Robust performance evaluation and improvement: Opening the black-box of weight space

Data envelopment analysis (DEA) may fall into the extreme weights during the performance evaluation process. To obtain robust evaluation results, a possible way is opening the black-box of weight space. In this scenario, there are two main challenges: i) how to ensure the repeatability of performance evaluation, and ii) how to find the optimal performance improvement path. In this paper, we first propose a grid generation algorithm that can sample the input-output weights non-randomly, which means the sampling result can be reproducible. Based on this, we can approach the efficiency ratio distribution curve of each decision-making unit (DMU), which reveals more detailed insights into efficiency assessment. To describe the evaluation result, we replace the concept of efficiency dominance by dominance efficiency probability (DEP), and analyze the ranking interval by employing ranking expectation and ranking variance. Several important properties are further proved. Moreover, we propose a step-by-step performance improvement algorithm based on the principle of efficiency elasticity maximization. Finally, we illustrate the availability of our method by a real-world case study. The main contributions include that i) we propose a weight sampling algorithm to open the black-box of weight space, which can ensure the evaluation result is reproducible; ii) we extend the performance evaluation indicator to the framework of DEP, ranking expectation and ranking variance, which can provide evaluation information for decision makers more comprehensively and robustly; iii) we propose a performance improvement algorithm from the new perspective of efficiency elasticity.