A DEA production technology and its usage for incorporation of collaboration in efficiency analysis: an axiomatic approach

Data envelopment analysis (DEA) is a method used to estimate the relative efficiency of decision-making units (DMUs) that use multiple inputs to produce multiple outputs. A number of different production possibility sets are defined from a dual point of view in the DEA literature; the convex cone, convex hull, free disposal hull, free replicability hull, and free coordination hull, each having different properties. This article introduces a novel DEA production technology that considers the possibility of aggregating units, so it assesses the performance of each unit compared with both individual and aggregated units. Hence, this technology provides a more competitive environment for DMUs to achieve an efficient frontier. On the other hand, possible collaboration between DMUs can be considered using this technology. The strength and practical relevance of the proposed technology is shown in the efficiency analysis of Danish hospitals in a collaborative environment. This yields a bi-classification of hospitals, namely resistant and nonresistant hospitals. The proposed technology has a general framework, and the associated model is easy to solve using standard DEA software. It follows that the current article could potentially be used in other theoretical and empirical research in the future.