Performance Evaluation of Bus Lines with Data Envelopment Analysis
and Geographic Information Systems
Yong Lao, Professor
Division of Social, Behavioral and Global Studies
California State University Monterey Bay
November 4, 2010
Project Background
• Currently public transit agencies are under increasing pressure to operate more efficiently as the level of government funding reduces, or as a result of changing ownerships or regulations.
• The majority of the existing research focuses on the operations of the public transit system, attempting to evaluate performances from the management perspective.
• The characteristics of local population and commuting pattern largely determine the passenger demand as well as operational scale for the public transit system.
The Goal
• To combine Data Envelopment Analysis (DEA) and Geographic Information Systems (GIS) to examine the performance of the public transit system in Monterey-Salinas area.
– Operational efficiency: measures the productivity of a public transit agency, focusing on the input elements controlled by the management.
– Spatial effectiveness: measures how well the general public is being served, focusing on the environmental elements often beyond the control of the management.
Questions Raised
• What are the operational costs and benefits associated with a bus line?
• How to identify and create the service corridor, demographic profile and travel pattern associated with a bus line?
• How to measure and compare the operational efficiency and spatial effectiveness of bus lines?
The Use of GIS
• Overlay and analyze demographic variables at census tract level.
– Population density (population per sq miles)
– Population 65 years and over
– Journey to work by bus
– Private vehicle occupancy
– Total disabilities
– Median household income
Using the Weighted Linear Combination Method to Model the Level of Demand
Data Variables Weight
Population 65 years and over 15%
Journey to work by bus 40%
Private vehicle occupancy 15%
Total disabilities 10%
Median household income 20%
The Level of Service
• Calculate the number of bus stops per census tract.
• Calculate the level of service by dividing the number of bus stops by the level of demand at each census tract.
Data Envelopment Analysis
• Data Envelopment Analysis (DEA) is a widely used optimization technique to evaluate efficiencies of decision making units
• First introduced by Charnes and Cooper in 1978
• Examples: banks, schools, libraries, government agencies, etc.
Using DEA to Evaluate MST Bus Lines
• Monterey Salinas Transit (MST)– Currently the MST transit system serves
a 280 square-mile area of Monterey County and Southern Santa Cruz County
– With an annual budget of $20.2 million, MST employs more than 2100 people, operating 86 vehicles and 50 routes.
• Each bus line is treated as a DMU in the DEA model.– There are 24 fixed bus lines
DEA Model Variables
• j: decision making units, j = 1,…,n
• i: input, i = 1,…,m
• r: output, r = 1,…,s
• xij: The i th input for DMU j
• yrj: the r th output for DMU j
• λj: the weight parameter for DMU j
• µ: the level of output
• θ: relative efficiency score, θ = 1/µ
The DEA Model
nj
sryy
mixxts
Max
j
n
j
jrjrj
n
j
jijij
,...,10
,...,1µ
,...,1.
µ
1
1
0
0
Input and Output Variables for the DEA Model
Input Variable Output Variable
Operational
Efficiency
Round Trip Distance
Number of Bus Stops
Operation Time
Total number of
passengers per year
Spatial
Effectiveness
Within ¼ mile of each
bus stop:
Commuters who use
buses
Population 65 and
older
Disabled population
Total number of
passengers per year
The Service Corridor Of A Bus Line
DEA Model Results and Recommendations
DMU Name
Operational Efficiency
Spatial Effectiveness
Group 1: Best performers, bench marks
Line10 1 1
Line26 1 1
Line41 1 1
Line43 0.98992 1
Line9 0.85952 0.71146
Line1 0.70888 0.9474
Line20 0.81071 0.79233
Group 2: Effective performers, should be
supported and subsidized
Line29 0.64766 0.95302
Line5 0.61046 0.9646
Line4 0.52416 1
Line44 0.50752 1
Line28 0.47374 1
Line2 0.4358 1
Line17 0.31974 1
Line24 0.24423 1
Line16 0.22729 0.63025
Group 3: Efficient performers, still has great
potentials to improve
Line25 1 0.0058
Line11 1 0.00649
Line46 1 0.18167
Line42 0.58767 0.02124
Group 4: Worst performers, should be re-planned
or eliminated
Line23 0.33705 0.31493
Line21 0.31237 0.15116
Line27 0.22978 0.05281
Line45 0.34507 0.04755
Comparison of Operational Efficiency and Spatial Effectiveness
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4
Bus Line Group
DE
A S
co
res Average Score of
Operational Efficiency
Average Score of
Spatial Effectiveness
Difference
Conclusions• By combining GIS and DEA, we are able to
closely monitor the commuting pattern, demographic information, and performance related to each bus line.
• GIS is mainly used for preparing and analyzing data for the DEA model.
• The DEA approach can help us to better understand the impact of socio-economic environment on business operations.
• The results of the study provide useful information for improving MST operations and services.