INFLUENCE OF BID QUANTITY ON ASPHALT UNIT PRICES IN THE
STATE OF OKLAHOMA
By
VINAY MEKKI BASAVARAJ
Bachelor of Science in Civil Engineering
M S RAMAIAH Institute of Technology
Bangalore, Karnataka
June, 2007
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 2011
ii
INFLUENCE OF BID QUANTITY ON ASPHALT UNIT PRICES IN THE
STATE OF OKLAHOMA
Thesis Approved:
Dr. M. Phil Lewis
Dr. John N. Veenstra
Dr.Gregory G. Wilber
Dr. Sheryl A. Tucker iii
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION………………………………………………………………………1
II. REVIEW OF LITERATURE…………………………………………………………..4
III. METHODOLOGY……………………………………………………………………7
IV. RESULTS…………………………………………………………………………....11
V. CONCLUSIONS……………………………………………………………………..38
VI RECOMMENDATIONS……………………………………………………………..40
VII REFERENCES............................................................................................................41iv
LIST OF TABLES
Table Page
1. Nominal maximum aggregate size (NMAS) for Superpave mix designs……………………………………………………………………………..2
2. Sample Data for S3 (PG 64-22) from ODOT Database…………………………..8
3. Total Observations of Each Mix Design by Year………………………………..12
4. Summary of Mix Design Observations with and without Outliers…………........12
5. Summary Statistics for S3 (PG 64-22) Unit Bid Prices ($/TON)………………..14
6. Summary Statistics for S4 (PG 64-22) Unit Bid Prices($/TON)…………...........15
7. Average Unit Price ($/Ton) based on Data Clustering for S3 (PG 64-22)…........20
8. Average Unit Price ($/Ton) based on Data Clustering for S4 (PG 64-22)…........25
9. Summary of Relationships between Bid Quantity and Unit Price…………........26
10. Quarterly Average Unit Bid Price ($/Ton) for S3 (PG 64-22)…………………..28
11. Quarterly Average Unit Bid Price ($/Ton) for S4 (PG 64-22)…………………..29
12. 12 Month Moving Average for S3 (PG 64-22) ($/Ton)……………………........31
13. 12 Month Moving Average for S4 (PG 64-22) ($/Ton)………………………....34
v
LIST OF FIGURES
Figure Page
1. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2004………………………….17
2. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2005………………………….17
3. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2006………………………….18
4. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2007………………………….18
5. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2008………………………….19
6. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2009 …………………………19
7. Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2010 …………………………20
8. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2004………………………….21
9. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2005 …………………………22
10. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2006 …………………………22
11. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2007 …………………………23
12. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2008 …………………………23
13. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2009 …………………………24
14. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2010 …………………………24
15. Trend of Average Unit Price ($/Ton) between 2004 and 2010………………….27
16. Quarterly average of unit Price for S3 (PG 64-22) between 2004 and 2010 …...29
17. Quarterly average of unit Price for S4 (PG 64-22) between 2004 and 2010 ……30
18. 12-month moving average for S3 (PG 64-22) between 2004 and 2010…............33vi
19. 12-month moving average for S4 (PG 64-22) between 2004 and 2010…………36
20. Comparison of 12-month moving average ($/Ton) between 2004 and 2010 for S3(PG64-22) and S4(PG 64-22) ……………………………………..………….37
1
CHAPTER I
INTRODUCTION
In the construction industry, there is a general belief that as the quantity increases the unit price of the material or product decreases. Although this inverse relationship is true in most cases, rarely does anyone seek to quantify that relationship or examine its true nature. It is important to study the true nature of this relationship that helps to improve the problem of price overrun especially in the highway construction. Examining this relationship provides useful information that may be used for construction estimate particularly for government organizations or public projects, in planning and programming of future highway construction projects. The construction estimate approximates how highway funds have to be spent on each bid item during the project and any fluctuation in the quantity of construction items makes a difference in the overall price of the project and may lead to price overrun (Kayode 1979). Project overruns may be caused by rising prices that are due to inflation, inadequate analysis, and inadequate information (Orji 1988).
With the limitations and deficiencies of the current research in mind, the purpose of this thesis is to find the factors that affect the increase in the price of the material over time. This paper focuses on finding the average unit price for various asphalt mix designs that are commonly used by the Oklahoma Department of Transportation (ODOT). Also, 2
this paper specifically addresses the relationship between unit bid price and bid quantity for various asphalt mix designs used in the state of Oklahoma.
The common Superpave mix designs used by the Oklahoma Department of Transportation (ODOT) are S-2(PG 64-22), S-3(PG 64-22), and S-4 (PG 64-22). “S2” “S3” and “S4” indicate the nominal maximum aggregate size (NMAS) of 1 inch, 0.75 inches and 0.5 inches, respectively. “PG 64-22” indicates the performance grade maximum and minimum temperatures in degree Celsius. When the ambient temperature exceeds the maximum temperature, it causes rutting of asphalt pavement and when it exceeds low temperature, it causes cracks on the asphalt pavement surface. Table 1 shows the common superpave mix designs used by and it is consistent with the use of asphalt mixes of different aggregate sizes but the same performance grade.
Table 1.Nominal maximum aggregate size (NMAS) for Superpave mix designs.
Superpave
Nominal Maximum aggregate size (Inch)
S-2
1.000
S-3
0.750
S-4
0.500
S-5
0.375
S-6
0.187
This paper quantifies the relationship between unit price and bid quantity for two commonly used asphalt mix designs, S3 (PG 64-22) and S4 (PG64-22). Over 500 observations for each mix design were collected and analyzed to assess the relationship between unit price and bid quantity. 3
The main objective of this thesis is to determine the average unit price of asphalt mix design from the ODOT projects and also to find the factors that influence the unit price. This paper will address the following research questions:
Is there a relationship between the unit prices of the mix designs and their bid quantities?
o If so, how strong is the relationship between unit price and bid quantity?
o Is the relationship between unit price and bid quantity positive or negative?
o How sensitive is unit price to an increase or decrease in bid quantity?
o Is bid quantity a good predictor of unit price?
