Transformation of urban public transport financing and its effect on operators’ efficiency: evidence from the Czech Republic

Abstract

The purpose of this study is to analyze changes in the efficiency of urban public transport in the Czech Republic. Network data envelopment analysis and cluster analysis were applied to data from 19 urban public transport systems during 2004–2016. The series structure of the network was considered, including production and consumption stages with three external inputs (employees, rolling stock, and energy), one final output (passengers), and two intermediate products (vehicle-kilometres and seat-kilometres). The relationship between changes in efficiency and the method of financing for the operation of transport services was explored through standard statistical methods. One of the main findings was that the efficiency of smaller transport systems with complicated access to sources of funding were systematically less efficient, particularly in the consumption stage. These trends were even more significant after the reorganization of urban public transport funding in 2010.

Appendix

The model defined in the Sect. 3.3 by the expressions (1)–(4) was derived as follows: multiplier form of BCC model with non-controllable variable $Z^N$ was chosen for both stages. Input orientation was used for the first stage and output orientation for the second stage, see models (5) and (6) below:

$$\begin{aligned}&\min \theta _1 \nonumber \\&X\lambda \le \theta _1 X_j\nonumber \\&Z\lambda \ge Z_j \nonumber \\&Z^N\lambda = Z^N_j \nonumber \\&e \lambda = 1 \nonumber \\&\lambda \ge 0 \nonumber \\&\theta _1\le 1 \end{aligned}$$

(5)

$$\begin{aligned}&\max \theta _2 \nonumber \\&Y\mu \ge \theta _2 Y_j \nonumber \\&Z\mu \le Z_j \nonumber \\&Z^N\mu = Z^N_j \nonumber \\&e \mu = 1 \nonumber \\&\mu \ge 0 \nonumber \\&\theta _2 \ge 1 \end{aligned}$$

(6)

The notation is defined in Table 3. The constraints of the model (6) can be appended to the model (5) without affecting its optimal value and vice versa. So we obtain two augmented models with common constraints (2), (3) and (4). The problem can be treated as bi-objective problem of linear programming. Multiplying the second objective by $-1$ transforms the model (6) into minimization problem. Aggregating both functions additively gives the single objective function (1) of the resulting model.