Relating efficiency with service compliance indices in public transportation using slack-based measure data envelopment analysis and shadow prices

In many countries, bus operators are private companies whose service has been leased by government agencies. These agencies develop service compliance indices or measures to keep track of factors such as passenger satisfaction, frequency, and regularity but do not necessarily include the objectives of the operators in the assessment. In this paper, we used slack-based measure data envelopment analysis (SBM) to investigate whether it is possible for a bus operator to be efficient (from a private perspective) and match required standards of frequency and regularity. In doing so, data collected from two major bus operators in Santiago, Chile has been used comprising 99 services. The results show that when private objectives, namely revenues, are included in the analysis, bus operators do not necessarily seek to improve the regularity of their service. Moreover, it was found that some bus services are on the efficient frontier while keeping low performance measure standards. Using the shadow prices of the models, it was also found that improving the performance measures will be hard for many bus services unless there is a significant change in factors that are not under control of the operators (i.e., number of stops, length of the route, etc.). This shows the difficulty of correctly aligning the private objectives of operators with agencies’ objectives.