A More Comprehensive Life Cycle Cost Analysis of Pavement Materials Alternatives
by
William Colby Dunn
Undergraduate in Materials Science and Engineering
Massachusetts Institute of Technology
Submitted to the Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements for the Degrees of
Bachelors of Science in Materials Science and Engineering
at the
Massachusetts Institute of Technology
June 2013
© 2013 Massachusetts Institute of Technology.
All rights reserved.
Signature of author
Department of Materials Science and Engineering
Materials Systems Laboratory
5/3/2013
Certified by
Joel P. Clark
Materials Systems Laboratory Faculty Director
Thesis Advisor
Accepted by
Jeffrey C. Grossman
Undergraduate Committee Chairman
Correspondence:
W. Colby Dunn
Phone: 617-548-9944
dunnwi@mit.edu
1 This page is left intentionally blank
2 ACKNOWLEDGMENTS
This research was implemented in tandem with the Materials Systems Laboratory at MIT.
The author is grateful to Omar Swei for his extensive technical input, and to Randolph
Kirchain and Joel Clark for their technical and literary support and mentorship.
Additionally, the author would like to thank MIT for seamless software implementation
and Applied Research Associates, Inc., which helped developed pavement designs used
in the analysis.
3 TABLE OF CONTENTS
I.
LIST OF FIGURES…………………………………………………………..….5
II.
LIST OF TABLES…………………………………………………………….....6
III.
ABSTRACT……………………………………………………...……………….7
IV.
INTRODUCTION …………………………………………….…………………8
V.
LITERATURE REVIEW …………………………….……………………..…12
a. Literature Review….……..….…...…….……….……….……………….12
b. Gap Analysis ….….………………………………………………………15
i. Part 1: Out-of-sample Forecasting ….……………………………15
ii. Part 2: Unit-cost Variability Due to Location and Cost…….……16
iii. Part 3: Case Study Methodology …………………….……..……16
VI.
METHODOLOGY ……………………………………………………..………17
a. Part 1: Out-of-sample Forecasting .………………………………………17
i. Section A: Stationary or Non-Stationary Classification
ii. Section B: Forecasting Based on Data Classification
iii. Section C: Accuracy of the Forecast vs. Baseline Case
b. Part 2: Unit-cost Variability Due to Location and Cost………………….21
c. Part 3: Case Study Methodology ……………………………………...…22
i. Section A: Unit Cost Relationship
ii. Section B: Uncertainty Characterization without Historical Data
iii. Section B: Perform and Interpret Simulations
VII.
RESULTS & ANALYSIS………………………………………………………24
a. Part 1: Out-of-sample Forecasting……………………………….………24
i. Section A: 40-year Results
ii. Section B: 60-year Results
b. Part 2: Unit-cost Variability Due to Location and Cost………………….28
c. Part 3: Case Study Methodology ………………………………………...36
VIII.
CONCLUSIONS AND FUTURE WORK …………………………………….42
IX.
WORKS CITED…………………………………………………………...……43
X.
APPENDICES ……………………………………………………………..……46 4 LIST OF FIGURES
1. Figure 1: Two Pavement Designs with Different Net Present Values (NPV) and
Risks………………………………………………………...…………………......8
2. Figure 2: The Life-Cycle of a Highway Construction Project….
page……………………………………………………………………………....10
3. Figure 3: The Initial and Life-Cycle Costs Associated with Highway
Construction Projects….…………………………………………………………10
4. Figure 4: The Historical Price Behavior of Dimensioned Stone….……..……...24
5. Figure 5: MAPE vs. Year into the Future (40-year Analysis)…………………..26
6. Figure 6: MAPE vs. Year into the Future (60-year Analysis)…………………..27
7. Figure 7: Florida linear regression analysis of unit-cost of HMA winning
pavement bids with respect to bid volume.………………..……………………..29
8. Figure 8: Aggregate (FL & CO) linear regression analysis of unit-cost of JPCP
winning pavement bids with respect to bid volume.……...….. ……………..…..30
9. Figure 9: Colorado linear regression analysis of unit-cost of HMA winning
pavement bids with respect to bid volume……………….……..………………..31
10. Figure 10: Colorado linear regression analysis of unit-cost of JPCP winning
pavement bids with respect to bid volume……………….……..………………..31
11. Figure 11: ARA Pavement Design Specifications………..…………………..…36
12. Figure 12: Initial, discounted rehabilitation, and life-cycle costs of JPCP and
HMA pavement designs in Florida and Colorado………..……………….…..…38
13. Figure 13: Florida probabilistic life-cycle cost of urban interstate road
alternatives (gray line represents HMA design, orange represents JPCP design).
The dashed lines represent the mean value from the analysis………..……...…..39
14. Figure 14: Colorado probabilistic life-cycle cost of urban interstate road
alternatives (gray line represents HMA design, orange represents JPCP design).
The dashed lines represent the mean value from the analysis………..……….…40
15. Figure 15: 40-year MAPE Analysis with Real dollars, No-change Model…..…49
16. Figure 16: 60-year MAPE Analysis with Real dollars, No-change Model…......50
5 LIST OF TABLES
1. Table 1: Florida quantification of unit-cost uncertainty for significant input
parameters. Values in parenthesis represent the standard error of the regression
coefficients………………..……………………….……………………………..33
2. Table 2: Colorado quantification of unit-cost uncertainty for significant input
parameters. Values in parenthesis represent the standard error of the regression
coefficients….………………..………………..…………………………..……..35
3. Table 3: MEPDG based JPCP and HMA pavement designs for the urban
interstate and local road case studies.……………………………………………46
4. Table 4: Maintenance schedule for JPCP and HMA pavement designs at MEPDG
specified 90% reliability for the urban interstate and local road case
studies………………..………………..………………………….…….………..47
5. Table 5: Florida Pavement Specifications….………………..…….………...…..48
6 ABSTRACT
Life Cycle Cost Analysis (LCCA) is a commonly used tool in analyzing the economic
viability of highway construction investments. The initial and life-cycle materials costs
associated with highway construction involve a high level of uncertainty and therefore
warrant extensive and dynamic cost analysis. These uncertainties derive from extensive
materials usage costs. Despite the advantages of implementing a probabilistic approach to
cost analysis, many state departments of transportation (DOTs) continue to employ a
deterministic model, thereby misjudging, and often altogether neglecting the underlying
uncertainty and risks. The goals of this paper are twofold: first, to validate forecasting as
a viable method to predict future materials’ prices, and second, to explore economies of
scale as a potential driver of uncertainty.
