© 2012 Operational Research Society Ltd. All rights reserved. 0160-5682/12
Journal of the Operational Research Society (2012), 1–13
www.palgrave-journals.com/jors/
Highway improvement project selection by the
joint consideration of cost-benefit and risk
criteria
1
2
2
3
P Kelle , H Schneider , C Raschke and H Shirazi
1
Department of Information Systems and Decision Sciences, Louisiana State University, Baton Rouge,
2
LA, USA; Highway Safety Research Group in the Department of Information Systems and Decision
3
Sciences, Louisiana State University, Baton Rouge, LA, USA; and Louisiana Department of
Transportation and Development, Baton Rouge, LA, USA
Since highway improvement project selection requires screening thousands of road segments with respect
to crashes for further analysis and final project selection, we provide a two-step project selection
methodology and describe an application case to demonstrate its advantages. In the first step of the
proposed methodology, we will use odds against observing a given crash count, injury count, run-off
road count and so on as measures of risk and a multi-criteria pre-selection technique with the objective
to decrease the number of prospective improvement locations. In the second step, the final project
selection is accomplished based on a composite efficiency measure of estimated cost, benefit and hazard
assessment (odds) under budget constraints. To demonstrate the two-step methodology, we will analyze
4 years of accident data at 23 000 locations where the final projects are selected out of several hundred of
potential locations.
Journal of the Operational Research Society advance online publication, 2 May 2012
doi:10.1057/jors.2012.55
Keywords: highway improvement project; decision support system; public project; transportation safety;
multiple criteria selection; data envelopment analysis
Introduction
The appropriate allocation of highway safety improvement
funds is an important issue due to the large safety and
cost consequences. A study by Blincoe et al (2002) showed
that the costs of traffic crashes were on the average
US$820 per capita in 2000 in the USA. During the same
year, $120 billion of federal highway funds were budgeted
in the USA of which 49% were allocated for traffic
improvements alone (see Blincoe et al, 2002). States
individually spend millions of dollars each year on road
safety projects. Every year transportation departments
have to screen thousands of road segments and preselect a
number of them for further evaluation and then, finally,
select a small number of road improvement projects to
meet the budget constraints.
While the pre-selection criteria often include a variety
of measures of road safety, a cost-benefit analysis is used to
evaluate this smaller number of road segments to make the
final selection of projects to be funded. The pre-selection
Correspondence: P Kelle, Department of Information Systems and
Decision Sciences, Louisiana State University, E J Ourso College of
Business Admin, 3195 Taylor Hall, Baton Rouge, LA 70803, USA.
E-mail: [email protected]
does usually not include any construction costs because
of the difficulty of assigning these to thousands of roads
segments with as yet unknown necessary countermeasures.
Thus the pre-selection focuses mostly on risk assessment.
We propose using the odds against observing a mean crash
count at or above the mean crash count at a location as a
criterion for pre-selection. The higher the odds against
observing a certain crash count at a randomly selected road
segment, the higher the potential hazard for the road
segment.
The cost-benefit analyses that are employed to obtain
a final project selection usually only consider the costs
of a construction project and the benefits in terms of crash
cost reduction. Thus, road projects with a larger reduction
in the number of crashes are favoured over those with
a smaller reduction provided the construction costs are
the same. This tends to favour crash locations with high
number of crashes to be included in the final selection,
regardless of the risk involved. On the one hand, highways
with high volume of traffic such as interstates also have
a high number of crashes, although these highways are
the safest with respect to crash rates per vehicle mile
travelled; on the other hand, highways with a low traffic
flow may exhibit a higher risk for drivers to be in a crash,
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Journal of the Operational Research Society
but these highways may not have enough crashes to be
selected through a cost-benefit analysis. Thus, taking into
consideration only costs and monetary benefits biases road
improvement project selection toward highways with a high
volume of traffic. While this seems sensible from a cost
perspective, it is unacceptable from a standpoint of safety.
The Ford Pinto case serves as an example where a
purely cost-benefit analysis had disastrous consequences.
The model became the focus of a public outcry when it
was alleged that the car’s design allowed its fuel tank to
be easily damaged in a rear-end collision which sometimes
resulted in deadly fires and explosions. Ford motor
allegedly was aware of this design flaw but refused to pay
for a redesign because a cost-benefit analysis showed that
it would be cheaper to pay off possible lawsuits for
resulting deaths. Although the company was acquitted of
criminal charges, it lost the confidence of the customers
and thereby tainted Ford’s name as well.
There are many situations where the public does not
accept decisions based solely on a cost-benefit analysis
because of the perception of an unacceptable risk. Many
public projects such as road safety improvements and
public health projects require more careful consideration
of other objectives besides cost and benefits. Therefore we
propose that a measure of hazard for a road segment be
included into the cost-benefit analysis. This paper discusses
a two-step approach, one for the pre-selection of road
segments for further analysis and another step for the final
selection of road improvement projects. Both steps will
include other criteria besides costs.
The paper is organized as follows: The next section provides an overview of related literature. In the subsequent
section we justify the proposed measures used to assess
the risk perception (road hazard). The latter section
introduces step one for the pre-selection of road segments
based on multi-criteria ranking and uses proxy criteria.
This step is necessary because it is difficult and time
consuming to provide project costs and benefits estimate
at thousands of prospective high-hazard or high-benefit
sites. In the subsequent section we discuss the second step,
the final project selection, which is accomplished based on
a composite efficiency measure of estimated cost, benefit,
and hazard assessment under budget constraint. The sixth
section provides an example using four years of crash data
from Louisiana. In the penultimate section we evaluate
and compare our proposed approach with other methods.
The last section summarizes the remaining problems and
future extension possibilities.
