An analytical framework for sustainability assessment under stochastic conditions

Measuring sustainability as an efficient tool to achieve sustainable development and improve economic, social, and environmental aspects is always fraught with complications. In this sense, developing a suitable approach for evaluating and recognizing the strengths and weaknesses across these dimensions is paramount. Given the inherent uncertainty in data for many real-world applications, the primary aim of this paper is to present a data envelopment analysis (DEA) model for evaluating sustainability within a stochastic environment. The proposed model is non-radial and incorporates undesirable outputs, enabling the assessment of overall sustainability as well as each of the economic, social, and environmental dimensions simultaneously. This multi-dimensional evaluation capability is a key advantage of the proposed model. Additionally, the proposed model is based on input excesses and output shortfalls. Another notable advantage is the incorporation of the assumption of managerial disposability when dealing with undesirable outputs. To demonstrate the applicability of the proposed model, data from 59 diverse countries across Africa, Europe, North America, and Asia were analyzed over a 12-year period (2010–2022). The country selection was designed to capture global heterogeneity in development levels, policies, and environmental conditions, allowing for robust cross-continental comparisons. Key findings reveal that: (1) Europe achieves the highest stochastic sustainability scores, while North America performs poorest; (2) Environmental sustainability shows the most success cases globally, whereas social sustainability lags; (3) Significant trade-offs exist between economic growth and environmental protection.