The paper will then apply these results to a case study methodology, looking at a
comparative LCCA of two materials alternative, asphalt vs. concrete pavement designs
for two states: Florida and Colorado. Endeavoring in this light, the author has
characterized uncertainty in a way that will be comprehensible by practitioners. This
research has successfully validated out-of-sample forecasting as a superior method of
forecasting materials prices, characterized uncertainty related to project quantity, and
delivered results using a relatable case study approach.
7 INTRODUCTION
Analyzing highway construction projects deterministically is a cursory methodology in
that it oversimplifies input parameters by assigning them a single, static value. These
simplified values effectively mask any uncertainty related to the investment decision on
hand, as shown in Figure 1 (Gransberg 2009). While this approach does provide the user
with a simple selection process, it bases its cost assessment off a limited number of
possible outcomes. Realistically, there are a vast multitude of nuanced scenarios that
could play out; the risk associated with such long-term investments therefore is much
more complicated than a single output. A probabilistic analysis will account for a range
of outcomes, thereby better incorporating the underlying risks associated with a project
(Swei 2013). With a better understanding of the risks associated with different highway
implementations practitioners will be better able to integrate risk-threshold levels into
Net Present Value their highway construction decisions.
Design A Design B Figure 1: Two pavement designs with different net present values (NPV) and
different associated risks (error bars). A deterministic approach would effectively
mask the underlying uncertainty here.
8 The concept of implementing a probabilistic LCCA is by no means novel. In fact, the
methodology has come strongly recommended by the Federal Highway Administration
(FHWA) since 1998 (Smith and Walls 1998; Temple and William 2004). The
implementers of such models, however, have been hesitant to switch from the traditional
deterministic model for several reasons. The first of which is that the implementation of a
probabilistic model is far more complex and multi-faceted than is its deterministic
counterpart. Secondly, practitioners have been provided little guidance regarding how to
characterize uncertainty regarding input parameters (Tighe 2001).
Life Cycle Cost Analysis (LCCA) is a commonly used analytical investment assessment
tool that accounts for total project costs beginning with the initial building and extending
to the final removal of the venture, as shown in Figure 2 (Lee 2002; Guo 2010). All costs
incurred in-between (e.g. routine maintenance and rehabilitation expenses) are included
(Smith 1998). It is therefore no surprise that projects warrant extensive materials usage,
and the importance of materials in the LCCA, therefore, cannot be stressed enough.
While highway investments extend far into the future (some reaching 50-years), recent
data has shown that practitioners continue to place a disproportionate weighting on initial
costs rather than their life-cycle counterparts (Rangaraju 2008). One explanation for this
phenomenon is that the level of uncertainty is far greater when forecasting costs that
extend far into the future. It is therefore reasonable to abstract that should practitioners be
provided with a framework to better understand potential future cost behavior, they are
likely to weigh life-cycle costs when selecting a paving material (Frangopol 2001).
Beyond uncertainties in future costs, investments in highways also warrant extensive
9 characterization of initial parameters, such as unit-cost of paving material inputs, which
likely vary as a function of quantity, location, and more as shown in Figure 3. With better
characterization of the impact of these two variables on cost, practitioners will be more
confident in their understanding of the variability associated with a specific pavement
materials selection.
Figure 2: The three main constituents of life-cycle costs in highway construction
projects. The final removal costs and user costs are excluded.
Figure 3: The initial and life-cycle costs associated with highway construction
investments. (Swei 2012)
10 The overarching theme of this paper is to provide LCCA practitioners with an improved
structure for understanding uncertainty related to highway costs, particularly uncertainty
related to future materials costs. In this vein, the paper will take a two-pronged approach
in first classifying uncertainty related to future materials prices, and testing whether
forecasting prices decades into the future is a plausible endeavor. The research will then
shift to characterizing the unit-cost of construction inputs associated with highway
construction, exploring how much of the variability can be explained through a likely
relationship which exists between cost and quantity and testing this for multiple
locations. Finally, the author has taken a case study approach in order to test the
implications of the characterized inputs on a probabilistic LCCA for pavement design
alternatives that are considered functionally equivalent. Specifically, an LCCA between
two materials alternatives, asphalt and concrete pavement designs in Florida and
Colorado will be compared. In so doing, drivers of uncertainty will be elucidated in a
way relatable to LCCA practitioners, thereby leading to an improved methodology for
understanding the uncertainty embedded in such long-term investments.
11 LITERATURE REVIEW
Economic feasibility is a fundamental concern when assessing any long-term investment
proposition, and highway construction projects are certainly no exception. With historical
LCCA model implementation ranging from thirty to fifty-five years, highways represent
just how important financial viability is to infrastructure projects (Frangopol 2001).
Culminating in what was a revolutionary ordinance in 1995, the Federal Highway
Administration (FHWA) forced all state DOTs to incorporate LCCA models into
highway projects that had estimated costs of over $25mm (National Highway System
Designation Act of 1995). The FHWA further emphasized the importance of sound
highway investment by outlining the shortcomings of a deterministic LCCA (Walls and
Smith 1998). Stressing the relative merits of a probabilistic dynamic model, the FHWA
has established itself as a prominent source of funding for such research.
After the 1995 legislation, teams of researchers set to work developing a more robust
LCCA model to accurately assess the economic performance of highway construction
projects. Specifically, Zimmerman and Peshkin focused their efforts on specifying
optimal maintenance schedules for pavements (Zimmerman and Peshkin 2003).
Embacher and Snyder evaluated the relative economic merits of asphalt (HMA) vs.
concrete (RMC) in low-volume pavement applications (Embacher and Snyder 2001).
Oberlander used factor analysis to make predictions for the cost of construction projects
(Oberlander 2003). The above research endeavors, while having contributed to the
development and implementation of LCCA in the field, are fundamentally flawed, as they
have taken a deterministic approach. In so doing, said research has failed to address the
12 uncertainty and risks previously discussed (Swei et al. 2013a). With that said, one
parameter that has traditionally been ignored is the forecasting of future material prices.
Before forecasting prices, however, it is first necessary to verify that statistical methods
exist, which are a superior method of predicting such uncertainties with a relatively high
level of precision.
