This document provides an overview of technical efficiency and its measurement and application to transportation systems. It defines technical efficiency as the maximum output produced from a given set of inputs using a technology. Two major methods to measure technical efficiency are then described: stochastic frontier analysis and data envelopment analysis. The document concludes by examining factors that can affect technical efficiency and providing empirical examples of efficiency measurements in the US airline, airport, and trucking industries.

1. Efficiency in Transportation
Dr. David Bouras
MATC Scholars Program
March 26, 2021 - April 9, 2021
University of Nebraska-Lincoln

2. OUTLINE
• Introduction
• Learning Objectives
• Learning Outcomes
• Session Presentation
• Conclusions

3. LEARNING OBJECTIVES
• To provide an overview about technical
efficiency.
• To survey various techniques of
measuring technical efficiency.
• To analyze applications of technical
efficiency analysis in different
transportation systems.
• To examine factors affecting technical
efficiency in transportation systems.

4. LEARNING OUTCOMES
• Knowledgeable about technical
efficiency
• Knowledgeable about two major
methods used to measure technical
efficiency
• Knowledgeable about the factors
affecting technical efficiency

5. INTRODUCTION
Efficiency analysis is a powerful managerial tool
that can be used to assess the performance of
firms, industries, and organizations. Because of its
positive features, efficiency analysis has been
widely used. Some of its applications include:
• Logistics Systems
• Transportation Systems
• Supply Chains
• Oil Refineries

6. WHAT IS TECHNICAL EFFICIENCY?
Technical efficiency was first introduced by Farrel
(1957). According to Coelli et al. (1999),
technical efficiency can be defined as the
maximum of output that can be produced from a
given set of inputs and using the same
technology.
Analytically, technical efficiency is the actual
level of output divided by the potential level of
output.

7. TECHNICAL EFFICIENCY: GRAPHICAL
ILLUSTRATION
Input
Output
A
Q
XA
Production Frontier
*
Q
A
*
A
A
A
<100%
Q
TE =
Q
Firm A
Firm B
XB
* 
Q Q
B B
*

B
B
B
100%
Q
TE =
Q
 
0 100%
TE

8. • There are two main methods: Stochastic
Frontier and Data Envelopment Analysis
• Stochastic Frontier:
• Consider an industry (e.g., airline industry)
consisting of n firms and producing an output Y
according to the following technology:
 
, 
it it it it it
,
Y =f E K L e
Where:
it
Y : The level of output produced by the ith firm at time t;
it
E : The amount of energy used by the ith firm at time t;
it
K : The amount of capital used by the ith firm at time t;
it
L : The amount of labor used by the ith firm at time t;
it
e : The error term.
TECHNICAL EFFICIENCY: MEASUREMENT

9. • Stochastic Frontier:
• The stochastic frontier technique (e.g.,
Battese & Coelli, 1995) consists of
decomposing the error term into two
components:
Where:
it
v : The idiosyncratic term;
it
u : The technical inefficiency term.
The technical efficiency score for the ith
firm is given by:
 
^

it
it it
it
= =exp
TE u
Y
Y
TECHNICAL EFFICIENCY: MEASUREMENT

10. • Stochastic Frontier:
The potential level of output is obtained by
estimating the following log-linear regression
model:
it
Y : The actual level of output produced by the ith
firm at time t.
ˆit
Y : The potential level of output produced by the ith
firm at time t.
       
E K L
     
it i it it it it it
+ + +
Log Y = Log E Log K Log L v u
TECHNICAL EFFICIENCY: MEASUREMENT

11. • Data Envelopment Analysis (DEA)
2.1. Assumptions:
• The starting point of the DEA model is a
transportation system consisting of n firms. Each
firm uses m inputs to produce s outputs.
• There two major types of DEA models: input-
oriented DEA and output-oriented DEA models
• Constant Returns to Scale/Variable Returns to
Scale
TECHNICAL EFFICIENCY: MEASUREMENT

12. 2.2 DEA Models
2.2.1 Output-Oriented DEA
Constant Returns to Scale
(Charnes et al. 1978)
Variable Returns to Scale
(Banker et al. 1984)
k
k

 







n
rk j rj
j=1
n
ik j ij
j=1
j
Subject to:
- 0 r =1,...,s
- 0 i =1,...,m
0 forall j=1,...,n
Maximize
Y Y
X X
k
k

 









n
rk j rj
j=1
n
ik j ij
j=1
n
j
j=1
j
Subject to:
- 0 r =1,...,s
- 0 i =1,...,m
=1
0 forall j=1,...,n
Maximize
Y Y
X X
rk
Y : The quantity of output r produced by the kth firm.
ik
X : The amount of input i used by the kth firm.
k
1 : The technical efficiency of the kth firm.
TECHNICAL EFFICIENCY: MEASUREMENT

