Abstract: The data envelopment analysis (DEA) is an important data-driven method for the performance evaluation and performance improvement of a set of peer decision making units (DMUs), involving multiple inputs and multiple outputs which are identified as performance indicators. However, some performance indicators, unlike conventional DEA models with one single value, may have more than one value because of different definitions or measurement standards referring to multi-valued indicators. In addition, the performance indicators reflect the current status of DMUs, which ignore the goals of decision-makers. We first propose two modified slacks-based DEA models to deal with multi-valued indicators and provide the Pareto-optimal solution in two common decision-making scenarios, namely the decentralized and centralized decision-making cases. Furthermore, we extend the models by incorporating with the goals of decision-makers to help the DMUs improve their performance and get close to the goals of decision-makers as much as possible. The slacks-based approaches and integration of goals enhance the discriminability of the models to DMUs and provide more practical improvement for some indicators. A case study of 22 cities in the Yangtze River delta region in China is used to illustrate the effectiveness and practicality of our proposed models.

Key words: Data envelopment analysis, multi-valued indicators, goals, decentralized decision-making, centralized decision-making