Convex or non-convex? A new meta-frontier data envelopment analysis framework considering technology compatibility

The convexity of meta-frontier is a debated topic in data envelopment analysis (DEA). This paper claims that meta-frontier is a non-convex hull, but the production activities between the non-convex meta-frontier and the convex traditional production frontier may be feasible. Therefore, technology compatibility is defined to explain this feasibility, and a modified DEA model is constructed to evaluate the efficiency of decision-making units with technology heterogeneity and technology compatibility. Sequentially, two new meta-frontier DEA frameworks are constructed to evaluate and decompose efficiency, thereby revealing the impact of technology heterogeneity and technology compatibility on efficiency. In addition, a series of discussions are presented to analyze these two new frameworks.