In order to forecast future cost behavior, one risk that must be considered is how
construction prices will evolve over time. To that extent, research has been geared
towards using statistics in assessing the merits of forecasting future materials prices (i.e.
whether or not historical data is a good predictor of future data). One such methodology,
known as “backcasting”, takes “out-of-sample” data and forecasts said data where the
future price point is known. Multiple studies have implemented these methods. Ashuri
and Lu (2010) created a Construction Cost Index (CCI) that uses an Autoregressive
Integrated Moving Average (ARIMA) model to forecast future costs. The two used a 12month out-of-sample forecast in tandem with Mean Square Error (MSE), Mean Absolute
Error, and Mean Absolute Percent Error (MAPE) metrics.
Hwang built upon such
research, using Mean Absolute Error (MAE) to access the precision of forecasting
materials prices for a 12-month and 24-month period using the CCI (Hwang 2009;
Hwang 2011). Xu and Moon (2013) used Mean Square Error (MSE) to determine the
validity of their 54-month vector autoregression (VAR) forecasts that established a
relationship between CCI and the Consumer Price Index (CPI). MIT’s Concrete
Sustainability Hub (CSH) have followed a similar methodology as Xu and Moon,
conducting cointegration between multiple time-series to construct a forecasting model
13 for asphalt and concretes (Swei 2013b). Moreover, “backcasting” techniques have been
employed, resulting in Mean Average Percent Error (MAPE) values that prove
forecasting future pavement commodity costs (asphalt and concrete constituent materials)
as a valid endeavor to reduce uncertainty (Swei et al. 2013b). In addition to long-term
costs, highway construction projects also warrant extensive risk characterization in shortterm inputs; accordingly, it is crucial to understand the developmental timeline of a
highway.
When assessing the economic viability of highway construction projects, it is important
to account for the substantial cash outflows that span over the highway lifespan. The
outflows can be separated into three distinct phases: the initial costs, use costs, and the
end-of-life costs. The initial costs include materials extraction and production,
transportation, and any costs associated with construction (i.e. equipment and labor).
After the highway is constructed, maintenance costs are incurred throughout the lifespan
of the highway. And, finally, the end-of-life costs (i.e. pavement removal and recycling)
are incurred when the highway is no longer in working condition (Swei et al. 2013a). It is
therefore clear that highway construction is not only a long-term investment venture but
also a multi-faceted project susceptible to uncertainties at phase. Accordingly, it is crucial
to develop as comprehensive an LCCA model as possible to ensure practitioners are not
only aware of the expected costs associated with a project but also cognizant of expected
uncertainties associated with such costs. This research focuses on the cost to the agency,
thereby excluding the user costs, in an attempt to focus the scope of the analysis.
14 Due to the increased recognized importance of accounting for uncertainty, researchers
have recently begun to endeavor in extensive research that is geared towards accessing
the uncertainties rooted in the classical deterministic methodology (Swei 2013b).
Specifically, Touran (2003) incorporated uncertainty in bid vs. actual construction costs
by accessing the data from a probabilistic standpoint. Tighe (2001) further contributed by
accessing pertinent inputs and overall construction costs with an emphasis on probability
distributions. Additionally, Osman (2005) employed a Weibull distribution to elucidate
some uncertainty related to pavement performance and maintenance over its life span. In
other words, much attention has been focused on the risks inherent in the input
parameters, with the goal of arriving at a more robust output. This improved model would
better indicate the uncertainty associated with particular highway constructions. In so
doing, the model will provide practitioners with a more robust and holistic perspective,
thereby enabling them to align their investment decisions with their risk thresholds (Swei
et al. 2013c).
GAP ANALYSIS
Part 1: Out-of-sample Forecasting
While a CCI is an invaluable and widely used dataset for forecasting, it is incomplete in
that it is a weighted average index comprised of material, labor, and construction costs.
This consolidation, as stated by Hwang et al., wrongfully assumes that all cost items will
grow at the same rate. (Hwang et al. 2011) It is therefore prudent to delineate each
constituent cost and forecast separately. Moreover, prior research has been limited in that
it has assessed forecasting for a short time period (i.e. 5-years); the novel aspect of this
research is that it will determine the relative merits of forecasting over extended periods
15 of time (i.e. 40 years). The research will also explore how much empirical data is needed
in order to forecast with a reasonable level of precision.
Part 2: Unit-cost Variability due to Location and Scale
Location with respect to state will be accessed through analyzing two distinct states. In
other words, this research will see if parameter characterization holds true from state to
state, and if not, by how much they differ. Secondly, establishing a relationship between
unit-cost and quantity for materials used in recent highway construction projects will
assess economies of scale as a potential driver of variability. This data will prove not only
worthwhile for academia but also relatable to practitioners in the field, thereby achieving
the penultimate goal of the research.
Part 3: Case Study Methodology
After validation of forecasting long-term costs and characterization of initial costs, this
paper will deliver the results using a case study methodology. Accordingly, state DOTs
will be able to better understand the implications of variable characterization on a
probabilistic LCCA.
16 METHODOLOGY
Part 1: Out-of-sample Forecasting
In order to validate backcasting as a viable means of forecasting, it is crucial to first
establish the historical behavior of the underlying data. In general terms, if the statistical
properties of a data set do not change over time, the data is deemed stationary, and
otherwise is classified as non-stationary. In other words, a joint distribution (Xt1 , Xtn ) is
the same as the joint distribution (Xt1+r , Xtn +r ) for all n and r, thereby depending only on
the distance between t1 and tn. (Nason et al. 2006). If a time series does not exhibit
stationarity as outlined above, it is deemed non-stationary. After establishing said
behavior, an appropriate forecast can be initiated using empirical data. The model used in
this paper will not be set to the strict standards of stationarity as outlined above, but will
rather adhere to a less rigid criterion, which will be discussed in the coming sections.
After initiating the forecast, the model will then be evaluated on the basis of accuracy
using MAPE against a baseline model that assumes future real prices that are in line with
inflation (Gneiting 2010; Baumeister 2012). Finally, the accuracy of said forecasts will
be compared on the basis of the time extent of the data set. In other words, the author will
assess the accuracy of the model for different sizes of the dataset, which will lead to a
better understanding of how much historical data is sufficient to produce superior results.