Literature review for highway improvement project
selection
There is a large body of research that deals with costbenefit analyses. We mention here only a few articles that
are directly relevant to our research and concentrate on
the cost or benefit of highway projects using various outcome measures. Sinha et al (1981) analysed the reduction in
the expected number of accidents due to highway improvements. The effect of improvements on the severity
of accidents was considered by Skinner (1985). Sinha and
Hu (1985) evaluated the safety impacts of highway projects
using various measures and Pal and Sinha (1998) estimated
the effectiveness of projects in reducing crashes. An incremental cost–benefit analysis approach toward highway
projects was applied by Farid et al (1994). More references
can be found in the papers cited.
The above-referred articles, like most other research
papers, deal with the evaluation of a single project.
However, transportation departments have to select a
limited number of road improvement projects to fund
out of thousands of prospective choices given a fixed
budget. To find an optimum selection of projects from a
limited set of projects, Melachrinoudis and Kozanidis
(2002) applied a mixed integer knapsack solution to
project selection maximizing the total reduction in the
expected number of accidents under a fixed budget
constraint. Most decisions on project selection involve
immediate costs while benefits spread over many years
into the future. Brown (1980) applied dynamic programming to obtain a set of projects which provide an
optimum, taking into consideration not only present
costs but also benefits over several years into the future.
A life-cycle cost evaluation method to highway safety
improvement projects was applied by Madanu et al
(2010).
Only few articles deal with the selection of public projects using criteria other than costs and monetary benefits.
For instance, Norese and Viale (2002) used a multi-criteria
sorting procedure to support public decisions; Yedla and
Shrestha (2003) discussed a selection method for environmentally sustainable transport systems; Hinloopen et al
(2004) applied ordinal and cardinal judgment criteria in the
planning of public transport systems; and Odeck (2006)
used the Data Envelopment Analysis (DEA) approach for
measuring target performance for traffic safety. Tudela
et al (2006) compared the cost-benefit analysis with a multicriteria method applied to transportation projects. While
all five articles support the need for other than pure
cost-benefit analyses they use different approaches. We
believe that the DEA in combination with a multi-criteria
decision-making approach is most suitable for the problem
under consideration in this paper.
There is a wealth of literature on multi-criteria
decision making (MCDM). In our review of the
literature we will concentrate on a few articles which
are related road project selections. Recently Ghorbani
and Rabbani (2009) published a multi-objective algorithm for project selection problem. Two objective
functions have been considered to maximize the total
P Kelle et al—Highway improvement project selection by multi-objectives
expected benefit of selected projects and minimize
the variation of allotted resources. Kozanidis (2009)
solved a knapsack problem with two objectives: profit
and equity. The second objective minimizes the maximum difference between the resource amounts allocated
to any two sets of activities. Zongzhi et al (2010) developed
a heuristic approach for a system-wide highway project
selection to achieve maximal total benefits. Teng et al
(2010) published an empirical study of the highway budget
allocations in northern Taiwan. Rudzianskaite-Kvaraciejiene
et al (2010) evaluated the effectiveness of road investment
projects in Lithuania based on several economic, social and
environmental criteria.
Summarizing the above contributions in public project
selection methodology, we observed that some critical
issues are missing that are integral parts of many public
projects selection, like our highway improvement case.
These include a consideration of the following issues: (1) an
evaluation of hazard perception, (2) a very large number
(several thousand) of potential projects, (3) a pre-selection
process based on proxy measures, and (4) a difficult and
expensive cost and benefit evaluation. Our project selection
method attempts to overcome the above deficiencies. In the
next section we describe a method for assessing hazard
perceptions.
benchmarks is to develop statistical models for crash
counts.
To model the number of crashes over many locations
with varying ADT, the Negative Binomial distribution has
been studied by many researchers. The Negative Binomial
distribution is constructed by assuming that the expected
value of the Poisson distribution is a random variable
described by the gamma distribution. The first application
of the Negative Binomial distribution to accident statistics
was discussed by Greenwood (1920) and Arbous (1951).
More recently, Miaou (1994), Poch and Mannering (1996),
and Hauer (1997) applied the negative binomial distribution to crash statistics on roadways. A cutting edge
research in crash-count analysis has been published lately
by Lord and Mannering (2010).
The Negative Binomial distribution assumes that counts
of crashes are drawn from a Poisson distribution. The
probabilities for yi crashes at road section i is given by
PðY ¼ yi jxi Þ ¼
eli Li ðli Li Þyi
yi !
ð1Þ
where xi is a vector describing the road characteristics
such as ADT and design features of the road, Li is the
length of the road section and the mean of the distribution
is parameterized as a log linear model:
Measuring hazard perception in road safety
Transportation departments often analyse crash data
and try to identify the so-called ‘black spot’ crash
locations which are road segments with a higher than
expected number of crashes for a specific site type.
Nevertheless, drivers involved in crashes often have
their own risk perception concerning road hazards and
file law suits against states. For instance, the State of
Louisiana spends on the average 30 million dollars each
year settling lawsuits with plaintiffs injured in crashes
which supposedly are due to hazardous road segments.
Short of finding a road defect, given the large variation
of highway types, Average Daily Traffic (ADT), and
the design features of highways, it is difficult to find a
single measure that reflects risk perception appropriately. In fact, it is doubtful that there is one single
criterion that is able to incorporate the wide array of
hazard perception of humans based on the available
data of crash reports. Some may consider a road to be
hazardous if there are too many crashes, or too many
injury crashes, or too many fatal crashes, or the crash
rate is too high, or the percentage of fatal crashes to all
crashes is too high; some safety professionals consider
the case of too many run-off road crashes, or too
many side impact crashes as a sign for a road section
to be hazardous. Clearly, one needs benchmarks to
determine what is ‘too many’. One approach of obtaining
3
0
ln li ¼ xi b
ð2Þ
where b is a parameter vector describing a linear relationship between the mean and the vector of covariates xi.