What is the trend of unit prices for each mix design over recent years?
Is there any pattern based on quarterly averages?
What are the 12 Month Moving Average unit bid prices for each mix design since 2005?
4
CHAPTER II
LITERATURE REVIEW
In the past, there were three ways in which highway construction prices were forecasted. First, unit rates of construction, such as dollars per mile by highway type, have been used to estimate construction prices in the short term (Hartgen and Talvitie 1995). However, this method has generally been found to be unreliable, because site conditions such as topography, in situ soil, land prices, environment, and traffic loads vary sufficiently from location to location to make average prices inaccurate estimates of the price of individual projects or even of all projects in a particular year (Hartgen and Talvitie 1995). Second, extrapolation of past trends, or time-series analysis, have been used to forecast future overall construction Prices (Koppula 1981; Hartgen et al. 1997).
Several researchers have addressed the problem associated with price estimation in the earlier stages of project development. Hegazy et al., (1998) used a neural network approach to manage construction price data and develop a parametric price estimating model for highway projects. They introduced two alternative techniques to train network weights: simplex optimization (Excel’s inherent solver function), and GAs (genetic algorithms). They showed that a wide variety of factors influence construction prices. A study conducted in Newfoundland found that season, location, type of project, contract duration, and contract size had a significant impact on individual contract prices. In addition, contract prices are influenced by input prices of material, labor, and equipment, 5
and the total volume of contracts bid each year (i.e., the so-called bid volume) (Herbsman 1986).
(Koehn et al. 1978; Elhag and Boussebaine 1998) found that variation in bid volume from year to year affected bid prices. Others found that government regulations, plan changes, quality of the contractor management team, priority on construction deadlines, and completeness and timeliness of project information have an impact on construction prices. It has also been suggested that qualitative factors, such as the match between the expertise of a contracting firm and the contract being advertised and the need a contractor has for a contract at that time, and the relationship the contractor has with the agency issuing the contract all affect individual contract prices significantly (Fayek 1998).
Gwang-Hee K. et al., (2004) examined different methods of price estimation models in the early stage of building construction projects such as multiple regression analysis, neural networks and case – based reasoning. However, when we compare the two analysis models, -regression based models and artificial neural network models-each has its disadvantages. The major disadvantage of regression-based techniques is their requirement for a defined mathematical form for the price function that best fits the available historical data (Creese and Li 1995). Another disadvantage is their unsuitability to account for the large number of variables present in a construction project and the numerous interactions among them. These limitations have contributed to the low accuracy of traditional models and their limited use in construction (Garza and Rouhana 1995). Likewise, the artificial neural network drawbacks include its "black box" nature, greater computational burden, proneness to over fitting, and the empirical nature of 6
model development. They concluded that neural networks performed the best prediction accuracy but case – based reasoning indicated better results in the long run.
Although it is commonly accepted that the unit price of a product or activity decreases as the quantity increases (Peurifoy and Oberlender 2002), in this paper we try to examine the inverse relationship between unit price and bid quantity to determine its true nature. This paper specifically addresses the relationship between the unit bid price and bid quantity for two common asphalt mix designs used in the state of Oklahoma.
7
CHAPTER III
METHODOLOGY
The data used in this analysis were obtained from ODOT construction project estimate summaries and are available for public review on the ODOT website (ODOT 2011). This study began in early 2011 and sufficient data was not available at that time to include 2011 in the analysis. The variables considered for the analysis are shown in Table 2 (ODOT 2011).
The categorical variables such as Location, Road Type and Prime Contractor are not considered in the analysis since alternative analyses are required for this type of data. This study focuses only on numerical data. The Length data considered for the analysis is actually the length of project and not the length of the Asphalt Pavement layer, so the length data was neglected and not considered in the analysis. This thesis focuses primarily on the effect of bid quantity on average unit price. The bid quantity data was categorized by year based on the bid let date and includes data from 2004 through 2010.
After the data had been sorted and classified by mix design and year, the dataset was analyzed to identify outliers. These unusually large or small observations may have a disproportionate influence on statistical results particularly averages, thus outliers were removed from the dataset.
.8
Table 2. Sample Data for S3 (PG 64-22) from ODOT Database
Description
Location
Type of Road
Prime Contractor
Zip Code
Month
Year
Length (Mi)
Bid Quantity (Ton)
UNIT PRICE ($/Ton)
RESURFACE (ASPHALT) SH-19: FROM THE US-81 JUNCTION, EXTEND EAST. PROJECT LENGTH = 5.0 MILES
GRADY
SH
T & G CONSTRUCTION
73501
3
2010
5.0 100 49.25
BRIDGE AND APPROACHES US-77: OVER A SUBSIDIARY OF RED BRANCH CREEK, 3.14 MILES NORTH OF THE SH-29 JCT.
GARVIN
US
WITTWER CONSTRUCTION CO.
74076
6
2010
3.1 101 84.00
INTERSECTION MODIFICATION AND TRAFFIC SIGNAL CITY STREET (86TH STREET): AT THE INTERSECTION OF GARNETT ROAD IN THE CITY OF OWASSO. PROJECT LENGTH = 0.066 MILES
TULSA
CITY STREET
CROSSLAND HEAVY CONTRACTORS
66725
6
2010
0.1 102 77.00
SAFETY IMPROVEMENT (TRAFFIC SIGNAL) SH-167: AT THE INTERSECTION OF SH-167 AND ROLLINS STREET IN THE CITY OF CATOOSA. PROJECT LENGTH = 0.296 MILES.
