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.