The subscript i denotes a specific road section, i ¼ 1, . . . N,
where N is the total number of road sections used in the
analysis. To account for the unobserved heterogeneity
between road sections one can specify
0
ln li ¼ xi b þ ln ui
ð3Þ
where ui is a random variable with mean 1 and variance
1/y. Using this, the unconditional (over u) distribution is
f ðyi jxi Þ ¼
Z1
f ðyi jxi ; uÞgðuÞdu
ð4Þ
0
Using a gamma distribution having the shape parameter
y as the reciprocal of the scale parameter we obtain the
probability distribution as
f ðyi jxi Þ ¼
Z1
0
eli Li ui ðli Li ui Þyi ðyLi ÞyLi uyLi 1 eyLi ui
dui ð5Þ
yi !
GðyLi Þ
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Journal of the Operational Research Society
Solving the integral yields the Negative Binomial
distribution for the crash count
f ðyi jxi Þ ¼
yi
GðyLi þ yi Þ
li
Gðyi þ 1ÞGðyLi Þ li þ yLi
yLi
yLi
li þ yLi
ð6Þ
variance of either the estimate of the overall mean or the
estimate of the individual mean. The posterior distribution
derived from prior and the observed data is used to
compute tail probabilities for the empirical Bayes estimate
(see for instance El-Basyouny and Tarek, 2006). The
empirical Bayes estimate is the weighted sum of the mean
crash count li and the observed crash count Yi
EBi ¼ wi li þ ð1 wi ÞYi
Thus for each site, i, it is assumed that the crash count
has a Negative Binomial distribution with parameters
depending on ADT, on the section-specific features, and on
a common so-called over-dispersion parameter y multiplied
by the length of the road section. The negative binomial
model has a longer tail than the Poisson distribution
depending on the magnitude of the dispersion parameter.
Note that li represents the mean number of crashes for
a specific time period which may be one year or multiple
years. If multiple years are used this will affect the mean
and the variance.
For the purpose of our methodology, the tail probability
of the distribution of the mean serves as a hazard or
risk assessment for a specific road segment. For instance,
for any given value, c, the fraction of road sections with
a mean above c is given by the tail probability of the prior
gamma distribution
Z1
c
ðyLi =li ÞyLi yyLi 1 eðyLi =li Þy
dy ¼ p
GðyLi Þ
ð7Þ
The smaller this probability is, the less likely it is to
find road segments that have such low probabilities.
Instead of using the small tail probabilities, one might
prefer the odds (1p)/p against observing a given mean
crash count larger than c based on the specified model.
Odds can easily be compared regardless of the mean or
variance and they have the advantage that non-experts
have a fairly good understanding of odds. For instance, if
the tail probability for c crashes is 0.001, then the interpretation is that it is 999 times more likely that we will
observe a mean crash count below c than for c or above for
a randomly selected road segment with identical ADT and
engineering features. Odds are widely used in risk applications and thus can be used to associate a hazard or risk
with a certain crash count of a road section. The larger the
odds are, the larger the hazard or risk is.
In most practical situations the true mean for crashes at
locations has to be estimated and the issue of confidence
intervals has to be addressed. Many authors (see for
instance Cheng and Washington, 2005 and El-Basyouny
and Tarek, 2006) have discussed the use of the empirical
Bayes estimate rather than the average as an estimate for
the mean. Morris (1983) showed that the mean squared
error for the empirical Bayes estimate is smaller than the
ð8Þ
and its variance is
VarðEBi Þ ¼ wi ð1 wi Þli þ ð1 wi Þ2 Yi
ð9Þ
where
wi ¼
1
1 þ z2i =s2i
ð10Þ
is the weight given to the overall mean li, and
s2i ¼ li Li
ð11Þ
is the within-sample variance and
ðli Li Þ2
ð12Þ
yLi
is the between-sample variance. Then the posterior distribution of the mean crash count is also gamma with
parameters depending on the mean and variance of the
empirical Bayes estimate. If we denote
z2i ¼
bi ¼
EBi
VarðEBi Þ
and
ai ¼ bi EBi
ð13Þ
then the fraction of road segments with a crash count at or
exceeding the value c is given by
Z1
c
bai i yai 1 ebi y
dy
Gðai Þ
ð14Þ
In continuing with the description of our approach,
we notice that the odds for the number of crashes are only
one measure of the potential road hazards. Other measures
that are suitable include the odds for injury crashes, run-off
road crashes, side impact intersection crashes, etc. The next
section will discuss a methodology to incorporate different
measures using multiple criteria ranking.
The pre-selection of road segments based on multi-criteria
ranking—hazard efficiency measure
A highway improvement project is an improvement type
applied to a site (road segment). Usually at each site
different safety improvement types (such as traffic flow
improvement, new pavement, traffic signs, etc) are possible
P Kelle et al—Highway improvement project selection by multi-objectives
with different costs and benefits of accident cost reduction.
For benefit estimates there are standard accident modification factors that have been developed by researchers.
However, improvement cost estimates are time consuming
and require costly engineering analysis; therefore in
practice only a small number of sites are considered for
improvement. We propose a pre-selection method to identify the prospective improvement sites for cost and benefit
estimates chosen from thousands of prospective road segments. The major goal of this pre-selection is not to identify
the best sites for safety improvements but to eliminate sites
that are not preferable from the point of view of any of
the criteria that are important for a particular study. For
instance, for rural road segments without intersections, the
number (odds) of run-off road crashes may be considered
important, while for an intersection study the number
(odds) of side-impact crashes is important.
Since the costs and benefits of the projects are not
readily available and require an in-depth analysis, for the
pre-selection we will apply the hazard measures discussed
in the previous section. These are proxy measures which
are related indirectly to the benefit measures derived
from available crash counts of our data. Since several measures of safety hazard may be appropriate, as pointed out
above, we will consider multi-criteria ranking to facilitate
the selection of the potentially important sites for safety
improvement. The goal of our pre-selection method is
to (1) eliminate thousands of road segments that do not
qualify for consideration of safety improvement, (2) to not
eliminate those sites which may be advantageous in any
one of the hazard criteria or in any weighted combination
of the criteria, (3) and to require minimal user input.
