Distributionally robust goal programming approach for planning a sustainable development problem

Sustainable development requires the implementation of appropriate policies to conduct resource allocation, and it often involves two main challenges related to the multiple conflicting objectives and imprecise distributions. This paper proposes a new distributionally robust goal programming model to balance three goals based on the priority structure and capture the distribution uncertainty of per capita contributions and unemployment rates using ambiguity sets. In our model, the three goals represent the minimizing the risks regarding the environment, economy and energy. Risk measures are characterized by mean semi-deviations. The proposed model is practical and effective because satisfactory policies can be obtained by solving its tractable robust counterpart model under ambiguous sets. The application of our model is demonstrated by a case study of the sustainable development of Gulf Cooperation Council (GCC) countries by the year 2030. The results indicate the appropriate development trends related to the environment, economy and energy and the sectors that the member countries should focus on to achieve sustainability. A sensitivity analysis reveals that the optimal decisions for different perturbation data are active. Comparison studies of our model with the nominal stochastic and deterministic models confirm that the proposed model with distribution uncertainty can provide more substantive decisions. © 2020 Elsevier Ltd