Section A: Time-Series Classification – Stationary or Non-Stationary
There are various tests that serve to characterize the historical behavior of a data set,
including the Augmented Dickey-Fuller (ADF) and the Phillip-Perron (PP) test.
(Leybourne 1999) Although the former are more common, the implementation is quite
time consuming, in particular for this research given that 40 different samples will be
17 analyzed for the time-series. As such, this research employs a “threshold” test that
utilizes the univariate ARIMA (p, d, q)1 model, seen in equation 1:
!
!
!
!! 1 −
!! !
!
!! !!
(1 − !) = ! + !! 1 −
!!!
!!!
(1)
!! : price in year t
!! : error term in year t
!! : autoregressive coefficient
!! : moving average coefficient
C: constant drift term
L: lag operator
If an ARIMA (1, 0, 0) model is used, it equates to the following, as shown in equation 2:
!! = !!!!! + ! + !!
(2)
Interestingly, the simplified, first-order auto-regressive process, ARIMA (1,0,0), as shown
in equation 2 bears a resemblance to the Ornstein-Uhlenbeck mean-reverting process,
shown in discretized form in equation 3:
!! = 1 − ! !!!! + !" + !!
(3)
K: speed of mean reversion
C: mean reversion value
!! : “white noise” error term
The first step is to determine the value of the autoregressive coefficient, ! in equation 2.
It is important to note that ! corresponds to 1-K, seen in equation 3, where K is the rate of
1
p: number of autoregressive terms
d: number of non-seasonal differences
q: number of moving average terms 18 mean reversion. The inverse of K symbolizes the time it takes for reversion to occur in a
data set; therefore, the higher the value of !, the lower the value of K, and the longer it
takes for reversion. Thus, this research uses a threshold test, in which the data is deemed
to exhibit autocorrelation and is classified as non-stationary if ! is greater than or equal
to 0.95 (Selke et al. (1999). It is also worth noting that the error term will be disregarded
in this analysis, as this research is only concerned with the precision of the forecast, and
so a confidence interval is not pertinent to the scope of this research. Additionally, the
0.95 threshold, which implies a process takes 20 years to revert back to its mean, is in
line with previous research that has found commodities’ can take up to a decade to show
reversion (Pindyck 1999).
Parameters are estimated using Stata and JMP 10, two statistical software packages (Stata
2012; JMP 2012). Excel will also be used extensively to prepare data for result analysis.
Section B: Forecasting Based on Data Classification
After characterizing the behavior of the time-series’ empirical data, the forecast will then
be implemented. If a sample set is classified as “stationary”, the ARIMA (1,0,0) (i.e.
Ornstein Uhlenbeck mean-reverting) model will be used, as was previously shown in
equation 3. If, however, the data are classified as “non-stationary”, this research will use
an ARIMA (1,1,0) model will be used. The ARIMA (1,1,0) is a first-order autoregressive
model that includes one order of non-seasonal differencing and a constant term, as shown
in equation 4.
19 !! = !!!!! (1 − !) + ! + !!
(4)
Section C: Accuracy of the Forecast vs. Baseline Case
After collating the results, the future prices will be compared to the baseline case using
MAPE, as defined in equation 5 and, as previously discussed, is one of the more
prevalent “scale-independent” measures of precision (Ahlburg 1992; Armstrong 2001;
Hyndman 2006; Rayer 2008; Swanson 2011)
100%
!"#$ =
!
!
!!!
!"#$%& − !"#$%&'#$
!"#$%&
(5)
n: number of years
The baseline case used is the “no change” model that assumes prices grow with inflation.
Thus, the forecasting model will be compared to the baseline case (i.e. inflation rate
model) to determine the relative merits of projecting future materials prices. Finally, this
research will vary the sample size of the data set that is used in each forecast, thereby
analyzing how much data is sufficient for forecasts that are more accurate than the
baseline case. Specifically, two simulations will be run, in which one trial uses at least
40-years of empirical data is used to estimate parameters, representing the amount of
available asphalt data, while the other uses at least 60-years of data to forecast future
prices and determine the precision as a function of the extent of the data set. A “well”
performing model will have MAPE values of approximately 10%. (Fan 2010)
20 Part 2: Unit-cost Variability due to Location and Scale
Basic economic theory implies that as the quantity associated with a project increases, the
corresponding unit cost will decrease. It is therefore prudent to apply this to the highway
construction data using publically-available bid data provided by state DOTs. Total costs
provided by the DOTs typically encompass both labor and materials into a single number.
It is therefore difficult to further separate the data based on cost specification;
nevertheless, it will likely prove valuable to establish what is likely to be a relationship
between unit price for materials-intensive construction activities and the quantity of those
activities. Specifically, the log-transformation of the average unit-cost will be plotted as a
function of the log-transformation of the bid volume associated with the project.
Statistical significance will then be gauged by the reported p-value of the dependent
variable through the use of a univariate regression analysis. In statistical analysis, the pvalue represents the probability of observing an extreme statistic in a data set, with the
assumption that the null hypothesis is warranted. In other words, for the scope of this
research, any statistical anomalies (i.e. outside of the 5% threshold) will be deemed
statistically insignificant.
Construction projects that are deemed statistically significant in respect to unit-cost vs.
quantity will then be used to project initial costs. It is important to note, however, that
this model does not effectively incorporate seasonality, location, and other more
qualitative drivers that may affect unit cost. These factors will instead be modeled using
the standard error of the univariate regression in the Monte Carlo simulations. In the case
21 that the relationship is not statistically significant, a chi-square best-fit log-normal
distribution will be fitted to the data.
Part 3: Case Study Methodology
Section A: Monte Carlo Simulations
A Monte Carlo simulation will be used to build a probabilistic distribution that
incorporates the characterized uncertainty while maintaining the structural integrity of the
model. It is thus of paramount importance that the model incorporates inter-variable
correlations and dependencies. For example, if concrete prices were being compared
between two projects, we would assume that the growth rate is constant between the two
alternatives. Along that vein, we assume the distance between concrete processing plants
are the same, and thus transportation costs associated with using concrete are constant
between projects. By accurately considering these relationships in the data, the model
will be able to select reasonable values that are representative of what one would expect
in the real world. There are many ways to interpret the results from the aforementioned
Monte Carlo simulation. The more common method of visualization in most fields is a
probability distribution function (PDF), but this research will use a cumulative
distribution function (CDF), as is standard in cost analysis.
