DESIGN COST ANALYSIS
OF TRANSPORTATION PROJECTS
Khaled M. Nassar1, Mohamed Y. Hegab2, and Nicholas W. Jack3
ABSTRACT
Transportation projects are usually designed in three phases: phase I is the preliminary design
report, phase II involves the preparation of the actual construction documents including plans
and specifications, and phase III involves the construction inspection and contract
administration of the project. The process of arriving at total design man-hours and the
related design costs is often the most contentious and difficult part of phase II for both the
consultant and the STA (State Transportation Agency). The main objective of this research is
to model the design costs of consultant designed projects. Actual data were collected from
The Illinois Department of Transportation (IDOT). Statistical modeling techniques were used
to predict the design costs. The models developed in the following pages will help
supplement the current methods of estimating design costs currently used by IDOT.
Currently the Illinois Department of Transportation maintains a set of manuals used by the
Bureau of Design and Environment for guiding engineers through the design phase for
highway projects. These manuals are very comprehensive covering all facets of the design
process. The models contained in this research could be implemented in the Design and
Environment manuals.
KEY WORDS
Design Cost, Transportation Projects, Construction, Statistical Analysis.
INTRODUCTION
Currently many consulting engineering firms are used by different state DOTs (Department
of Transportation) to supplement their own engineering staff. There are three distinct types of
projects done by consulting firms. The three types of projects are Phase I, Phase II and Phase
III. The Phase I project is the preliminary design report and all of the necessary documents. A
Phase II project involves the preparation of the actual construction documents including
plans and specifications. The final type is the Phase III project. A Phase III project is when a
consulting firm is hired to perform the construction inspection and contract administration on
a project. This paper presents the results of a study to model the design costs associated with
Phase II projects solicited by the Illinois Department of Transportation (IDOT). First, the
1
2
3
Ph.D, Associate Professor, Department of Technology, University of Maryland Eastern Shore, Email:
knassar@umes.edu
Ph.D., P.E., Assistant Professor, Civil Engineering & Applied Mechanics Department, California State
University Northridge,. Email: mhegab@csun.edu
P.E., Engineer, Illinois Department of Transportation, Peoria, Illinois.
activities performed in the design process of Phase II will be identified. Second, the results of
the statistical analysis performed on data collected from actual transportation projects are
presented. Finally the developed stochastic cost models are discussed along with conclusions
and recommendations for future research are presented.
ACTIVITIES OF DESIGN PROCESS
Estimating the design costs of highway project accurately in advance is an important aspect
of increasing the planning effectiveness of the various DOTs. Estimating these costs when an
outside consultant is hired is even more challenging since the estimate by the DOT involves
external factors and resources. The one fact however is evident about hiring an outside
consultant is that they are considered more expensive than in-house staff in the majority of
cases. (Wilmot et al 1999) surveyed 17 studies that were in the past 20 years to investigate
the comparative cost of conducting preconstruction engineering designs by in-house and
consulting staff (Table 1). With the cost of consultants being higher than those of in-house
staff, it is in the best interest of the public to be able to control these costs.
Table 1: Consultant Costs
Study
Cost
Roy Jorgensen and Associates, 1977
Western Association of State Highway and Transportation
Officials, 1979
Consultants 100% more expensive
11 states (83%) said consultants are more expensive. 2
(17%) said costs are the same
Maryland Department of Transportation, 1981
Transportation Research Board, 1984
Consultants 80% to 120% more expensive
Consultants are not cheaper
Vermont Department of Transportation, 1986
Center for Transportation Research, University of Texas,
Austin, 1986
Texas Transportation Institute, Texas A&M University,
1986
Ernst and Whinney, 1986
Alabama Department of Transportation, 1989
Professional Services Management Journal, 1990?