Although the literature of multi-criteria ranking and
selection methods is very rich, the majority of those
methods are not applicable under the above conditions. Non-parametric methods, such as PROMETHEE,
SMART, ELECTRE, and the AHP-based methods (see,
eg, in Brans et al, 1985, or Salminen et al, 1998) use cross
efficiency ranking that requires user input of pairwise
comparisons; therefore, they are not applicable for
thousands of sites as in our case. Parametric methods,
such as weighted scores, are applicable for ranking
thousands of projects in theory, but in practice it is
difficult to obtain user input on the appropriate weights.
We propose the use of DEA which is based on preference
weights without user input. DEA was first developed by
Farrell (1957) and consolidated by Charnes et al (1978) as a
non-parametric procedure that compares decision units
using performance indicators. The DEA method has been
applied for ranking in several different areas (see, eg, Cooper
et al, 1999, which contains a list of over 1500 references).
Recent extensions and applications include a matrix-type
network DEA algorithm (Amatatsu et al, 2012) and its
application for the performance measurement of a transportation network (Zhao et al, 2011).
5
In DEA, the preference weights are calculated by linear
programming, a method which can easily be applied to
evaluate and rank thousands of sites. DEA is an extreme
point method, that is, it compares each site to all other sites
with weights calculated to be the most favourable for the
particular site being evaluated. This is the major advantage
for our goal because it ensures that none of those sites
which may be advantageous in any one of the important
criteria (or in any weighted combination of the criteria) are
eliminated. Only those sites are eliminated that are not
preferable according to any weighted combination of the
criteria, including the most favourable one.
In DEA, the efficiency of the decision-making unit
(DMU) is the weighted output over weighted input. The
objective of the DEA is to identify the DMU that produces
the largest values of outputs by consuming the least
amount of inputs. For instance, the input would be the cost
of the project, and the output would be the gain in safety
which can be measured by the crash cost reduction. Let s
be the number of different output criteria and m be the
number of input criteria used and let N be the number of
different sites (DMUs). Let us consider a specific site
k ¼ 1, 2, . . . , N, where Rik represents the measure of the ith
output criterion (i ¼ 1, 2, . . . , s) and Vjk represents the
measure of the jth input criterion ( j ¼ 1, 2, . . . , m) for site
k. The efficiency of site k is measured as the weighted sum
of outputs over the weighted sum of inputs (as in
productivity measures)
Ps
vik Rik
Ekk ¼ Pmi¼1
ð15Þ
u
j¼1 jk Vjk
By using DEA we attempt to find optimal weights, ujk,
and vik, for each DMU that maximizes the site efficiency,
Ekk, by comparing each site, k, with all other sites subject
to the restriction such that the weights are nonnegative and
all Eknp1 for n ¼ 1, 2, . . . , N. For each site, k, the above
optimization problem can be described as the equivalent
linear programming problem
Ek ¼ max Ekk
Ps
vik Rin
s:t: Ekn ¼ Pmi¼1
p1
j¼1 ujk Vjn
vik X0
ðn ¼ 1; :::; NÞ
ði ¼ 1; :::; sÞ ujk X0
ðj ¼ 1; :::; mÞ
ð16Þ
with Ekk defined in (15). The efficiency of a DMU, the Ek
value, is the DEA efficiency measure for site k. There are
two basic cases:
Ek ¼ 1 site k is efficient (Pareto-optimal site), and
Eko1 site k is not efficient; it is dominated by other
site(s).
To illustrate this concept, consider two output criteria
such as the odds for a crash count and the percentage
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Journal of the Operational Research Society
of injury crashes at each road segment. For two criteria
the idea of DEA can be shown in a graph. In Figure 1, the
points A, P and B represent the road segments. The line
y2-A-B-x2 is the efficient envelope. Any road segment that
has a weighted average of the two criterions inside the
envelope is not as efficient as the points on the envelope.
The road segment P has an efficiency computed as the
distance OP divided by the distance OD.
Note that higher efficiency of a site in our context means
better selection for safety improvement. Therefore, for the
pre-selection we consider only output measures that are to
be maximized without any input measures included. Also,
rather than considering the hard-to-measure improvement
in safety, we use the hazard perception measures described
in the previous section, as proxies that are based on readily
available data. The objective is to evaluate road segments
based on different criteria, such as high odds for mean
crash counts, a high percentage of injury crashes, a high
percentage of run-off road crashes, etc and combinations
of these measures.
Based on the DEA method of (16), for each site we calculate the HEk ¼ Ek value. This is considered as the Hazard
Efficiency Measure of site k. This measure can be applied
when the sites are ranked based on hazard because it provides an efficiency comparison using the distance to the
efficient surface.
The literature mentions the potential disadvantages
in using DEA ranking, such as too many efficient sites,
the sensitivity of the selection of the sites included in the list
of sites, and the data estimation error. Since the goal of
our pre-selection is to rank thousands of road segments
and eliminate road segments that are dominated by other
road segments the disadvantages of the DEA ranking are
of little concern.
The main advantage of the proposed Hazard Efficiency
Measure based on DEA ranking is that it produces
a single hazard score for each road segment and thus
A
Criterion Y
y2
D
P
B
y1
allows ranking them and selecting a fixed number of topranked sites with the highest hazard scores for further
analysis.
Methodology of the project selection under budget
constraint considering benefit and risk objectives
jointly—composite efficiency measure
The above pre-selection (Step 1) provides a set of sites that
have the highest potential hazardous conditions dominating the rest of the sites and are thus candidates for an
evaluation by traffic engineers. For the pre-selected sites,
the following estimates are prepared:
K
K
expected crash cost reduction (benefit) and
project cost estimates.
Both measures depend on two variables, the site and
improvement type and require a detailed engineering
analysis. Different improvement types are possible at each
site which are considered separate projects, although
usually only one of these improvements is selected at a site.
The final project selection is an MCDM problem of
selecting a set of projects with the following objectives:
K
K
maximum benefits in accident cost reduction,
located at maximum risk sites,
subject to a fixed budget constraint for the total cost of the
selected projects.