ROGER
SH
BECCO CONTRACTORS
74157
2
2010
0.3 190 55.00 9
Outliers were defined as observations that were found to be outside of 1.5 times the interquartile range (Q3 – Q1). Boxplots for the data were also graphed using Minitab statistical software to help identify outlying observations (Minitab 2010).
Summary statistics for each year are used to summarize the set of large data observations. The summary statistics that are included in the analysis are number of observations, mean, average percentage increase from the previous year, median, maximum, minimum, standard deviation and 95% confidence interval. Furthermore, scatterplots of unit price vs. bid quantity for each year were graphed and a simple linear regression line was fit to the data and correlation coefficients were calculated for each mix design and each year.
In order to find the relationship between bid quantity and unit price, the correlation coefficients were determined for each annual dataset. Correlation coefficients address the strength and direction (positive or negative) of the relationship between bid quantity and unit price ; typically, correlation coefficients near +1.0 or -1.0 indicate a strong linear relationship, correlation coefficients near +0.5 or -0.5 represent moderate linear relationships, and correlation coefficients near 0.0 signify weak or no linear relationship. The slope of the regression line indicates the sensitivity in the data; in this case, the rate of change of slope of the regression line indicates the sensitivity in the data, in this case, the rate of change (either positive or negative) of the unit price with a corresponding change in bid quantity. The R2 values represent the percentage of variability in the dependent variable (unit price) that is explained by the independent variable (bid quantity). Values of R2 near 1.0 indicate that the independent variable 10
explains a high percentage of variability in the dependent variable, whereas values near 0.0 do not (Rumsey 2007).
Another parameter that was examined was the y-intercept of the regression line equations. This value represents the unit price for a negligible quantity (actually zero) of the particular mix design. The cluster of bid quantity can be observed and the average unit price ($/Ton) for the cluster of bid quantity was calculated for each year. Furthermore, to verify if a particular month in a year has an impact on the average unit price and bid quantity, Quarterly averages of unit price ($/Ton) was plotted to determine if there was a pattern based on quarterly averages.
Finally the 12 Month Moving Average was calculated. A graph of 12-Month Moving average between 2004 and 2010 for S3 (PG 64-22) and S4 (PG 64-22) were plotted. These moving averages can be used to identify the direction of the trend or define potential support and resistance levels.
11
CHAPTER IV
RESULTS
Table 3 summarizes the total number of observations, with outliers, for each mix design and for each year in the data collected from ODOT. The mix designs with the most observations were S3 (PG 64-22) and S4 (PG 64-22). Each of these mix designs had over 500 total observations, thus there were sufficient data to perform a meaningful statistical analysis. Table 4 Summarizes the mix designs with the most observations S3 (PG 64-22) and S4 (PG 64-22) with and without outliers, for each mix design and for each year from the data. Each of these mix designs had over 500 total observations and over 35 observations for each year. The numbers in parentheses indicate the number of data points that were analyzed after the outliers had been removed. By selecting these two mix designs, it was possible to compare two mixes with the same performance grade but with different aggregate sizes (Lewis and Basavaraj 2011).
12
Table 3. Total Observations of Each Mix Design by Year
YEAR
S2 (64-22)
S3 (76-28)
S3 (70-28)
S3 (64-22)
S4 (76-28)
S4 (70-28)
S4 (64-22)
S5 (76-28)
S5 (70-28)
S5 (64-22)
S6 (64-22)
2003
1
1
1
2
1
2
1
N/A
N/A
N/A
N/A
2004
20
11
17
41
12
19
37
1
N/A
N/A
N/A
2005
11
11
14
54
17
28
56
1
7
6
4
2006
23
12
26
86
17
37
88
N/A
3
6
1
2007
20
16
30
95
18
48
86
1
6
3
N/A
2008
11
15
25
84
21
39
87
N/A
4
2
1
2009
15
28
28
105
36
52
8
1
6
6
2
2010
5
9
16
76
13
28
76
2
2
3
N/A
Total
106
103 157 543 135 253 539
6
22
26
8
Table 4. Summary of Mix Design Observations with and without Outliers
YEAR
S3
(PG 64-22)
S4
(PG 64-22)
2004
41 (38)
37 (35)
2005
54 (45)
56 (50)
2006
86 (77)
88 (80)
2007
95 (86)
86 (75)
2008
84 (81)
87 (84)
2009
105 (95)
108 (101)
2010
76 (67)
76 (73)
Total
543 (489)
539 (498)
To summarize the analysis of large sets of data observations for each year, summary statistics were used. Table 5 and Table 6 show the summary statistics for S3 (PG 64-22) and S4 (PG 64-22) without outliers for each year. Table 5 also includes the average unit price for each year, percentage increase or decrease from the previous year, standard deviation and 95% confidence interval. 13
Based on Table 5, the maximum observations occurred in the year 2009 (n=95), compared to the minimum of 38 in the year 2004. The maximum average unit price of $150/Ton, with a median value of $80.10/Ton was observed in the year 2008. The minimum of $ 25 /Ton with a median of $39.64/Ton were observed in the year 2004. It can also be seen that as the average unit price increases since 2004 except in the year 2009, when there is a decrease in the average unit price. In 2005, there is 16.4% increase followed by a 27.8% increase in 2006 when compared to just 5.9% in the year 2007. In 2008, there is a higher percentage of increase when compared to all the years, which is approximately 33.5%, but the following years there is a decrease of 20.9% in 2009 and 0.1% in 2010.
Assuming normal distribution of the data, the standard deviation is used to show how much variation there is from the average. For example a variation of 8.55 in the year 2004 indicates that the datasets observed are close to the average and lies between the range (35-43) i.e. (39.83+8.55/2) and (39.83-8.55/2). Variation of about 23.76 is observed in the year 2008 which lies in the range of (71-95). Considering the confidence interval of 95% for the mix design in 2004, the observed data were not lying in the desired interval level. Between the years 2004 and 2010, the deviation from the confidence interval for the year 2008 was the highest and 2004 was the lowest.