North Carolina Department of Transportation, 1990
Consultant 16% to 240% more expensive
Consultants more expensive
Wisconsin Legislative Audit Bureau, 1990
Michigan Department of Transportation, 1991
University of California, Berkeley, 1992
Legislative Analyst, California, 1993
Missouri Highway and Transportation Department 1993
Louisiana Department of Transportation and Development,
1998
Cost the same
Consultants 33% more expensive
Cost the same
Consultants more expensive
Consultants 31 % more expensive
Consultants approximately 20% more expensive
Consultants more expensive
Consultants generally more expensive
Consultants 69% to 100% more expensive
Consultants cheaper than in-house staff
Consultants more expensive
After a consultant is selected, a list of tasks and an estimate of man-hours needed to complete
the job is usually developed. Design firms usually rely only on activity-analysis methods of
engineering estimates (Hudgens & Lavelle 1995). This is a very common method also used
by engineering firms performing work for DOTs, The consultant will then submit these manhours to the DOT and both parties then agree on the total projected hours and design costs.
There are two main problems with this current method. First, the process of arriving at
total man-hours and design costs to perform the work is often painful for both the consultant
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and IDOT. From the view of the DOT, consultant’s hours often seem to be inflated with the
hopes of getting more hours than required to perform the job, while the consultant usually
perceives the DOT estimates as being unrealistic. Second, the submittal from the consultant
to the DOT will include the number of man-hours per task as broken down by the consultant.
Each consultant may break their hours down differently than the next consultant. As a result,
it is difficult to compare man-hours per task per consultant per job.
Table 2: Determination of the Complexity Factor (CF) as determined by IDOT
LOW COMPLEXITY
CF = 0.000
Location/Design Report
MEDIUM COMPLEXITY
CF = 0.035
SEA
Small Rural Projects
Surveys
Roads and Streets
Location/Design
Report(Reconstruction/Major
Rehabilitation)
CEA
Small Urban Projects
Freeways
Freeway interchanges
Highway Structures: Simple
Construction Engineering (Rural
Freeway)
Traffic Signals
Lighting
Projects on New Alignment
Construction Engineering(Urban Freeway
& Major Structures)
Highway Structures: Typical
Railroad Structures
Aerial Mapping
Traffic Signals (SCAT)
Asbestos Abatement
Hazardous Waste
Pumping Stations
Subsurface Utility Engineering
(SUE)
Hydraulic Reports, Waterways: Typical
Hydraulic Reports, Pump Stations
Quality Assurance: Typical
HIGH COMPLEXITY
CF = 0.070
Location/Design Report (New
Construction/Major
Reconstruction
EIS
Major Urban Freeways
Multi-level Interchanges
Highway Structures: Advanced
Typical
Highway Structures: Complex
Major River Bridges
Movable Bridges
Major Engineering Studies
Requiring
Special Expertise
Traffic Signals with Railroad
Interconnect
Hydraulic Reports, Waterway:
Complex
Quality Assurance: Complex
Bituminous Mix Designs: Complex
Geotechnical Engineering:
Complex
Bituminous Mix Designs: Typical
Geotechnical Engineering: Typical
Another factor which enters the Phase II design process is the complexity factor. In each
Professional Transportation Bulletin advertisement published by IDOT for example, a factor
called the complexity factor is assigned to each job. This is a numeric value is assigned to a
project based on its anticipated difficulty to design. Although, arriving at the appropriate
complexity factor for each project is guided somehow by the information in Table 2, the CF
alone is not sufficient to accurately estimate the design costs and is also a controversial
process.
Therefore, there is a need to develop an objective model to predict the transportation
design costs or to at least augment the current practices with a scientific analysis of existing
data.
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DATA COLLECTION
Data were collected from fifty-nine projects from different Districts of IDOT. The data were
extracted from the databases of IDOT. The jobs used in the data set were obtained by careful
study of the published Professional Transportation Bulletins (PTB). The PTB is a publication
usually published by DOTs listing all of the upcoming projects consultants can submit
statements of interest for. The Professional Transportation Bulletins were studied carefully to
find suitable jobs to include in the study. The jobs selected for the data set needed to meet
certain requirements. The major reason for this is jobs often change in scope as the design
process proceeds. By reducing the number of jobs with this potential, the construction cost
would be closer to the PTB cost.
The data included design costs (DC), programmed costs (initial planned construction
costs) (PC), complexity factors (CF), percent of bridges in projects (BR), and percent of
roadways in projects (RD). Two of the necessary variables could be obtained from the PTB
advertisement. These were the complexity factor and the PTB cost. In order to obtain the
actual design costs, a freedom of information request was filed with the IDOT’s Central
Office. The Central office then supplied the Phase II Consultant Design Cost. The rest of the
variables were obtained using a cross reference number in IDOT database.
