Measuring the Efficiency of Regional Bus Lines Using DEA

Problem

In Switzerland there are many regional bus lines. In every larger town there is a company - very often a urban public transportation organisation - which transports the passengers. They are operating more or less efficiently. We wanted to investigate that rate of efficiency. The crucial question was: Are the transportation organisations in bigger cities more efficient than in smaller towns, or is there no difference between larger and smaller transportation organisations?

Abstract

There are many regional bus lines present here in Switzerland, each with its own attributes and goals. These transport companies may operate in cities or in rural districts. Every bus line is characterized by some physical values that represent different relevant properties of the line, such as the amount of transported passengers or the total fuel consumption.
The aim of this project was to analyze the performance of the different lines using DEA (Data Envelopment Analysis). Only economical properties of the bus lines - such as costs and incomes - were influencing the performance. We omitted non-measurable properties such as the activity area or the quality of the service.
To calculate the performance rates with DEA (Data Envelopment Analysis) you have to specify inputs and outputs. To be as much fair as possible the outputs for all our models were the passengers-kilometers and the vehicle-kilometers. Furthermore we distinguished between Technical and Cost Efficiency. In the first model we compared the companies only by technical inputs such as number of busses or number of employees. For the cost efficiency models the inputs were either the total variable costs (personnel, material, fuel) or only the total costs. We also considered Constant Return to Scale and Variable Return to Scale. Thus overall we had 5 different models, each giving a different insight to the problem.

There is not an unique result, because all 5 models were reasonable but slightly different. Unfortunately, some problems with DEA arose: This mathematical tool is very sensitive with respect to the data measurements. DEA assumes that different companies are all similar, which was not satisfied here. They had very different structures (public/private, old/new busses, accounting standards, etc.). Omitting these objections, it was not possible to show any significant influence of company size on the efficiency. However, further research - focusing on data quality and specific characteristics of the different bus companies - might give interesting insights.