We calculate a Composite Efficiency measure, CEp, for
each prospective project p, as a composite of estimated
cost, benefit, and hazard assessment. In order to avoid the
requirement for a significant user input for the weight
selection (pairwise comparison or subjective grading), we
apply the DEA method (16) as in the previous section
for the Hazard Efficiency measure. However, besides the
hazard measures we include here the benefit and cost
measures creating a Composite Efficiency measure. We use
the hazard measures and project benefit as output (to maximize) over the project cost as an input (to minimize).
The goal of the final selection is to maximize the
composite efficiency scores, CEp, of the selected projects
under the available budget, K. Let Cp be the cost for
project p, then the MCDM problem is reduced to the
following 0–1 Knapsack Model
Max Sp xp CEp
subject to Sp xp Cp pK;
xp ¼ 0 or 1
0
x1
ð17Þ
x2
Criterion X
Figure 1 A DEA illustration.
where each project p is either selected (xp ¼ 1), or not
selected (xp ¼ 0).
P Kelle et al—Highway improvement project selection by multi-objectives
The method of combining the DEA ranking with
MCDM has been used for different applications. For
instance, Golany (1998) combined interactive, multipleobjective linear programming with DEA; Stewart (1996)
compared the concepts of efficiency and Pareto Optimality
in DEA and MCDM. Furthermore, Belton and Stewart
(1999) stated that MCDM is generally applied to ex-ante
problem areas where data are not readily available such as
in the case of future technologies. DEA, on the other hand,
provides an ex post analysis of the past as a basis to learn.
Since our project selection case is based primarily on
existing statistical data related to such areas as accident
risk, cost, and benefits, the DEA ranking gives valuable
information for selecting the future improvement projects.
We believe that the advantage of our methodology
is that it can be applied to project selections in which
(1) tens of projects are to be selected out of hundreds of
potential projects pre-selected from thousands of potential
sites and (2) the selection is based on multi-criteria objectives which require no user input information regarding
the weights or pairwise comparison of the projects. We
illustrate the two-step procedure through an application
in the following section.
Case discussion and analysis
Our case study is based on four years of accident data from
Louisiana comprising over 160 000 crashes per year at
more than 23 000 locations with estimated crash costs close
to $6.5 billion. The data base we are using is the result of a
large project between Louisiana Highway Safety Commission (LHSC), the Department of Transportation and
Development (DOTD) and the Highway Safety Research
Group (HSRG) at Louisiana State University. The
statistical data are based on information obtained on
traffic crashes submitted by state, sheriff, and local police
agencies throughout the state of Louisiana. We demonstrate the use of our procedure with a specific example of
5091 rural two-lane two-way roadway segments without
intersections.
the section ‘Measuring hazard perception in road safety’
using four years of Louisiana crash data. The covariates
included ADT, lane width, and shoulder width. Other
variables such as shoulder type, roadside hazard rating,
driveway density, horizontal curvature, vertical curvature,
centreline rumble stripes, passing lanes, lighting, and grade
level could have been considered but were not readily
available. This lack of availability of complete information
on each road segment does not in any way affect the
methodology as a whole; however, the more covariates are
available the smaller is the unexplained variation in the
regression model. Once the pre-selection of road segments
has been done, for a manageable number of sites the
additional road design features can be easily provided for
the final selection. We also want to point out that this case
serves only as an example to demonstrate the methodology.
Measuring the hazard perception, we use the odds
against observing the specific average number of crashes
for each site. A Negative Binomial model was fitted for the
base condition with a shoulder width of six feet and a
pavement width of 24 feet for the three sets of crash counts
(number of total crashes, injury crashes and run-off-road
crashes). Next the accident modification factors published
in the Highway Safety Manual were applied for the 5091
locations to obtain predicted crash counts. The ratio of
total actual crash counts and total predicted crash counts
was used to adjust the parameter bo to better reflect the
level at all 5091 locations. Based on these three models, the
probability (and the associated odds) of the mean crash
count exceeding the estimated crash count was computed
for each road segment. We derived the following three
hazard measures based on readily available data:
K
K
K
To prepare the hazard measure (odds) for the pre-selection,
a Negative Binomial regression model is fitted according to
R1: the odds against total crashes,
R2: the odds against injury crashes,
R3: the odds against run-off-road crashes.
All three measures are of interest for rural highways
without intersections. The estimates for each of the three
models are displayed in Table 1.
A fourth measure was added for further examination:
K
Hazard efficiency measures
7
R4: the total crash cost for site k.
Note that those sites which have the worst hazard measures
(higher odds) and higher crash costs are preferable for
Table 1 Estimates for negative binomial models
Model
All crashes
Injury crashes
ROR crashes
Standard errors are in brackets.
Intercept b0
b1
ln(y)
6.1213 (0.982)
8.6568 (1.258)
6.5884 (1.2861)
0.74698 (0.109)
0.92685 (0.152)
0.67074 (0.1563)
0.063 (0.018)
0.01157 (0.0233)
0.010006 (0.0205)
8
Journal of the Operational Research Society
Table 2 An overlap of road segment selection results for
different selection criteria
Criterion
R1
R2
R3
R4 DEA 1–3 DEA 1–4
(%) (%) (%) (%)
(%)
(%)
R1
R2
R3
R4
DEA 1–4
DEA 1–3
100
68
63
52
56
78
68
100
60
57
60
73
63
60
100
48
51
78
52
57
48
100
93
56
56
60
51
93
100
62
78
73
78
56
62
100
improvement selection; thus R1-R4 are all output measures to maximize in (16). We pre-selected 5% of the
23 000 sites using different combinations of the above
four criteria (R1-R4) and compared the different sets of
road segments obtained by using different criteria. Table 2
shows the percentage of overlap when using different ranking criteria. The pre-selected sites arranged by
their score according to the odds R1, R2, and R3, the crash
cost, R4, and the DEA 1–4 score (using all four criteria,
R1-R4) and the DEA 1–3 score (using just three criteria,
R1-R3).