This research has incorporated additional sources of uncertainty, such as pavement
deterioration and maintenance, inputs that lack historical data, and future materials prices.
Specifically, in terms of future maintenance schedules, the recently developed
Mechanistic Empirical Pavement Design Guide (MEPDG) combines pavement design
parameters (e.g. pavement type, thickness, etc.) with contextual conditions (e.g. climate,
22 traffic flows, etc.) into a predicted level of pavement performance (15). This design guide
uses models validated from the Long-Term Pavement Performance (LTPP) program (21).
This performance is measured through distress levels that incorporate top-down and
bottom-up cracking. Furthermore, variables that lack historical data, such as layer
thickness, have been quantified by using a pedigree matrix approach, a method used by
the life cycle assessment (LCA) community.
Section B: Case Study
The aforementioned results will then be collated and applied to two urban interstate case
studies located in Florida and Colorado. The case studies will be analyzing the relative
economic merits of concrete vs. asphalt pavement designs using the recently developed
Mechanistic-Empirical Pavement Design Guide (MEPDG) software, the new state of the
art pavement design tool.
23 RESULTS AND ANALYSIS
The results and subsequent analysis can be separated into this paper’s three inexorably
linked pieces: out-of-sample forecasts, unit-cost relationship, and the case study
methodology. These three sections will discuss and analyze explanatory drivers of
uncertainty in the highway selection process and validate the probabilistic model as a
more comprehensive and prudent implementation of LCCA.
Part 1: Out-of-sample Forecasting
Data for dimensioned stone has been collected through publically available databases at
the United States Geological Service (USGS), as shown in Figure 4. Dimensioned stone
was selected as part of this analysis since it is a common input for construction activities
and because there is sufficient data that extends as far back as 1900, making it possible to
backcast (Kelly 2012).
Price ('98$/ton) 400 Price (98$/t) 300 200 100 0 1900 1930 1960 1990 2020 Year Figure 4: Dimensioned Stone historical price behavior.
24 Out-of-sample forecasting has been conducted using at least 40-years of empirical data
using the previously discussed ARIMA (1,0,0) for stationary time-series, ARIMA (1,1,0)
for non-stationary time-series, as well as a real-dollars, no-change model. The MAPE of
each model was used to gauge precision. Out-of sample forecasts have been constructed
between 1945 and 1986, with the minimum amount of data used being 40 years (for the
1945 forecast) and the maximum being 80 years (for the 1985 forecast). In each forecast,
the precision of the forecast is measured for up to 40 years, if possible. Of course, it is
impossible to track an out-of-sample forecast made after 1970 for 40 years, and so the
sample size of the MAPE reduces for further years out. The selection of 40-years as a
bottom threshold is because there are only 40-years of empirical data for asphalt. Having
said this, the calculated MAPE is conducted using the forecast errors made between 1966
and 1986, in order to understand if increasing the sample size improves the relative
performance of the forecasting model.
Section A: 40-year Results
Figure 5 shows the calculated MAPE values of the data set over time with at least 40years of empirical data. It is clear that the no-change performs substantially better for the
first 30-years. After this midpoint, however, the ARIMA (1,0,0) begins to outperform its
counterpart, representing the stationary characteristics of the data set.
25 30% MAPE 20% 10% DS No Change (1940 -­‐ 1986) DS (1,0,0) (1940 -­‐ 1986) 0% 0 10 20 30 Years into the Future 40 Figure 5: MAPE vs. Years into the Future (at least 40-years of empirical data)
Section B: 60-year Results
Figure 6 shows a similar analysis but for at least 60-years of empirical data. The two
models are shown again, as outlined in the graphic. It is clear to see a similar trend with
the 40-year data: the real-dollars no change outperform the ARIMA (1,0,0) model at the
onset of forecasting. However, after 20-years (unlike 30-years previously), the ARIMA
(1,0,0) model begins to outperform. Therefore, not only is it more accurate to use more
empirical data, but it also takes less time for to observe reversion in the 60-year data set
than it does in the 40-year data set. This is an interesting observation, as it shows that
with more empirical data, practitioners will be better able to access future price trends of
26 materials costs, thereby reducing uncertainty and incorporating their risk threshold into
pavement selection.
45.00% DS No Change (1960 -­‐ 1986) 30.00% MAPE DS (1,0,0) (1960 -­‐ 1986) 15.00% 0.00% 0 10 20 30 Years into the Future 40 Figure 6: MAPE vs. Years into the Future (at least 60-years of empirical data)
Not only do these results show that with more empirical data, more accurate forecasts can
be generated, but these data also validate forecasting as a worthwhile endeavor to
understand future price behavior that extends decades into the future (i.e. a timeline in
line with a highway’s life-cycle). Furthermore, it shows that by applying such models
going forward, practitioners will be able to better quantify the uncertainty related to
materials prices relevant to their projects.
27 Part 2: Unit-cost Variability Due to Location and Scale
Tables 1 and 2 show the linear regression analysis of construction bid projects for Florida
and Colorado, respectively. Materials used in the projects were broken down into
Concrete, Basestone, Asphalt, and repair costs (i.e. patching, milling, and grinding), in
accordance with outlines set forth in Table 5. The repair and basestone cost show very
little statistical significance, while most other material constituent costs show a
determination coefficient of at least 0.50, implying that 50% of the variation in the data
can be explained by economies of scale. In the Florida data, there were not enough JPCP
data points to create a statistically meaningful regression; therefore, a regression was run
on all JPCP data (Colorado and Florida), as shown in Figure 8. This aggregation will
likely increase uncertainty, but with such a low JPCP construction rate in Florida, the
endeavor is uncertain as it is. It is also worth noting that one of the base stones in the
Colorado data is the only material for which we found a p-value greater than the 0.05
threshold value.
Figures 7-10 show the regression analysis of the unit-price of HMA and JPCP pavement
designs as a function of bid quantity over a 36-month span in Florida and Colorado,
respectively. Figure 7 shows the regression data of winning bids of HMA pavement
designs in Florida. The corresponding equation shows that approximately 65% of the
uncertainty related to HMA pavement development projects can be explained by
economies of scale.
