Abstract
This paper proposes a method to measure robustness of weighted goal programming (WGP) models by focusing on random percentage changes in the set of observed technological coefficients that characterize the goal equations. The issue under consideration is to estimate the impact of the random percentage changes on the WGP deviations from the goal targets, the solution to the model before changes being kept equal. Normally distributed and independent percentage changes are assumed. As a result, a measure of robustness is obtained dependent on the parameters of the model, standard deviations of percentage changes, and the solution to the model before changes. A demonstration of the proposed robustness measure on an offshore wind-farm site location model from the literature is developed. The results indicate that robustness of proposed solution to the energy project is high. Conclusions are drawn as to the practicality and usage of the proposed model in comparison to other methodologies for handling uncertainty within the goal programming model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdelaziz, F. (2012). Solution approaches for the multiobjective stochastic programming. European Journal of Operational Research, 216, 1–16.
Aouni, B., Colapinto, C., & La Torre, D. (2014). Financial portfolio management through the goal programming model: Current state-of-the-art. European Journal of Operational Research, 234, 536–545.
Arrow, K. J. (1951). Social choice and individual values. New York: Wiley.
Chang, C. T. (2011). Multi-choice goal programming with utility functions. European Journal of Operational Research, 215, 439–445.
Charnes, A., & Cooper, W. W. (1961). Management models and industrial applications of linear programming. New York: Willey.
Chen, A., & Xu, X. (2012). Goal programming approach to solving network design problem with multiple objectives and demand uncertainty. Expert Systems with Applications, 39(4), 4160–4170.
DECC (2014). Energy trends section 5: Electricity. UK Department of Energy and Climate Change Report. https://www.gov.uk/government/publications/electricity-section-5-energy-trends. Accessed June 6th, 2014.
DEFRA (2014). Marine protected areas in the UK. UK Department for Food, Environment and Rural Affairs Report. http://jncc.defra.gov.uk/page-5201. Accessed June 6th, 2014.
Diaby, V., & Goeree, R. (2014). How to use multi-criteria decision analysis methods for reimbursement decision-making in healthcare: A step-by-step guide. Expert Review of Pharmacoeconomics and Outcomes Research, 14(1), 81–99.
Ernst & Young (2009). Cost of and financial support for offshore wind. Ernst & Young report for the Department of Energy and Climate Change, DECC, London. http://webarchive.nationalarchives.gov.uk; http://www.berr.gov.uk/files/file51142.pdf. Accessed on January 16, 2015.
Flood, D. (2012). Round 3 offshore wind farms. UK Future Energy Scenarios seminar 2012. Forewind Report. http://www.google.co.uk/url?; http://www2.nationalgrid.com/WorkArea/DownloadAsset.aspx%3Fid%3D10466&rct=j&frm=1&q=&esrc=s&sa=U&ei=W5yRU5_ZCNKg7AbEyYDIAw&ved=0CEkQFjAH&sig2=oTA_83U-_31DgsFrH7RRZw&usg=AFQjCNGuw68f1p1qjXYeoYF1TDyFHwbk2A. Accessed June 6th, 2014.
Geanakoplos, J. (2005). Three brief proofs of Arrow’s Impossibility Theorem. Economic Theory, 26(1), 211–215.
Gilliams, S., Raymaekers, D., Muys, B., et al. (2005). Comparing multiple criteria decision methods to extend a geographical information system on afforestation. Computers and Electronics in Agriculture, 49(1), 142–158.
Greenacre, P., Gross, R. & Heptonstall, P., (2010). Great expectations: The cost of offshore wind in UK waters. UK Energy Research Centre, London. https://spiral.imperial.ac.uk/bitstream/10044/1/12649/6/Great%20Expectations%20-%20The%20cost%20of%20offshore%20wind%20in%20UK%20waters.pdf. Accessed on January 16, 2015.
Jones, D. F. (2011). A practical weight sensitivity algorithm for goal and multiple objective programming. European Journal of Operational Research, 213(1), 238–245.
Jones, D. F., & Jimenez, M. (2013). Incorporating additional meta-objectives into the extended lexicographic goal programming framework. European Journal of Operational Research, 227(2), 343–349.
Jones, D. F., & Tamiz, M. (2010). Practical goal programming. New York: Springer.
Jones, D. F., & Wall, G. (2015). An extended goal programming model for site selection in the offshore wind farm sector. Annals of Operations Research,. doi:10.1007/s10479-015-1828-2.
Kosmidou, K., & Zopounidis, C. (2004). Goal programming techniques for bank asset liability management (2004th ed.). New York: Springer.
Marine Management Organisation (2013). UK sea fisheries statistics 2012. A national statistics report. http://www.marinemanagement.org.uk/fisheries/statistics/documents/ukseafish/2012/final.pdf. Accessed 6th June 2014.
Oxford Economics (2013). Tourism: Jobs and growth. The economic contribution of the tourism economy in the UK. http://www.visitbritain.org/Images/Final%20proof%2015%20Nov_tcm29-39296.pdf. Accessed June 6th, 2014.
Pertin, E. (2013). 2OM Project Website. http://www.2om-project.eu/. Accessed 04/03/2014.
Ramboll Offshore Wind (2010). Focus on foundations: Offshore wind conference. Wind Power Monthly, London: Larger wind power stations further offshore and avoid costly delays.
Saaty, T. L., & Ozdemir, M. S. (2003). Why the magic number seven plus or minus two. Mathematical and Computer Modeling, 38(3–4), 233–244.
Saaty, T. L., & Vargas, L. G. (2012). Models, methods, concepts and applications of the analytic hierarchy process. New York: Springer.
Yaghoobi, M. A., Jones, D. F., & Tamiz, M. (2008). Weighted additive models for solving fuzzy goal programming problems. Asia-Pacific Journal of Operational Research, 25, 715–773.
Acknowledgements
This work is devoted to the memory of Professor Enrique Ballestero for his selfless dedication to it. The authors would also like to thank the two anonymous referees whose comments helped shape the final version of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bravo, M., Jones, D., Pla-Santamaria, D. et al. Robustness of weighted goal programming models: an analytical measure and its application to offshore wind-farm site selection in United Kingdom. Ann Oper Res 267, 65–79 (2018). https://doi.org/10.1007/s10479-017-2437-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-017-2437-z