Stepwise benchmarking based on production function: Selecting path towards closest target

Data Envelopment Analysis (DEA) is used for not only assessing the performance of a set of homogeneous decision-making units (DMUs), but finding the target operating points to improve inefficient DMUs. When inefficient DMUs are far from their target, it will be impossible to reach those in a single move, therefore, a strategy of gradual improvements with intermediate targets has been proposed. In this study, we propose a method to determine benchmarking paths, which consider the improvement steps as the learning of the production functions, not the learning of inputs and outputs. Under the constant returns-to-scale (CRS) assumption, the paper, for each inefficient DMU, sets the ultimate target as the closest target and determines the shortest improvement path with existing DMUs by Dijkstra's algorithm, and this is illustrated with a numerical experiment. As a real-world example, the method is introduced to the irons and steel enterprises in China, so that the specific steps to make efficient ones has been pointed out. The proposed method is the first study to discuss stepwise benchmarking path from the perspective of the production function.