28 Natural Log of Unit Price ($/CY) 6.00 4.00 2.00 LN (unit-cost) = 5.58 - 0.13 * LN (quantity)
R² = 0.65
-­‐ -­‐ 4.00 8.00 12.00 Natural Log of Quantity (Cubic Yards) Figure 7: Florida linear regression analysis of unit-cost of HMA winning pavement bids
with respect to bid volume.
Figure 8 then shows the same result for the aggregate JPCP designs in Florida and
Colorado. This aggregation is a result of Florida not having statistically sufficient data for
analysis, as was previously discussed. As shown in Figure 8, 38% of uncertainty in this
aggregation of JPCP designs can be explained by economies of scale.
29 Natural Log of Unit Price ($/CY) 8.00 6.00 4.00 LN (unit-cost) = 6.20 - 0.12 * LN (quantity)
R² = 0.38
2.00 -­‐ -­‐ 4.00 8.00 12.00 Natural Log of Quantity (Cubic Yards) Figure 8: Florida and Colorado linear regression analysis of unit-cost of JPCP winning
pavement bids with respect to bid volume.
Figures 9 and 10 show the same results for HMA and JPCP, respectively for winning bids
in Colorado. As shown in figure 9, approximately 57% of the uncertainty in HMA data
can be explained by economies of scale. Analogously, figure 10 shows that 44% of
uncertainty in JPCP bids can be attributed to cost-quantity relationships.
30 Natural Log of Unit Price ($/CY) 8.00 6.00 4.00 2.00 LN (unit-cost) = 7.36 - 0.35 * LN (quantity) R² = 0.57
0.00 0.00 4.00 8.00 12.00 Natural Log of Quantity (Cubic Yards) Natural Log of Unit Price ($/CY) Figure 9: Colorado linear regression analysis of unit-cost of HMA winning pavement
bids with respect to bid volume.
8.00 6.00 4.00 LN (unit-cost) = 6.15 - 0.13 * LN(quantity)
R² = 0.44
2.00 -­‐ -­‐ 4.00 8.00 12.00 Natural Log of Quantity (Cubic Yards) Figure 10: Colorado linear regression analysis of unit-cost of JPCP winning pavement
bids with respect to bid volume.
31 In both states, regression coefficients are similar, while the determination coefficients
vary dramatically between the HMA and the JPCP selections. This discrepancy
represents the need for probabilistic LCCA models, as it has been proven that an
uncertain cost is not the only factor to consider when assessing highway construction
projects. Moreover, the figures show a clear relationship between cost and quantity,
accounting for at least 44% of the variance in bid prices. Looking at the data from an
inter-state perspective, it can be observed that economies of scale play a more prominent
role in the Colorado data than it does in the Florida data. Tables 1 and 2 have collated the
statistical results for all constituent materials related to winning bid prices for Florida and
Colorado, respectively. As shown, bid data are delineated into concrete and base
materials, asphalt designs, and maintenance expenses relevant to the two designs. Table 1
shows the data and pertinent statistical parameters in the winning bids in Florida. As was
previously discussed, the data lacked a sufficient sample size to analyze JPCP bids, while
the HMA bids mostly show high determination coefficients, owing to the role economies
of scale has in pavement construction projects.
32 Table 1: Florida quantification of unit-cost uncertainty for significant input
parameters. Values in parenthesis represent the standard error of the regression
coefficients.
Input
Units
P-Value
R2
Regression Equation
Ln(P)=a*Ln(Q)+b
Best-fit LogNormal
Distribution
Concrete and Bases
JPCP
Base Group 06
Base Group 09
Base Group 15
Asphalt Inc. Bit.
(PG: 76-22)
Asphalt Traffic B
(PG: 76-22)
Asphalt Traffic C
(PG: 76-22)
Asphalt Traffic D
(PG: 76-22)
Asphalt Superpave
Traffic A
Asphalt Superpave
Traffic B
Asphalt Superpave
Traffic C
Asphalt Superpave
Traffic D
Asphalt Traffic E
Square
Yards
Square
Yards
Square
Yards
Tons
Tons
Tons
Tons
Tons
Tons
Tons
Tons
Tons
Small Sample Size, Aggregate Regression Conducted
a = -0.26 (0.053)
<0.0001
0.39
b = 4.65 (0.38)
a = -0.18 (0.042)
<0.0001
0.26
b = 4.29 (0.33)
a = -0.39 (0.038)
<0.0001
0.56
b = 5.61 (0.29)
Initial Asphalt Design
a = -0.14 (0.019)
<0.0001
0.63
b = 5.88 (0.15)
a = -0.056 (0.010)
<0.0001
0.42
b = 4.92 (0.077)
a = -0.13 (0.010)
<0.0001
0.65
b = 5.58 (0.080)
a = -0.17 (0.014)
<0.0001
0.49
b = 5.02 (0.091)
a = -0.17 (0.017)
<0.0001
0.71
b = 5.73 (0.12)
a = -0.16 (0.020)
<0.0001
0.65
b = 5.69 (0.15)
a = -0.11 (0.0092)
<0.0001
0.60
b = 5.33 (0.069)
a = -0.12 (0.018)
<0.0001
0.75
b = 5.49 (0.13)
a = -0.18 (0.039)
<0.0001
0.71
b = 6.22 (0.36)
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Tack Coat
Asphalt Milling
Concrete Grinding
Concrete Removal
Concrete Slab
Replacement
Maintenance Specific Input Parameters
Cubic
a = -0.28 (0.017)
<0.0001
0.40
Yards
b = 5.42 (0.11)
Square
a = -0.26 (0.020)
<0.0001
0.97
Yards
b = 4.03 (0.22)
Square
a = -0.18 (0.030)
<0.0001
0.20
Yards
b = 3.78 (0.19)
Cubic
a = -0.097 (0.028)
<0.0001
0.55
Yards
b = 6.58 (0.19)
N/A
N/A
N/A
N/A
33 Table 2 shows similar data for winning bids in Colorado. Again, these data have been
separated into concrete and bases, asphalt designs, and maintenance expenses. Statistical
parameters are shown, and it is worth noting that the final base stone was the only
material that did not fit within the p-value threshold. These final base stone data have
thus been fit to a lognormal distribution, as opposed to the linear regression. It is also
worth noting that the uncertainty in HMA designs attributable to economies of scale
varies much more than does the Florida data, which will prove interesting when accessing
the comparative LCCA from a probabilistic standpoint. Finally, most of the maintenance
data show very little statistical significance.