14
Table 5. Summary Statistics for S3 (PG 64-22) Unit Bid Prices ($/TON)
Year
Count
(n)
Avg
% Increase
Median
Standard Deviation
Min
Max
95 % Cl
( + / - )
2004
38
39.83
N/A
39.64
8.55
25.00
58.30
2.81
2005
45
46.35
16.36
45.40
8.85
28.53
65.00
2.66
2006
77
59.22
27.77
55.00
14.04
37.00
103.95
3.19
2007
87
62.73
5.93
56.97
15.36
40.00
105.87
3.27
2008
81
83.73
33.47
80.10
23.76
45.00
150.00
5.25
2009
95
66.27
-20.85
65.00
12.63
44.00
98.00
2.57
2010
67
66.18
-0.14
64.80
12.56
42.95
95.71
3.06
Total
490
Similarly, from the summary statistics for S4 (PG 64-22) shown in Table 6, a maximum of 101 observations occurred in the year 2009 and a minimum of 35 observations occurred in the year 2004. The maximum average unit price of $145/Ton with a median of $76.78/Ton occurred in the year 2010 when compared to a minimum of $27.88/Ton with a median of $58.85/Ton were observed in the year 2009. It can be seen from Table 6 that there is little variation in the unit price between years 2004 to 2010 with low unit price of $ 61.14 / Ton in the year 2004 and a high value of $ 76.78/Ton in the year 2010. In 2005, there is a 2.1% increase followed by a higher percentage of increase when compared to all the years which is approximately 15.06 % in the year 2006. In 2007, there is a decrease of 4.3% when compared to a slight increase of 5.8% in 2008 followed by a decrease of 7% in 2009 and 13.5% increase in 2010.
Assuming the normal distribution of the data, the standard deviation of 17.88 in the year 2009 indicates that the data observed are close to the average and lies between the range (59-77). Considering the 95% confidence interval for the mix design S4 (PG 15
64-22) between the years 2004-2010, the deviation from the confidence interval for the year 2010 is highest and 2009 was the lowest.
Table 6. Summary Statistics for S4 (PG 64-22) Unit Bid Prices ($/TON)
Year
Count
(n)
Avg
% Increase
Median
Standard Deviation
Min
Max
95 % Cl
( + / - )
2004
35
61.14
N/A
58.85
24.19
31.76
128.10
8.31
2005
50
62.43
2.10
54.65
23.78
31.31
125.00
6.76
2006
80
71.83
15.06
65.15
21.78
30.00
139.20
4.85
2007
75
68.75
-4.29
62.30
20.15
32.94
121.71
4.64
2008
84
72.72
5.78
69.62
20.43
40.00
125.00
4.43
2009
101
67.63
-7.00
66.20
17.88
27.88
109.76
3.53
2010
73
76.78
13.52
71.24
26.80
30.90
145.00
6.25
Total
498
From Table 5 and Table 6 it can be seen that the average unit price for S4 (PG 64-22) since the year 2004 has slight variation, that is, the unit price ranges from $61.14/Ton to $76.78/Ton when compared to the average unit price for S3(PG 64-22) which ranges from $39.83 /Ton to $83.73 /Ton.
For further analysis, the scatterplots of unit price versus bid quantity for S3 (PG 64-22) and S4 (PG 64-22) are plotted for each year. The scatterplots show average unit price ($/Ton) based on data clustering along with the equation of the simple linear regression line in the form of y=mx+b, as well as the goodness of fit (R2). The data clustering was performed by visual inspection of the data.
Figures 1-7 show the scatterplots of unit Price ($/Ton) vs Bid Quantity (Ton) for S3(PG 64-22) from 2004 to 2010 and the scatterplot results are tabulated in the Table 7. From the figures and tabulated results, it can be seen that there is a negative or inverse 16
relationship between unit price and bid quantity; that is, as the bid quantity increases, the unit price decreases except in the years 2004 and 2008 which has a small number of observations. This can be illustrated by the slope of the regression line which quantifies the relationship- an increase of one Ton in bid quantity results in a decrease of $m per Ton of the unit bid price. For example, in Figure 1, an increase in bid quantity of 1000 Tons results in a decrease of approximately $0.90 per Ton in unit Price for S3(PG 64-22) for the year 2004. The data clustering average unit price for S3 (PG 64-22) between the years 2004 to 2010, range from $31/Ton in the year 2004 to as high as $88.32/Ton in the year 2008.
In addition to showing the nature of relationship between unit price and bid quantity, the scatterplot results also provide insight into the variability in the data. The wide spread or high variability in the data for the mix designs may be characterized by the goodness of the fit, or R2 values associated with the regression lines. The scatterplot R2 value for each of the plots S3(PG 64-22) lies below 0.3 which means bid quantity accounts for less than 30% of variability in the unit price. Finally, the bid quantity data clustering for most of years ranges from 2,500 Ton to as high as 42,000 Ton which shows high variability in the bid quantity for S3(PG 64-22). 17
Figure 1 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2004
Figure 2 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2005
R² = 0.3002
y = -0.0009x + 44.338
0
10
20
30
40
50
60
70
0
5,000
10,000
15,000
20,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
40.00
31.0
34.0
R² = 0.1846
y = -0.0004x + 49.517
0
10
20
30
40
50
60
70
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
48.53
44.00
40.99 18
Figure 3 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2006
Figure 4 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2007
R² = 0.1395
y = -0.0006x + 62.972
0
20
40
60
80
100
120
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
54.26
46.84
R² = 0.1692
y = -0.0009x + 67.801
0
20
40
60
80
100
120
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
52.33
62.02
64.09 19
Figure 5 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2008
Figure 6 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2009
R² = 0.1925
y = -0.0013x + 91.661
0
20
40
60
80
100
120
140
160
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
88.32
62.76
64.47
R² = 0.282
y = -0.0007x + 71.643
0
20
40
60
80
100
120
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
68.22
60.37
52.74
49.38 20
Figure 7 .Unit Price vs. Bid Quantity for S3 (PG 64-22) in 2010
Table 7: Average Unit Price ($/Ton) based on Data Clustering for S3 (PG 64-22)
Year
Data Clustering Range
Count (n)
Avg.
