Performance Evaluation of Public Bus Transpor- tation by Using DEA Models and Shannon’s Entropy: An Example From a Company in a Large City of China Zicheng Liu, Naiqi Wu, Fellow, IEEE, Yan Qiao, Member, IEEE, and Zhiwu Li, Fellow, IEEE Abstract—The purpose of this paper is to assess the operational efficiency of a public bus transportation via a case study from a company in a large city of China by using data envelopment analysis (DEA) model and Shannon’s entropy. This company operates 37 main routes on the backbone roads. Thus, it plays a significant role in public transportation in the city. According to bus industry norms, an efficiency evaluation index system is constructed from the perspective of both company operations and passenger demands. For passenger satisfaction, passenger waiting time and passenger-crowding degree are considered, and they are undesirable indicators. To describe such indicators, a super- efficient DEA model is constructed. With this model, by using actual data, efficiency is evaluated for each bus route. Results show that the DEA model with Shannon’s entropy being combined achieves more reasonable results. Also, sensitivity analysis is presented. Therefore, the results are meaningful for the company to improve its operations and management. Index Terms—Performance evaluation, public transportation system, Shannon’s entropy, super-efficiency data envelopment analysis, undesirable outputs.   I. Introduction A S a part of urban infrastructure, public transport plays an important role in the economic development and every one’s daily life, and has a pilot effect on the urban economy, especially for large cities. For resource-saving, environment protection, sustainable development, and congestion reduction, it is of a high priority to develop public transport. Therefore, efficient operations of a public transportation system are a critical issue. For efficiency, the general purpose of bus operators is to reduce operating expenses while meeting passenger demands. Therefore, on the one hand, in the viewpoint of a bus operator, the performance is reflected by corresponding inputs and outputs, and can be assessed by indicators of overall cost efficiency, vehicle utilization, and labor utilization. On the other hand, in the viewpoint of passengers, a public transport should make passengers feel that their daily travel demands can be met at a lower cost. In other words, the performance should also be measured by service utilization (number of passengers), service satisfaction, and service quality [1]. Thus, to efficiently operate a public transport system, the performances from the viewpoints of both the operator and passengers should be taken into account. Therefore, for the evaluation of public transport performance, it involves multiple inputs and multiple outputs. Many scholars regard public transportation services as production processes with multiple inputs and outputs. Presently, public transportation operation performance evaluation methods can be mainly classified into two categories: 1) non-parametric analysis methods represented by data envelopment analysis (DEA) [2]–[6], and 2) parametric analysis methods represented by stochastic frontier analysis (SFA) with super logarithm production function models [7]–[10]. In the use of parametric analysis, it is necessary to clarify function structures and there are different function structures in the existing parametric analysis methods. Since there is no corresponding theoretical basis for a cost structure, it is impossible to determine which function setting form is reasonable, leading to that such a type of methods is difficult to be applied. However, there is no such a problem if a non- parametric analysis method is applied. Furthermore, the evaluation problem can be expressed in a physical form when multiple-input and multiple-output descriptions are formulated [11]. Therefore, the non-parametric analysis is widely used for performance evaluation of public transportation systems. In this paper, a non-parametric analysis method is adopted to evaluate the performance for a case problem. DEA is the typical representative of non-parametric analysis methods. In 1957, economist Farrell proposed a method for measuring the efficiency of decision-making units (DMUs) Manuscript received March 24, 2020; accepted April 25, 2020. This work was supported in part by the Science and Technology Development Fund (FDCT), Macau SAR (0017/2019/A1, 0002/2020/AKP), and in part by the National Natural Science Foundation of China (61803397). Recommended by Associate Editor MengChu Zhou. (Corresponding author: Naiqi Wu.) Citation: Z. C. Liu, N. Q. Wu, Y. Qiao, and Z. W. Li, “Performance evaluation of public bus transportation by using DEA models and Shannon’s entropy: An example from a company in a large city of China,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 779–795, Apr. 2021. Z. C. Liu, Y. Qiao, and Z. W. Li are with the Institute of Systems Engineering and the Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology, Macau, China (e- mail: liuzicheng7@163.com; yqiao@must.edu.mo; zwli@must.edu.mo). N. Q. Wu is with the Institute of Systems Engineering and the Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology, and also with the State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangdong University of Technology, Guangzhou 510006, China (e-mail: nqwu@must.edu.mo). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2020.1003405 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 4, APRIL 2021 779