34 Table 2: Colorado quantification of unit-cost uncertainty for significant input
parameters. Values in parenthesis represent the standard error of the regression
coefficients.
Input
Units
P-Value
R2
Regression Equation
Ln(P)=a*Ln(Q)+b
Best-fit LogNormal
Distribution
Concrete and Bases
Concrete
Base Stone
Class 6
Base Stone
Specification
Asphalt
(PG: 58-28)
Asphalt
(PG: 58-34)
Asphalt
(PG: 64-22)
Asphalt Traffic D
(PG: 64-28)
Asphalt Traffic D
(PG: 76-28)
Tack Coat
Asphalt Patching
Concrete Grinding
Concrete Patching
Cubic
Yards
Cubic
Yards
Cubic
Yards
<0.0001
0.44
<0.0001
0.41
0.16
0.12
a = -0.13 (0.015)
b = 6.14 (0.098)
a = -0.16 (0.023)
b = 4.60 (0.15)
N/A
Initial Asphalt Design
a = -0.28 (0.053)
Tons
<0.0001
0.32
b = 7.18 (0.42)
a = -0.49 (0.067)
Tons
<0.0001
0.87
b = 9.16 (0.52)
a = -0.20 (0.045)
Tons
<0.0001
0.27
b = 5.95 (0.36)
a = -0.60 (0.16)
Tons
<0.0001
0.57
b = 10.01 (1.37)
a = -0.33 (0.044)
Tons
<0.0001
0.56
b = 7.22 (0.35)
a = -0.26 (0.033)
Gal
<0.0001
0.37
b = 3.18 (0.27)
Maintenance Specific Input Parameters
a = -0.19 (0.020)
Tons
<0.0001
0.27
b = 5.86 (0.10)
Square
a = -0.18 (0.045)
0.0003
0.27
Yards
b = 3.82 (0.32)
Cubic
a = -0.67 (0.12)
<0.0001
0.68
Yards
b = 8.07 (0.50)
N/A
N/A
Mean = 3.04
St. Dev. = 0.75
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
35 Part 3: Case Study Methodology
A third-party associate, namely the Applied Research Associates (ARA), have developed
Hot Mix Asphalt (HMA) and Joint Plain Concrete Pavement (JPCP) designs that
although made with different materials, are “functionally” equivalent (Fig. 11). The goal
of this section is to apply the characterized uncertainty values in realistic pavement
decisions in order to understand how they could potentially impact the likely pavement
selection.
Hot Mixed Asphalt
(HMA)
Jointed Plain
Concrete
Pavement (JPCP)
@"#;0AB6/<#125C6D.#
E"#;0AB6/<##F+<.59##
>"#?60.##
@G"#H-DI#?60.##
J6<.5*6/##
!!"#$%&%##
'(#!)#*+##,-'./0#
89:"#;445.46<.#123=
360.#
1234567.#
#
1234567.#
36 Figure 11: Applied Research Associates (ARA) Pavement Design Specifications
Tables 3 and Table 4 show these designs and their respective maintenance schedules with
a corresponding reliability of 90%. The MEPDG software has been constructed for a
major highways consisting of three lanes of traffic in each direction with an expected
Annual Daily Truck Traffic (AADTT) of 8,000. Finally, the life-cycle costs have been
discounted at a 4% annual rate (consistent with FHWA ordinances) over a maintenance
schedule that extends 50-years into the future.
Deterministic Analysis:
A deterministic model has been implemented to predict the likely pavement selection
under the current state DOT methodology. Historical bid data was collated for Florida
and Colorado for the past 36-months using Oman bid tabs database. Figure 3 presents the
initial, discounted rehabilitation, and discounted life-cycle costs for HMA and JPCP
designs in both Florida and Colorado. The analysis shows that all costs associated with
HMA design selection are lower than their JPCP counterparts. Additionally, the
differences between the initial costs in Florida are statistically insignificant, while all
other costs (Florida and Colorado) vary significantly. As was previously noted, however,
the deterministic analysis lacks sufficient characterization of risk. It is therefore prudent
to endeavor in the same way using a probabilistic model in order to observe the
differences.
37 Concrete Net Present Value (millions of $'s per mile) 3.5 Asphalt 3 2.5 2 1.5 1 0.5 0 FL Initial Costs FL FL Life Discounted Cycle Rehab. Costs Costs CO Initial Costs CO Life Cycle Costs CO Discounted Rehab. Costs Figure 12: Initial, life cycle, and discounted rehabilitation costs of JPCP and
HMA pavement designs in Florida and Colorado
Probabilistic Analysis:
Figures 13 and 14 show the analysis for the same data using a probabilistic model for
Florida and Colorado, respectively. The analysis shows that the expected net present
value (ENPV) of the HMA design is, in fact, more expensive than its JPCP alternative.
Given that rehabilitation costs account for a larger proportion of HMA pavement
investment, a probabilistic LCCA, which considers all reliability levels rather than 90%
as does its deterministic counterpart, could potentially favor the HMA mean values.
38 Figure 13 shows the CDF plots for JPCP (gray) and HMA (black) life-cycle costs in
Florida. The symmetry in the plot shows that one’s pavement design selection should not
change as one’s risk threshold changes. Moreover, one can see the mean costs associated
with each pavement design; specifically, the mean cost per mile for JPCP design is
$1.83mm, while its HMA counterpart $2.52mm per mile. Perhaps the budget-conscious
state DOTs would benefit from a risk-threshold analysis, wherein practitioners could
analyze the cost of a project with a level of certainty. For instance, an LCCA practitioner
could use these data to say with 95% certainty that the highest JPCP life-cycle cost per
Cumula1ve Probability mile would be $2.44mm, while its asphalt counterpart would be $3.25mm.
100% 80% 60% 40% 20% Asphalt Concrete 0% 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Life Cycle Cost (millions of $’s per mile) Figure 13: Florida probabilistic life-cycle cost of urban interstate road
alternatives (black line represents HMA design, gray represents JPCP design).