2004
0-2,500
16
44.00
2,500-5,500
11
40.00
8,500-9,500
04
31.00
11,500-17,500
07
34.00
2005
0-7,500
32
48.53
9,000-35,000
13
40.99
2006
0-6,000
55
62.02
8,500-17,000
16
54.26
20,000-42,000
06
46.84
2007
0-12,500
77
64.09
15,000-35,000
10
52.33
2008
0-10,000
66
88.32
10,000-17,500
08
62.76
22,000-41,000
07
64.47
2009
0-16,000
82
68.22
16,000-19,000
03
60.37
22,000-30,000
08
52.74
39,000-42,000
02
49.38
2010
0-9,000
59
67.53
9,000-11,000
04
56.00
11,000-20,000
04
56.12
R² = 0.1238
y = -0.001x + 69.898
0
20
40
60
80
100
120
0
5,000
10,000
15,000
20,000
25,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
56.00
56.12
67.53 21
Similarly, Figure 8- 14 show the scatterplots of unit Price ($/Ton) vs Bid Quantity(Ton) for S4(PG 64-22) between 2004 to 2010 and the scatterplot results are tabulated in the Table 8. From the figures and tabulated results, it can be observed that bid quantity generally has a small influence on decreasing the unit bid price and the R2 values are too negligible, that is, bid quantity accounts for less than 6% of the variability in the unit price for most number of years. The data clustering average unit price for S4 (PG 64-22) between the years 2004 to 2010, range from $39.93/Ton in the year 2004 to as high as $87.50/Ton in the year 2009. However S4 (PG 64-22) bid quantity data clustering for most of years ranges within 17,000 Ton.
Figure 8 .Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2004
R² = 0.063
y = -0.0009x + 65.625
0
20
40
60
80
100
120
140
0
5,000
10,000
15,000
20,000
25,000
UNIT PRICE ($/Ton)
BID QUANTITY (TON)
68.1
39.93
47.28
57.25 22
Figure 9 .Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2005
Figure 10 .Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2006
R² = 0.0539
y = -0.0017x + 68.024
0
20
40
60
80
100
120
140
0
2,000
4,000
6,000
8,000
10,000
12,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
56.51
R² = 0.0052
y = -0.0007x + 73.444
0
20
40
60
80
100
120
140
160
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
71.40
64.73
71.94 23
Figure 11. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2007
Figure 12. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2008
R² = 0.0692
y = -0.0026x + 74.064
0
20
40
60
80
100
120
140
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
55.43
R² = 0.057
y = -0.0024x + 77.352
0
20
40
60
80
100
120
140
0
2,000
4,000
6,000
8,000
10,000
12,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
73.60
63.02
70.80 24
Figure 13. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2009
Figure 14. Unit Price vs. Bid Quantity for S4 (PG 64-22) in 2010
R² = 0.01
y = 0.0005x + 66.356
0
20
40
60
80
100
120
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
67.01
62.3
87.50
R² = 0.1296
y = -0.0049x + 84.958
0
20
40
60
80
100
120
140
160
0
2,000
4,000
6,000
8,000
10,000
UNIT PRICE ($/Ton)
BID QUANTITY (TONS)
79.54
50.70 25
Table 8 Average Unit Price ($/Ton) based on Data Clustering for S4 (PG 64-22)
Year
Data Clustering Range
Count (n)
Avg.
2004
0-2,700
22
68.19
3,500-7,500
07
47.28
11,000-12,500
02
39.93
19,000-24,000
04
57.25
2005
0-4,500
36
64.73
4,500-11,500
14
56.51
2006
0-4,000
63
71.94
4,000-9,000
17
71.40
2007
0-5,000
65
70.80
5,000-7,500
10
55.43
2008
0-5,000
77
73.60
5,000-11,000
07
63.02
2009
0-5,000
88
67.01
6,000-11,500
09
62.34
15,000-17,000
04
87.50
2010
0-3,500
66
79.54
5,000-10,000
07
50.70
The correlation coefficient(r), average of R2, slope of regression line (m) and y-intercept for both the mix designs S3 (PG 64-22) and S4 (PG 64-22) are tabulated in the Table 9 to summarize and compare the relationship between unit price and bid quantity for the two mix designs.
Based on the information in Table 9,there is a negative, or inverse, relationship between unit price and bid quantity, that is, as the bid quantity increases, the unit price decreases (except for S4 2009 which had a very slight positive relationship). According to the r values, this relationship may be broadly classified as moderate for S3 (PG 64-22) (average r=0.44) and weak for S4 (PG 64-22) (average r=0.19). Therefore, an increase in bid quantity generally has a small influence on decreasing the unit price. This relationship is quantified by the slope of the regression line. On average, the slope of the regression line for S3 (PG 64-22) was 0.0008 and 0.0018 for S4 (PG64-22). Thus, on 26
average, the unit bid Price for S4 (PG 64-22) is more sensitive than S3 (PG 64-22) to increases in bid quantity.
In addition to showing the nature of the relationship between unit price and bid quantity, the scatterplot results also provide insight into the variability in the data. Although a general negative relationship between unit price and bid quantity can be observed, there is a wide spread, or high variability, in the data for both mix designs. This variability may be characterized by the goodness-of-fit, or R2 values associated with the regression lines. On average, the R2 values are 0.20 and 0.06 for S3 (PG 64-22) and S4 (PG 64-22) respectively, that is, bid quantity accounts for approximately 20% of the variability in the unit Price for S3 (PG 64-22) and about 6% in S4 (PG 64-22). Although there is a linear relationship between bid quantity and unit price, bid quantity alone is not a good predictor of unit price for these two mix designs (Lewis and Mekki Basavaraj 2011).
