Robustness of weighted goal programming models: an analytical measure and its application to offshore wind-farm site selection in United Kingdom

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.