The dashed lines represent the mean value from the analysis
Figure 14 shows the same plot for the results from the Colorado data. The probabilistic
results are much less symmetric than are the data in Florida, indicating that design
selection could potentially be impacted by one’s risk threshold. It can be seen that the
39 mean cost for a JPCP design is $2.21mm per mile, while the mean cost associated with a
HMA design is $2.72mm per mile. From a risk-threshold perspective, one can say with
95% certainty that the JPCP design would be $2.87mm per mile, while the equivalent
metric for HMA design is not included on the graph due to the asymmetry of the
distribution. This discrepancy in the distribution, as compared to the Florida data, can be
attributed to the difference in standard errors in the regression data. Specifically, the
average standard error in the HMA design was approximately 43% higher in the
Cumula1ve Probability Colorado data than it was in the Florida data.
100% 80% 60% 40% Asphalt 20% Concrete 0% 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Life Cycle Cost (millions of $’s per mile) Figure 14: Colorado probabilistic life-cycle cost of urban interstate road
alternatives (black line represents HMA design, gray represents JPCP design).
The dashed lines represent the mean value from the analysis
These data have successfully classified various uncertainties relevant to highway
pavement construction projects. Additionally, the results have been presented in a case
study framework that will be easy to interpret for the average pavement LCCA
practitioner. It was this case study that found that the JPCP design was a cost effective
40 alternative to HMA for all risk thresholds, and while data varied between Florida and
Colorado, both states showed JPCP as a superior alternative (both in the deterministic and
the probabilistic case). Of course there are more factors that play a role in pavement
design selection, including government ordinances, environmental implications,
surrounding environment, single project as opposed to highway network perspective, and
more. These results will provide practitioners with a cost analysis that will prove useful
in the larger selection process.
41 CONCLUSIONS AND FUTURE WORK
This research has validated out-of-sample, long-term (i.e. multiple decades) forecasting
as a viable methodology for predicting future materials prices. Moreover, economies of
scale have been quantitatively classified as a driver of variability in bid prices for
materials-intensive activities. By collating results and implementing the MEPDG
framework, this paper has assessed the relative merits of a probabilistic LCCA model. In
so doing, this research has established the shortcomings of the deterministic LCCA
approach, and has established the importance of characterizing uncertainties and risks in
any project involving materials selection and investment.
One of the limitations of this research is that the forecasts neglected a confidence
interval. Further research into the reliability of such forecasts would prove valuable to
augment the validation of backcasting. Furthermore, while state variation was briefly
mentioned, it would prove valuable to look at additional drivers of uncertainty, such as
seasonality, timing of construction (i.e. night vs. day), intrastate location (i.e. county or
north vs. south), and more. Additional characterization of such inputs would inevitably
lead to a more comprehensive understanding of the probabilistic implementation of the
LCCA model for highway construction projects.
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45 APPENDIX
Table 3: Florida and Colorado MEPDG based JPCP and HMA pavement designs
for the urban interstate and local road case studies.
Florida Road Design (Initial AADTT of 8,000)
JPCP Design
HMA Design
Layer
Thickness
JPCP
11 in (27.9 cm)
Aggregate
Base
6 in (15.2 cm)
Layer
HMA ½ in. mix with PG 7622
HMA ¾ in. mix with AC-30
(PG 67-22)
HMA 1 in. mix with PG 6422
Limerock Base
Stabilized Embankment
A-3
Thickness
2.5 in (6.4 cm)
4 in (10.2 cm)
6 in (15.2 cm)
6 in (15.2 cm)
12 in (30.5 cm)
Semi-infinite
Colorado Road Design (Initial AADTT of 8,000)
JPCP Design
HMA Design
Layer
Thickness
JPCP
7.5 in (19.1cm)
Aggregate
Base
4 in (10.2 cm)
Layer
HMA ½ in. mix (SMA) with
PG 76-28
HMA ½ in. mix (SX 100)
with PG 76-28
HMA ¾ in. mix (S 100) with
PG 64-22
A-1-a
Thickness
4 in (10 cm)
A-1-a
6 in (15 cm)
A-2-4
Semi-infinite
2 in (5 cm)
8 in (20 cm)
4 in (10 cm)
46 Table 4: Maintenance schedule for JPCP and HMA pavement designs at MEPDG
specified 90% reliability for the urban interstate and local road case studies.
Florida Road Design (Initial AADTT of 8,000)
JPCP Design
HMA Design
Maintenance
Number
Year of
Occurrence
Rehab Type
Year of
Occurrence
Rehab Type
1
30
100% Diamond
Grinding and Full
Depth Repair
14
2.5” Mill/Overlay and
Patching
28
2.5” Mill/Overlay and
Patching
40
2.5” Mill/Overlay and
Patching
Colorado Road Design (Initial AADTT of 8,000)
JPCP Design
Maintenance
Number
Year of
Occurrence
Rehab Type
HMA Design
Year of
Occurrence
Rehab Type
13
2.” Mill/Overlay and
Patching
1
20
Full Depth Repair
30
2” Mill/Overlay and
Patching
2
40
Full Depth Repair
40
2” Mill/Overlay and
Patching
47 Table 5: Florida Pavement Specifications
Florida Pavement Specifications*
Traffic
Level Million ESAL's
A
< 0.3
Typical Applications
Local roads, county roads, city streets where truck traffic is
light or prohibited
B
0.3 - < 3.0
Collector roads, access streets. Medium duty city streets
and majority of county roadways
C
3.0 - < 10.0
Collector roads, access streets. Medium duty city streets
and majority of county roadways
D
10.0 - <30.0
Medium to heavy traffic city streets, many state routes, US
highways, some rural interstates
E
>= 30.0
US Interstate class roadways
*Asphalt designs were separated by performance grade and traffic levels but not by
friction course
Note: Colorado Asphalt designs were separated by performance grade, gyration level,
and aggregate gradiation specifications.
48 45% MAPE 30% 15% DS No Change (1940 -­‐ 1986) DS (1,0,0) (1940 -­‐ 1986) DS (1,1,0) (1940 -­‐ 1986) 0% 0 10 20 30 40 Years into the Future Figure 5: MAPE vs. Years into the Future (at least 40-years of empirical data)
49 60% DS No Change (1960 -­‐ 1986) 45% MAPE DS (1,0,0) (1960 -­‐ 1986) DS (1,1,0) (1960 -­‐ 1986) 30% 15% 0% 0 10 20 30 40 Years into the Future Figure 6: MAPE vs. Years into the Future (at least 60-years of empirical data)
50