Table 9. Summary of Relationships between Bid Quantity and Unit Price
Year
Correlation Coefficient ( r )
Goodness-of-Fit (R2)
Slope(m) ($/Ton/Ton)
y-intercept ($/Ton)
S3
S4
S3
S4
S3
S4
S3
S4
2004
-0.55
-0.25
0.30
0.06
-0.0009
-0.0009
44.34
65.63
2005
-0.43
-0.23
0.18
0.05
-0.0004
-0.0017
49.52
68.02
2006
-0.37
-0.07
0.14
0.01
-0.0006
-0.0007
62.97
73.44
2007
-0.41
-0.26
0.17
0.07
-0.0009
-0.0026
67.8
74.06
2008
-0.44
-0.23
0.19
0.06
-0.0013
-0.0024
91.66
77.35
2009
-0.53
+0.10
0.28
0.01
-0.0007
0.00050
71.64
66.36
2010
-0.35
-0.36
0.12
0.13
-0.0010
-0.0049
69.90
84.96
Average
-0.44
-0.19
0.20
0.06
-0.0008
-0.0018
65.40
72.83
27
Figure 15, shows the trend of the y-intercept base unit prices over time for each year from 2004 through 2010. The base unit price for S4 (PG 64-22) is higher than the base unit price for S3 (PG 64-22) in all years except 2008 and 2009. The base unit price for S3 (PG 64-22) increased by 35% from the previous year compared to a 4% increase in S4 (PG 64-22). In 2009, S3 (PG 64-22) decreased by 22% but S4 (PG 64-22) decreased by 14%, thus the base unit price for S3 (PG 64-22) was still higher than S4 (PG 64-22). In 2010, S4 (PG 64-22) increased by 28% from the previous year and S3 (PG 64-22) had a slight 2% decrease; thus, the base unit price of S4 (PG 64-22) was once again higher than S3 (PG 64-22). Although this analysis does not address the causation of these changes, these results do reflect the volatility of unit prices for S3(PG64-22) and S4 (PG64-22) since 2007.
Figure 15. Trend of Average Unit Price ($/Ton) between 2004 and 2010
0
10
20
30
40
50
60
70
80
90
2004
2005
2006
2007
2008
2009
2010
Average Unit Price ($/Ton)
Year
S3(PG 64-22)
S4(PG 64-22)28
Furthermore, quarterly average of unit price ($/Ton) over time was plotted to verify if a particular month in a year had an impact on the average unit Price. From Table 10 and Figure 16, it can be assessed that the average unit price ($/Ton) in Quarter 4 is greater than other quarters in the year 2004 through 2007, whereas for the years between 2008 through 2010 Quarter 3 average unit Price ($/Ton) is greater. Quarter 2 shows an increasing trend from the year 2004 to 2008 and decreases in the year 2009 and 2010. Similarly, Quarter 3 shows an increasing trend from the year 2004 to 2008 and decreases in 2009 and again shows an increasing trend in the year 2010. Apart from this, there is no pattern is observed based on quarterly averages.
Table 10. Quarterly Average Unit Bid Price ($/Ton) for S3 (PG 64-22)
Year
QTR 1
QTR 2
QTR 3
QTR 4
2004
36.86
33.18
40.27
43.31
2005
39.00
45.84
52.11
49.95
2006
55.26
55.26
60.16
63.89
2007
55.70
59.58
67.95
63.32
2008
58.80
82.11
98.6
88.56
2009
67.40
68.69
67.01
60.43
2010
62.36
64.83
73.27
57.40
29
Figure 16. Quarterly Average Unit Price for S3 (PG 64-22) between 2004 and 2010
From Table 11 and Figure 17 it can be inferred that the quarterly average unit Price($/Ton) for Quarter 3 was greater than other quarters except in the year 2006 and 2009 where Quarter 1 and Quarter 2 is slightly greater than Quarter 3. Quarter 2 and Quarter 3 shows an increasing trend from 2004 to 2010 except in the year 2009 where there is a slight decrease in the quarterly average unit price ($/Ton). Apart from this, there is no pattern based on quarterly averages.
Table 11. Quarterly Average Unit Bid Price ($/Ton) for S4 (PG 64-22)
Year
QTR 1
QTR 2
QTR 3
QTR 4
2004
48.93
45.96
65.41
65.44
2005
49.84
57.76
73.00
73.14
2006
74.83
65.81
73.52
72.68
2007
64.43
66.02
76.08
59.33
2008
66.66
74.73
77.57
71.20
2009
66.55
70.19
68.36
64.76
2010
73.91
75.37
85.76
66.00
0
20
40
60
80
100
120
Avg Unit Price ($/Ton)
Year
QTR 1
QTR 2
QTR 3
QTR 4
2004
2005
2006
2007
2008
2009
2010 30
Figure 17. Quarterly average unit price for S4 (PG 64-22) between 2004 and 2010.
Table 12 shows the 12-month moving average for S3 (PG 64-22). A simple moving average is formed by computing the average unit price of S3 (PG 64-22) for a period from 2004 to 2010. As the name implies, a moving average is an average that moves. Old data is dropped as new data comes available. This causes the average to move along the time scale. Below is an example of a 12 month moving average for S3(PG 64-22) evolving over six years that is from the year 2004 to 2010. The maximum 12-month moving average unit price is found to be $84.43/Ton in April 2009 when compared to the minimum unit price of $36.72/Ton in January 2005.