Using R1, R2, or R3, individually, results in over 70% of
the selected sites overlapping with the DEA 1–3 score
(using R1, R2 and R3 combined). The DEA 1–4 score
(using R1, R2, R3 and R4 combined) has more overlap
(90%) with R4 than with R1, R2 or R3 (which ranges from
50 to 60%). We note that we will not use the crash cost R4
in Step 2 but rather R5, which measures the crash costs
reduction.
Federal guidelines require that states list at least 5% of
the most hazardous road segments. Federal requirements
(Sections 148(c)(1)(D) and 148(g)(3)(A), of Title 23, United
States Code) stipulate that each state describe at least 5%
of its locations currently exhibiting the most severe highway safety needs. The number of hazardous pre-selected
sites may be larger for our project selection method
depending on how many engineering work hours are
available to analyse the pre-selected sites. This selection
should contain road segments that are preferable to other
sites to be considered for improvement. However, because
of limited funds, cost and benefits need to be taken into
consideration in the final project selection.
Composite efficiency measure
For the final project selection (Step 2), the following
estimates are prepared for safety improvement projects at
the pre-selected sites:
K
R5: the expected crash cost reduction (benefit) of a
project that depends on two variables, the site and
improvement type.
K
V1: the cost estimate of a project that is also dependent
on site and improvement type, requiring a detailed
engineering analysis.
Note that R5 is an output measure to be maximized and
V1 is an input measure to be minimized in (16). At each
site, different improvement types are possible which are
considered as separate projects, but usually only one of
these improvements is selected at a site.
The Highway Safety Manual provides accident modification factors that have been used to predict the expected reduction rate in accidents as a consequence of the
improvement type. For simplicity, in our example we use
only two possible actions, namely widening the road to
a standard width of 24 feet and widening the shoulder to
6 feet. The cost estimate of these actions is based on a cost
of $2.5 million per mile plus a proportional cost for the
increase in the lane width and the shoulder width of the
road segment. Although this estimate is a simplification, it
is suitable for demonstrating the methodology. Obtaining
an exact estimate of the costs for improvements is not
feasible for our example.
The new ranking which takes into account the hazard
measures (R1, R2, R3) and benefits R5 has about 46 to
55% of road segments overlapping with the set obtained
using the individual ranking R1, R2, R3, and 58% with the
set obtained through the ranking of DEA 1–4 score and
53% with the set based on ranking the DEA 1–3 score.
We applied the zero-one Knapsack Model (17) to select
the improvement projects by maximizing the Composite
Efficiency measure based on the DEA scores of the projects
(CEp, based on the criteria of cost, benefit, and hazard)
subject to the budget constraint. For planning purposes,
different geographical areas and budget alternatives have
been evaluated which required an efficient ‘what-if’
analysis, trade-off curves, and other practical decision
support tools. By applying Boolean constraints (as and/or
selections), it is easier to consider sites with multiple project
options where not more than one option can be selected.
Also groups of joint projects can be handled in which
either all or none are to be selected.
We developed a PC-based computerized decision support system which can easily be accessed in Excel. The
input data including the crash information along with
other site characteristics which may need user input are
also available in Excel. The algorithmic part is run by
VBA macros, which support a ‘what-if’ analysis based on
different budgets, on subsets of sites to be considered, and
which allows different pre-selection criteria and selection
limits. The output possibilities are also easy to modify
using Excel. The imbedded LINGO (Extended Version
3.01, 1999, LINDO System Inc.) procedures effectively
handle the large problems which need to be solved such as
the dual LP for DEA evaluating up to thousands of projects
in solving (16) and the 0–1 knapsack problem solution for
P Kelle et al—Highway improvement project selection by multi-objectives
several hundred pre-selected projects, using a branch and
bound procedure in (17). Alternatively, Excel Solver can
also be used, but it requires a longer computation time.
In the section ‘Composite efficiency measure’ we
discussed how the ranking is affected by using the different
measures R1, R2, R3 and R5. In the following section we
compare the proposed composite efficiency method for
project selection to a pure cost-benefit analysis approach
and a pure hazard approach and demonstrate some of the
advantages of the composite selection method.
Comparison with other project selection methods
Our Composite method jointly considers benefit and hazard
objectives expressed in the project Composite Efficiency
score which is the weighted average of benefit, hazard,
and cost objectives. The weights are calculated with the
DEA method (16). For comparison, we considered two
alternative selection methods with a single objective each:
K
K
Benefit method: selecting the projects with the highest
benefit and
Hazard method: selecting the projects on the sites with
the highest hazard.
In summary, the Benefit method is biased toward
including fewer large projects with large benefits while
9
the Hazard method is biased toward including smaller
projects with higher risk road segments. Overall, the
Composite method provides a good compromise between
obtaining a large benefit in crash cost reduction and
including more projects with high-risk road segments.
The results of the three methods are illustrated in the
columns of Table 3 and Table 4. In Table 3 we illustrate
the results for three different budgets in millions, $200,
$400, and $600 million, while in Table 4 we summarize
the statistics (average, standard deviation, and percent
differences) for a large number of runs with different
number of pre-selected sites and a large set of different
budgets.
The tables show the result of selecting the highest
objective value under a fixed budget constraint solving the
optimization problem (17). The three different objectives
are displayed in different columns, respectively.
