Integrating AI with nonparametric frontier models: an FDH-RBF approach for non-convex production possibility set approximation

Traditional data envelopment analysis (DEA) models are limited by their inherent assumption of convexity, which hampers their ability to effectively approximate non-convex production possibility sets (PPS). While artificial intelligence (AI) methods offer greater flexibility by overcoming convexity constraints, they can be adversely influenced by decision-making units that fail to maintain monotonicity. To address this challenge, we propose a novel hybrid approach that integrates the Free Disposal Hull (FDH) method for preprocessing data with the Radial Basis Function (RBF) network, an AI algorithm, to estimate production frontiers and efficiency scores. By combining the nonparametric capabilities of FDH with the smooth surface approximation of RBF network, this method harnesses the strengths of both AI and optimization. A simulation based on the Cobb–Douglas production function demonstrates the superiority of the FDH-RBF approach, particularly in scenarios exhibiting increasing marginal returns, where it outperforms traditional methods in terms of accuracy. Applying this method to estimate the production frontiers of Chinese cities reveals a potential ‘medium-sized efficiency trap,’ where medium-sized cities consistently underperform. These findings illustrate the value of integrating AI and optimization models for complex production scenarios, offering more accurate and adaptable solutions.