13. 2.2 DEA Models
2.2.2 Input-Oriented DEA
Constant Returns to Scale
(Charnes et al. 1978)
Variable Returns to Scale
(Banker et al. 1984)
k
k
θ
θ








n
rk j rj
j=1
n
ik j ij
j=1
j
Subject to:
- 0 r =1,...,s
- 0 i =1,...,m
0 for all j=1,...,n
Minimize
Y Y
X X
k
k
θ
θ










n
rk j rj
j=1
n
ik j ij
j=1
n
j
j=1
j
Subject to:
- 0 r =1,...,s
- 0 i =1,...,m
=1
0 for all j=1,...,n
Minimize
Y Y
X X
rk
Y : The quantity of output r produced by the kth firm.
ik
X : The amount of input i used by the kth firm.
k
 : The technical efficiency of the kth firm.
TECHNICAL EFFICIENCY: MEASUREMENT

14. TECHNICAL EFFICIENCY MEASUREMENT:
A NUMERICAL EXAMPLE
A shipping industry consists of 3 firms: A, B, and
C. The firms produce one output (ton-mile) using a
single input (capital).
Let’s compute the efficiency score for each firm
assuming constant returns to scale technology and
using the input-oriented DEA model.
Firm
Input Output
(Capital) (Ton-mile)
A 3 4
B 5 5
C 4 3

15. • Step 1: Compute Productivity Index (PI) for
each firm
Firm
Input Output Productivity Index (PI)
(Capital) (Ton-mile) PI =Output/Input
A 3 4 1.33
B 5 5 1
C 4 3 0.75
TECHNICAL EFFICIENCY MEASUREMENT:
A NUMERICAL EXAMPLE

16. • Step 2: Select the firm with the highest
Productivity Index and use it as the benchmark for
computing efficiency scores.
Firm
Productivity
Index (PI)
Efficiency Score (ES) Waste
Output/Input
PI for Individual Firm
Benchmark PI 100-ES
A 1.33 100% 0%
B 1 75% 25%
C 0.75 56% 44%
TECHNICAL EFFICIENCY MEASUREMENT:
A NUMERICAL EXAMPLE

17. TECHNICAL EFFICIENCY MEASUREMENT:
A NUMERICAL EXAMPLE GRAPHICAL
ILLUSTRATION

18. TECHNICAL EFFICIENCY: APPLICATIONS
IN TRANSPORTATION SYSTEMS
• Input/Output Selection
• Railway Industry
• Output: Freight in units of ton-kilometer and
Passenger in units of passenger-kilometer.
• Inputs:
– Length of lines
– Number of locomotives and cars
– Number of employees
– Energy

19. • Input/Output Selection
• Airline Industry
• Output:
– Revenue passenger-miles
– Ton-miles.
– Number of passengers
• Inputs:
– Number of planes
– Number of employees
– Gallons of fuel used
TECHNICAL EFFICIENCY: APPLICATIONS
IN TRANSPORTATION SYSTEMS

20. • Input/Output Selection
• Container Port
• Output:
– Container throughput
• Inputs:
– Terminal area
– Quay length
– Draft
– Quay crane
– Yard equipment
– Labor
TECHNICAL EFFICIENCY: APPLICATIONS
IN TRANSPORTATION SYSTEMS

21. • Input/Output Selection
• Trucking Industry
• Output:
– Revenue
• Inputs:
– Number of trucks
– Labor
– Fuel
– Maintenance expenditures on highways
– Miles of Interstate
– Miles of Non-Interstate roadways
TECHNICAL EFFICIENCY: APPLICATIONS
IN TRANSPORTATION SYSTEMS

22. • Information Technology
• Company Size (economies of scale)
• Mergers and Acquisitions
• Ownership (public/ private)
• Population Density
• Network Structure
• Technical Progress
• Human Capital
• Investment
FACTORS AFFECTING TECHNICAL
EFFICIENCY

23. EMPIRICAL EXAMPLES
1. US Airlines:
Company Efficiency score: 82.6% -100% (Atul
Rai, 2013).
2. US Airports:
Average Efficiency score: 73.6% -83.6% (Joseph
Sarkis, 2000).
3. US Trucking Industry:
Average Efficiency score: 91.9% -94.7% (Weber
et al., 2004).

24. CONCLUSION
• Efficiency analysis has been widely used by
various areas (e.g., transportation, supply chain,
etc.).
• Two major methods to measure technical
efficiency: Parametric (SF) and Non-Parametric
(DEA).
• The estimation of technical efficiency requires the
specification of inputs and outputs.
• Technical efficiency is affected by several factors
(e.g., size of companies, ownership, etc.).

25. Slide design © 2009, Mid-America Transportation Center. All rights reserved.
Dr. David Bouras
Professor
Lincoln University
School of Business
101 Stamper Hall, Room #113
824 Chestnut Street
Jefferson City, Missouri 65101
bourasd@lincolnu.edu
CREDITS