The costs as received from the Illinois Department of Transportation were not adjusted
for the time value of money. Therefore, it was necessary to bring the values of the money
forward in time. This was accomplished with the use of the Engineering News Record
Construction Cost Index. The cost values were adjusted for the years 1980 through 2003.
DATA ANALYSIS
DATA SPLITTING
The design cost model was developed using statistical regression techniques. The data was
first divided into two sets; for model development and validation. The two data sets were
selected by assigning random numbers and the data were sorted according to the random
numbers in an ascending order. The first 15% of the data were selected for model validation
and the remaining 85% were for model development.
MULTICOLLINEARITY
Multicollinearity between two independent variables indicates a strong relationship between
them. If multicollinearity exists, they may be both describing the same relationship of
dependent variables. Moreover, multicollinearity is not recommended in multiple regression
analysis as it weakens the ability to estimate the dependent variable. A high degree of
multicollinearity suggests one or the other variable would be unnecessary (Ryan, 1997). In
some cases, it may be difficult to get rid of a certain variable. In this case, existence of
multicollinearity is accepted. In this study, the Variance inflation factor (VIF) was used as a
measure of the multicollinearity between independent variables. Each independent variable
has a VIF value associated with it (MINITAB, 2000). Multicollinearity was checked between
the selected four factors; programmed costs (initial planned construction costs) (PC),
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complexity factors (CF), percent of bridges in projects (BR), and percent of roadways in
projects (RD).
Table 3, shows the VIF values for the independent variables. Based on VIF, however,
multicollinearity exists between these variables; so simple regression will not be an easy task.
Table 3: VIF for the different factors
VIF Value (1)
Opinion (2)
VIF=1
No relation
5>VIF>1
Multicollinearity exists but acceptable
VIF>5
Poor regression
These values are reproduced of Montgomery and Peck (1982).
TRANSFORMATION
A nonlinear regression model with power transformation was developed for the cost model.
Power transformation is one of the common transformations (Young, 1999). The degree of a
polynomial regression equation was selected on steps. After deciding the required
significance level, transformation was performed for both the dependent and independent
variables to create a linear relation between them. Different power transformations, squares,
cubic power, square roots, cubic roots, and logarithms were checked. Having more than one
variable made it difficult to apply the common rules in power transformation. Accordingly,
for each factor including the dependent one, five transformations plus the original factor were
considered in calculations. The appropriate transformation of factors was selected using Pvalue and the normal probability plot of the residuals as shown in Figure 1. Regression
analysis of the original variables was performed to check the P-value for each variable and
the residual fitted plot for normal probability distribution.
Figure 1: Normal Plot of the Residuals
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MODEL FACTORS’ ANALYSIS
Continuing after transformation, the fitted residual plot to a normal probability plot was
curved. A second level factorial analysis was performed between the suggested independent
variables. Factorial analysis aims to reduce the variance by adding the appropriate
combination of variables to the model. Interactions between candidate variables were
considered with the candidate variables in the process of model factors’ selection. These
variables were checked using linear regression to identify the significant variables to be
considered in the statistical analysis. The P-value for each variable judged if the variable was
significant. Multicollinearity existed between some insignificant variables. Therefore,
removing one of them can switch the other to be significant. Accordingly, removing the
insignificant variables should be performed on steps (Montgomery and Peck, 1982).
Therefore, thirty variables were introduced for possible consideration as independent
variables in the penetration models. These candidate variables were the original variables,
their square root, third root, square, logarithm of base 10, and their second level interactions.
Five transformations, DC2, DC3, DC , ln DC and log DC, added to the dependent variables
were considered.
STEPWISE REGRESSION
Stepwise regression was used to select the significant variables. Stepwise regression removes
and adds variables to the regression model by setting a significance level to enter or leave the
model. Montgomery and Peck (1982) suggested setting the entering and leaving significance
level at 15%. Applying the stepwise regression technique, log PC, ln PC, log RD, and CF
were found to be the best independent variable to represent log DC and ln DC.
