Convention on Climate Change (UNFCCC) (2012) Available: http://unfccc.int
  36. Vose D (1996) Quantitative risk analysis: a guide to Monte Carlo simulation modeling. Wiley, UKMATHGoogle Scholar
  37. Vose D (2006) Risk analysis: a quantitative guide, 2nd edn. Wiley, UKGoogle Scholar
  38. WWDR4 (2012) UN World Water Development Report, 4th edn, vol 1.UNESCO p 380. Available: http://www.unesco.org/new/en/natural-sciences/environment/water/wwap/wwdr/wwdr4-2012
  39. Zanakis SH, Mandakovic T, Gupta SK, Sahay S, Hong S (1995) a review of program evaluation and fund allocation methods within the service and government sectors. Socio-Econ Plann Sci 29:59–79CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Laboratory of Industrial and Energy Economics, School of Chemical EngineeringNational Technical University of AthensAthensGreece

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