K
K
The Benefit method with the crash cost reduction as
single objective (denoted by R5 in Section ‘Methodology
of the project selection under budget constraint considering benefit and risk objectives jointly—composite
efficiency measure’);
The Composite method with highest Composite Efficiency scores (described in Section ‘Methodology of the
project selection under budget constraint considering
benefit and risk objectives jointly—composite efficiency
measure’);
Table 3 A comparison of the project selection methods for different budget constraints
200
Budget ($million)
Objective
600
400
Benefit
Composite
Hazard
Benefit
Composite
Hazard
Benefit
Composite
Hazard
11
NA
7.1
NA
17
55%
3.6
49.6%
16
45%
2.9
59.8%
22
NA
10.8
NA
27
23%*
8.3
23.3%
27
23%
5.2
52.1%
30
NA
12.8
NA
36
20%
10.9
14.6%
37
23%
9.1
28.8%
23.8
64%
8.3
101%
19.2
33%
5.8
40%
14.5
NA
4.1
NA
23.8
64%
8.4
183%
14.5
0%
2.5
16%
14.5
NA
3.0
NA
Remaining R2 hazard (odds of injury crashes, 1 to million):
Maximum R2
111.1
111.1
37.0
111.1
Hazard increase
200%
200%
NA
267%
Average R2
11.2
11.1
7.8
11.3
Hazard increase
43%
42%
NA
60%
30.3
0%
7.0
2%
30.3
NA
7.1
NA
111.1
400%
13.1
196%
30.3
36%
6.8
54%
22.2
NA
4.4
NA
Remaining R3 hazard (odds of run-of-road crashes, 1 to million):
Maximum R3
58.8
32.3
32.3
58.8
Hazard increase
82%
0%
NA
129%
Average R3
15.9
12.4
12.3
17.6
Hazard increase
29%
0%
NA
64%
31.3
22%
11.3
5%
25.6
NA
10.8
NA
58.8
224%
19.9
79%
25.6
41%
10.9
3%
18.2
NA
11.2
NA
# Projects selected
Increase
Benefit in $million
Loss in benefit
Remaining R1 hazard (odds of total crashes, 1 to million):
Maximum R1
23.8
19.2
19.2
Hazard increase
24%
0%
NA
Average R1
7.7
5.4
5.6
Hazard increase
36%
4%
NA
Percentage increase above baseline denoted by NA. Bold entries show the example explained in text.
10
Journal of the Operational Research Society
Table 4 A summary of comparisons for the different project selection methods
Objective
# Projects selected
Benefit in $million
Remaining max R1
Remaining avrg. R1
Remaining max R2
Remaining avrg. R2
Remaining max R3
Remaining avrg. R3
Overall average
Standard deviation
Average loss %
(compared with the best)
Benefit
Composite
Hazard
Benefit
Composite
Hazard
Benefit
(%)
Composite
(%)
Hazard
(%)
23.67
10.91
23.81
8.46
111.11
12.16
58.82
17.88
29.00
8.36
15.90
4.34
42.00
7.07
28.47
11.08
29.00
6.60
14.57
3.64
29.85
6.60
25.19
11.14
9.44
2.38
0.00
0.71
0.00
0.95
0.00
1.59
8.67
3.22
4.22
1.70
34.00
2.13
5.62
1.17
9.12
3.02
5.03
1.54
6.63
1.65
6.09
1.33
18.4
0.0
63.4*
132.5
272.2
84.3
133.5
60.5
0.0
23.3
9.1
19.2
40.7
7.2
13.0
0.6
0.0
39.5
0.0
0.0
0.0
0.0
0.0
0.0
*Bold entries are discussed in the text.
300.0%
Percent increase in:
The Hazard method with highest Hazard Efficiency
scores (described in Section ‘The pre-selection of road
segments based on multi-criteria ranking—hazard efficiency measure’).
250.0%
Although this is a case study limited to road projects in
Louisiana, the analysis suggests several general trends.
(1) The number of projects selected (first row in Tables 3
and 4).
The Benefit method is biased toward larger projects
and thus selects fewer projects for a given budget. The
Composite and Hazard methods select a larger number
of projects. For instance, for a budget of $200 million, the
Benefit method selects 11 projects while the Composite
method selects 17 projects and the Hazard method selects
16 projects (see in Table 3). On the average, 18.4% fewer
projects are selected by the Benefit method than with the
other methods (see in Table 4).
50.0%
K
(2) The benefits in millions of dollars (third row in Tables 3
and 4).
The Benefit method provides the largest benefit and
the Hazard method the lowest benefit as expected. For
instance, for a budget of $600 million, the benefit for
the 37 projects selected by the Benefit method is $12.8
million while the Composite method provides a benefit
of $10.9 million for the 36 projects and the Hazard
method provides a benefit of $9.1 million for the 37
projects (see in Table 3). The benefit loss of the Hazard
method is 39.5% on the average (see Table 4). The
Composite method provides benefits in between the two
(23.3% average loss in benefit). However, a major
hazard reduction is the trade-off for benefit loss as we
see in Figures 2 and 3.
Benefit loss
200.0%
max hazard R2
max hazard R3
100.0%
0.0%
Benefit
Composite
Hazard
Figure 2 Risk/benefit trade-off for different project selection
methods (with maximum hazard comparison).
Percent increase in:
Benefit loss
140.0%
120.0%
avrg. hazard R1
100.0%
avrg. hazard R2
80.0%
avrg. hazard R3
60.0%
40.0%
20.0%
0.0%
Method:
-20.0%
Benefit
Composite
Hazard
Figure 3 Risk/benefit trade-off for different project selection
methods (with average hazard comparison).
The hazard at the unselected sites represents the
remaining hazard after the selected sites is improved. The
hazard is evaluated using two different measures
K
K
maximum hazard at the unselected sites (worst case) and
average hazard at the unselected sites.
In our case, we consider the following hazard types:
K
(3) The remaining hazard (starting in row five in Tables 3
and 4).
max hazard R1
150.0%
K
K
R1: the odds against total crashes,
R2: the odds against injury crashes,
R3: the odds against run-off-road crashes.
P Kelle et al—Highway improvement project selection by multi-objectives
For the measures of hazard given above, the hazard
reduction is between 33 and 62% for the Composite
method and 38 to 73% for the Hazard method (see
Figures 2 and 3).
The hazard evaluation requires a more detailed explanation. Each hazard in Tables 3 and 4 is expressed as
the odds of one million to 1. For instance, at a given
location, if the odds are 2 million:1, then the odds are
2 million to 1 against this specific average number of
crashes occurring if a road section with the specific site
features had been chosen at random.