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Avg. Unit Price ($/Ton)
Year
QTR 1
QTR 2
QTR 3
QTR 4
2005
2004
2006
2007
2008
2009
2010 31
Figure 18 shows a graph of 12-month moving average unit price ($/Ton) vs month for S3 (PG 64-22) between the years 2004 to 2010. The 12 month moving average does not predict average unit price direction, but rather defines the current direction with a lag as they are based on past average unit prices. The 12 month moving average uses the past data for the current period which create a smoothed line for the price data to form a trend indicator as shown in the figure 18.
Table 12. 12-Month Moving Average for S3 (PG 64-22) ($/Ton)
Year
Month
Avg.
12 Month MovingAvg.
2004
1
25.60
2
28.00
3
46.92
4
31.65
5
39.57
6
25.00
7
37.52
8
36.80
9
45.12
10
45.26
11
42.44
12
N/A
2005
1
39.91
36.72
2
35.30
38.02
3
39.26
38.68
4
44.15
37.99
5
45.58
39.12
6
48.33
39.67
7
45.99
41.79
8
51.53
42.56
9
59.00
43.90
10
49.97
45.16
11
49.90
45.59
12
N/A
46.26
2006
1
55.56
46.26
2
53.26
47.69
3
63.05
49.32
4
54.02
51.48
5
59.43
52.38
6
52.09
53.64
7
64.23
53.98
8
62.10
55.64
9
61.25
56.60
10
70.72
56.80
11
60.67
58.69
12
62.98
59.67 32
Table 12. Continued
2007
1
54.71
59.95
2
59.70
59.87
3
55.70
60.41
4
57.52
59.80
5
60.95
60.09
6
61.39
60.22
7
70.36
60.99
8
57.78
61.50
9
72.71
61.14
10
63.16
62.10
11
63.61
61.47
12
N/A
61.71
2008
1
59.74
61.60
2
56.38
62.05
3
59.25
61.75
4
82.84
62.08
5
66.08
64.38
6
93.21
64.84
7
104.90
67.74
8
107.61
70.88
9
90.62
75.41
10
90.41
77.03
11
87.27
79.51
12
N/A
81.66
2009
1
74.02
81.66
2
72.46
82.96
3
59.38
84.42
4
73.30
84.43
5
64.01
83.57
6
64.74
83.38
7
73.73
80.79
8
63.63
77.96
9
64.50
73.96
10
59.75
71.58
11
59.50
68.80
12
64.52
66.27
2010
1
65.05
66.13
2
57.36
65.38
3
62.97
64.12
4
56.19
64.42
5
66.15
63.00
6
66.72
63.17
7
76.36
63.34
8
69.66
63.56
9
60.90
64.06
10
57.40
63.76
11
N/A
63.56
12
N/A
63.93
33
Figure 18. 12-Month Moving Average for S3 (PG 64-22) between 2004 and 2010
Table 13 shows the 12-month moving average for S4 (PG 64-22). A simple moving average is formed by computing the average unit price of S4 (PG 64-22) for a period from 2004 to 2010. Below is an example of a 12 month moving average for S4 (PG 64-22) evolving over six years that is from year 2004 to 2010. The maximum 12- month moving average unit price is found to be $75.12 /Ton in September 2010 compared to the minimum unit price of $54.47 /Ton in March 2005.
Figure 19 shows a graph of the 12-month moving average unit price ($/Ton) vs month for S3(PG 64-22) between the years 2004 to 2010.
0
20
40
60
80
100
120
0
12
24
36
48
60
72
12 month avergage unit price ($/Ton)
Month
average
12 Month
Rolling Avg34
Table 13. 12-Month Moving Average for S4 (PG 64-22) ($/Ton)
Year
Month
Avg.
12 Month Moving Avg.
2004
1
N/A
2
64.00
3
33.85
4
55.55
5
36.79
6
35.50
7
61.01
8
72.78
9
62.03
10
78.03
11
56.45
12
N/A
2005
1
55.08
55.60
2
52.05
55.55
3
45.14
54.47
4
45.03
55.49
5
62.43
54.54
6
66.94
56.87
7
96.25
59.73
8
74.52
62.93
9
64.48
63.09
10
69.09
63.31
11
78.82
62.50
12
N/A
64.53
2006
1
75.90
64.53
2
67.52
66.42
3
96.00
67.83
4
58.72
72.45
5
62.79
73.70
6
72.51
73.73
7
68.23
74.24
8
73.09
71.69
9
86.64
71.56
10
80.17
73.57
11
71.43
74.58
12
54.00
73.91
2007
1
67.69
72.25
2
55.22
71.57
3
72.54
70.54
4
67.46
68.59
5
69.92
69.31
6
61.23
69.91
7
78.97
68.97
8
75.41
69.86
9
71.06
70.06
10
60.55
68.76 35
Table 13. Continued
11
56.90
67.12
12
N/A
65.91
2008
1
63.79
67.00
2
59.83
66.64
3
77.07
67.06
4
90.44
67.47
5
66.12
69.56
6
67.32
69.21
7
83.23
69.77
8
75.91
70.16
9
74.35
70.20
10
71.29
70.50
11
71.13
71.48
12
N/A
72.77
2009
1
77.56
72.77
2
46.77
74.02
3
67.70
72.84
4
77.60
71.98
5
62.82
70.82
6
69.06
70.52
7
70.84
70.68
8
61.04
69.55
9
72.58
68.20
10
62.97
68.04
11
81.50
67.28
12
60.55
68.22
2010
1
78.33
67.58
2
73.95
67.65
3
69.84
69.91
4
87.79
70.09
5
71.03
70.94
6
74.74
71.62
7
88.41
72.10
8
84.31
73.56
9
65.00
75.50
10
66.00
74.87
11
N/A
75.12
12
N/A
74.54
36
Figure 19. 12-Month Moving Average for S4 (PG 64-22) between 2004 and 2010.