BEST SUBSET REGRESSION
Best subset regression is an effective way to select a good model with few variables
(MINITAB, 2000). Best subset regression recognizes the best regression models that can be
constructed with the specified variables. All the possible subsets for the given variables are
introduced. Models should be evaluated based on R2, adjusted R2, PRESS, and S (standard
deviation). R2, which is the coefficient of determination, describes the percentage of variance
between data and their regression model. Adjusted R2 is similar to R2 but it takes a number of
variables and a number of data points into consideration. PRESS value is a measure to select
the best model that represents the data (Draper and Smith, 1998).
The best three models were selected based on the values of R2 (adjusted), Cp, and S. High
R2 (adjusted), a low PRESS value, and a low S value were the judging criteria in selecting
the best three models. Accordingly, the best three models were selected out (Table 4).
Table 4: Results for best subset regression analysis for different clusters
Model
(1)
1
2
3
# Var
(2)
1
2
1
R2
(3)
0.805
0.805
0.800
R2 (adj)
(4)
0.798
0.798
0.797
S
(5)
0.4323
0.1877
0.1882
VIF
(6)
NA
1.3
NA
# Var: Number of Variables
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PRESS
(7)
11.462
2.162
2.113
MSPR
(8)
0.00324
0.00061
0.00061
MULTIPLE LINEAR REGRESSION
The multiple linear regression technique was used to predict the relationship between the
dependent variable and independent variables. The best three models are as follows:
Model 1:
lnDC = 2.30 + 0.698 lnPC
[1]
Model 2:
logDC = 1.16 + 0.668 logPC + 1.77 CF
[2]
Model 3:
logDC = 0.998 + 0.698 logPC
[3]
These models are limited to project of initial construction cost of $27 Million.
VALIDATION
The best model was selected from the suggested three models based on its prediction
capability. Validation of the models’ prediction capabilities was performed using the
validation data sets. The predictive capability of a model is measured by calculating the
dependent variable from that model using a new data set, then calculating the mean square
prediction error (MSPR). The model with lower MSPR was considered the best model in
predicting the dependant variable (Neter et al., 1996). The model that meets the previous
criteria and has the best prediction capabilities was selected. This model is Model 3
(Equation 3).
CONCLUSION
The research conducted here was intended to provide quantitative methods for estimating the
design costs charged by a consulting engineering firm for a project that is under contract with
the a state DOT. Design cost for transportation projects can be predicted with a certain
degree of accuracy using the developed mathematical model. The model provides another
indication of the design cost to be used as guidance when negotiating the design cost. The
model should be used in conjunction with other procedures currently in place. The model
was developed from real data from IDOT, which can continually be refined and enhanced. It
is important to note that the model is limited to projects of initial construction cost up to $27
Million. Other DOTs can use this model for guidance but an individual model for each DOT
should be developed.
REFERENCES
Draper, N. and Smith, H. (1998). Applied Regression Analysis. 3rd ed., J. Wiley&Sons, NY.
Hudgins, D.W. and Lavelle, J.P. (1995) “Estimating Engineering Design Costs.” Engineering
Management Journal, September 1995, 17-23.
Johnson, R. (1994). “Miller and Freund’s Probability & Statistics for Engineers.” Prentice
Hall, Englewood Cliffs, New Jersey.
MINITAB (2000). “MINITAB StatGuide.” MINITAB, Inc., State College, Pennsylvania.
Montgomery, D. and Peck, E. (1982). “Introduction to Linear Regression Analysis.” John
Wiley & Sons, New York.
Neter, J., Kutner, M., Nachtsheim, C., and Wasserman, W. (1996). “Applied Linear
Statistical Model.” IRWIN, McGraw-Hill Companies, USA.
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Ryan, T. (1997). “Modern Regression Methods.” John Wiley & Sons, New York.
Young, D. (1999). “Model Building in Regression.” Module B, Introductory Statistics, 5th
Ed., Weiss, N., Addison-Wesley, Addison Wesley Longman, New York.
Wilmot, C.G., D.R. Deis, H. Schneider, and C.H. Coates, Jr. “In-House Versus Consultant
Design Costs in State Depts. of Transportation.” Transp. Res. Record 1654:153-160.
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