We complete a detailed comparison for all three
hazard measures for each selection method. The Benefit
method leaves many high risk sites (higher odds) out of the
selection. The Composite method results in odds that are in
between the Benefit and Hazard methods. As illustrated in
Table 3, the hazard increase is different for the three
different hazard measures R1, R2, and R3 considering both
the maximum and the average odds for the unselected sites.
For instance, for a budget of $400 million, the maximum
R1 which is not selected with the Hazard method is 14.5:1
(odds of mean crashes is 14.5 million to 1), with the
Composite method it is 19.2:1, and with the Benefit method
it is 23.8:1. For this case the hazard increase is 33% for the
Composite method and 64% for the Benefit method,
compared with the best, namely the Hazard method. Using
the average rather than the maximum odds R1 of projects
not selected the increase is 40% for the Composite method
and 101% for the Benefit method. Table 3 also shows
the percentage increases in the R2 and R3 odds for the
three methods. While the Hazard method results in a 52.1%
loss in benefits, the Composite method results in a 23.3%
loss of benefits compared with the Benefit method.
The Hazard method selects the sites with the highest
hazard efficiency score (the weighted average of odds R1,
R2, and R3 in our case); therefore we expect that the
Hazard method selects the sites with the highest odds for
each hazard measure R1, R2, and R3, respectively. However, there are cases where the Composite method provides
lower hazard in one of the measures (indicated by a
negative hazard increase in Table 3) but still a higher
hazard in the other measures.
The statistical results based on a large number of runs
are summarized in Table 4. This table contains the overall
averages, the standard deviations, and the average loss
percent compared with the best solution. For instance,
when using the Benefit method there is a 63.4% increase in
the maximum of R1 of the site not selected and a 132%
increase in the average R1 for sites not selected. In contrast
to the Benefit method when using the Composite method the
hazard increase is only 9.1 and 19.2%, respectively. Similar
results are obtained for R2 and R3. The increase in the
maximum hazard of sites not selected is very high for
the Benefit method and slightly higher for the Composite
method when compared with the Hazard method. For
11
instance, the increase in the maximum hazard for the Benefit method is 27.2 and 133.5% for R2 and R3, respectively.
These increases are only 40.7 and 13.0% for the Composite
method. Figures 2 and 3 depict the percentage loss for the
maximum hazard and the average hazard criteria, respectively. The figures show the loss in benefits as well as the
loss in maximum and average hazard for not selected sites.
It demonstrates that the Composite method is a compromise between the two extreme methods, that is, using only
cost/benefits or using only hazard.
Discussion and extensions
This paper is dealing with the selection of safety improvements projects allocating the fund that is federally
mandated for safety improvements. The major goal is to
decrease the accident rate using the available budget. This
leads to the practice of applying cost-benefit criteria for the
safety improvement project selection. From an economic
point of view it can be argued that a pure cost-benefit analysis should be used, but this criterion may leave a number
of high-risk sites unselected where the traffic is small.
Examples such as the Pinto and the recent Shell Oil well
disaster cases show that the pure cost-benefit considerations are sometimes unacceptable for the public. For this
reason, government and industry often sets limits on risk
for products and services and they try to find the best
compromise between benefit and risk.
We suggest a methodology that includes risk measures
combined with benefit and cost measures in the safety
improvement project selection process. The numerical
example of a case demonstrates the advantages of our
multi-criteria decision support method.
We propose a new hazard estimation method using the
tail probability of the Negative Binomial distribution to
express the odds against observing a given crash count at a
specific road segment. These odds and other readily available crash statistics are used to pre-select prospective
sites for road improvements in the first step, eliminating
thousands of sites. For a reasonable number of pre-selected
sites a detailed project evaluation can be prepared by the
engineers and safety experts. For the multi-criteria ranking
we used the DEA to create a single Hazard Efficiency score
for each site. This method can be used to rank thousands
of sites since it requires minimal user input and it is computationally efficient. The DEA method insures that those
sites are not eliminated which may be advantageous in any
one of the criterion or in any combination of the criteria.
For the pre-selected sites the detailed cost and benefit
evaluation results and the hazard scores were combined to
create a single Composite Efficiency score for each prospective project used in the final project selection. Overall, the
project selection method based on the above Composite
Efficiency score provides a good compromise between
12
Journal of the Operational Research Society
obtaining a large benefit in crash cost reduction and
including more projects on high risk road segments.
To summarize, our method can resolve the following
issues that were not adequately handled in previous
methods published in literature: (1) the evaluation of
hazard perception, (2) the very large number (several
thousand) of potential sites, (3) the pre-selection process
based on readily available proxy measures, (4) a final
project selection based on the composite measure of cost,
benefits and risk.
There are some possible extensions to our approach. For
instance, one of the inputs requires the estimation of
project cost and the estimates of the monetary benefit of
an improvement project. However, providing accurate
estimates for hundreds of projects may not be feasible.
Thus approximate cost estimates as computed for our
example may have to be used. The resulting uncertainty
motivates the stochastic extensions for the project selection. Therefore, a chance constrained DEA seems to be
a possible extension to apply in the future for traffic project
ranking and selection. Some recent publications applying
this methodology include Cooper et al (2004), Srinivas et al
(2006), and Lahdelma and Salminen (2006). Nevertheless,
the extensions for fuzzy DEA methodology may also be
considered (see eg in Chiou et al, 2005 and Dimova et al,
2006). Other possibilities include the application of the
stochastic dominance approach as in Nowak (2007) and
the combination of simulation and optimization suggested
recently in Scott et al (2007). The major difficulty that
arises with these methods is the large number of projects to
be considered.
Another direction of extensions of our approach
includes more user input for the final step where the
number of projects to consider is smaller. An extension of
the DEA ranking method is the integration of criteria
preference scores provided by the users such as, for
example, the use of assurance regions (upper and lower
bounds for each criterion) for the restriction of weights
in DEA which is an approach to include user preferences
(see Thompson et al, 1990 and Wong and Beasley, 1990).
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Received December 2011;
accepted March 2012