Figure 20 shows a graph of 12-month moving average unit price ($/Ton) vs month for S3 (PG 64-22) and S4 (PG 64-22) between the years 2005 to 2010. It shows a comparison between S3(PG 64-22) and S4(PG 64-22) since the year 2005. From the figure, it can be seen that S3 (PG 64-22) shows an increasing trend from 2005 to 2008 and then it shows a decreasing trend whereas S4 (PG 64-22) shows a varying trend between the years 2005 to 2010. S3 (PG 64-22) shows a high variation in the average unit price, approximately $50/Ton between 2005 to 2010, that is $85/Ton in the year 2009 to $36/Ton in the year 2005. S4 (PG 64-22) shows a little variation in the average unit price that is $76/Ton in the year 2010 to $54/Ton in the year 2005.
0.00
20.00
40.00
60.00
80.00
100.00
120.00
0
12
24
36
48
60
72
12 month moving avg. unit price ($/ton)
Month
Average
12 month moving avg
unit cost ($/ton)37
Figure 20. Comparison of 12-Month Moving Average ($/Ton) between 2004 and 2010 for S3 (PG 64-22) and S4 (PG 64-22)
0
10
20
30
40
50
60
70
80
90
0
12
24
36
48
60
72
12 Month Moving Avg. ($/Ton)
Month
S3(PG 64-22)
S4(PG 64-22)38
CHAPTER V
CONCLUSIONS
Based on the results of the research presented in this thesis, the original research questions are addressed as follows:
1) Is there a relationship between the unit prices of the mix designs and their bid quantities?
a) If so, how strong is the relationship between unit price and bid quantity?
b) Is the relationship between unit price and bid quantity positive or negative?
c) How sensitive is unit price to an increase or decrease in bid quantity?
d) Is bid quantity a good predictor of unit price?
Based on data from highway projects in the state of Oklahoma, asphalt unit prices tend to decrease as the bid quantity increases, specifically for S3(PG 64-22) and S4(PG 62-22). Whereas this may be an expected finding, the decrease in unit price with respect to bid quantity is small. On average, S3 (PG 64-22) unit prices decrease approximately $0.80 per Ton with an increase of 1,000 Tons in bid quantity and S4 (PG 64-22) prices decrease by about $1.80 per Ton with a similar increase in bid quantity. In general, there is a moderate negative relationship between unit price and bid quantity for S3 (PG 64-22) and a weak negative relationship for S4 (PG64-22).
Although it can be stated that there is a consistent negative relationship between unit price and bid quantity for the asphalt mix designs analyzed in this work, bid quantity 39
is not a good predictor of unit price for S3(PG 64-22) and S4(PG 64-22). Bid quantity accounts for approximately 20% of the variability in unit price for S3 (PG 64-22) and about 6% for S4 (PG 64-22); bid quantity accounts for only partial variability in unit price for various asphalt mix designs, so it is necessary to consider the other variables in addition to bid quantity when trying to forecast the unit price of these asphalt mix designs.
2) What is the trend of unit prices for each mix design over recent years? Is there any pattern based on quarterly averages?
The Trend of y-intercept base unit prices over time for each year from 2004 through 2010 shows that base unit price for S4(PG 64-22) is higher than the base unit price for S3(PG 64-22). From the data clustering of bid quantity it can be observed that most of the data ranges within 7,500 tons of bid quantity. Based on quarterly averages, it can be observed that average unit price for S3(PG 64-22) in Quarter 4 is greater than other quarters in the year 2004 to 2007, whereas for the years between 2008 through 2010 Quarter 3 average unit price is greater. Quarter 3 average unit price for S4 (PG 64-22) is greater than other quarters except in the year 2006 and 2009.
3) What is the 12-month moving average unit bid price for each mix design since 2005?
From the 12 month moving average, S3 (PG 64-22) shows an increasing trend from 2005 to 2008 and then it shows a decreasing trend, whereas S4 (PG 64-22) shows a varying trend between the years 2005 to 2010. S3 (PG 64-22) shows a high variation in the average unit price approximately $ 50 per Ton since 2005(Ranges from $85/Ton in the year 2009 to $36/Ton, whereas S4 (PG 64-22) shows a little variation in the average unit price that is 76($/Ton) in the year 2010 to 54($/Ton) in year 2005. 40
CHAPTER VI
RECCOMENDATIONS
As might be expected, the base unit price of these two mix designs has trended upward since 2004. However, since 2007, there has been volatility in unit prices for both mix designs that was characterized by sharp increases followed by sharp decreases. Although this study does not address the cause of this finding, it does reflect the recent instability in the unit prices for these mix designs. Therefore, it is recommended that additional research be performed to address the reasons for the sudden changes in the unit prices of each mix design.
This paper deals with quantitative analysis that addresses only the variables with numerical values such as bid quantity, month, year. Thus, future work can account for categorical variables such as Location, Road Type and Prime Contractor.
This paper uses Regression analysis approach to analyze highway construction price data. Other techniques like Neural Network Approach and data mining techniques can be used to analyze construction price data and can develop a parametric price estimating model for highway projects. Other simulation software, like Crystal Ball (an addin) to a Microsoft excel can also be used.
41
CHAPTER VII
REFERENCES
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VINAY MEKKI BASAVARAJ
Candidate for the Degree of
Master of Science
Thesis: INFLUENCE OF BID QUANTITY ON ASPHALT UNIT PRICES IN STATE OF OKLAHOMA
Major Field: Civil Engineering
Education:
Completed the requirements for the Master of Science in Civil (Construction Management) Engineering at Oklahoma State University, Stillwater, OK in December, 2011.
Completed the requirements for the Bachelor of Science in Civil Engineering at M S Ramaiah Institute of Technology, Bangalore, Karnataka, India in 2007.
Experience:
Engineering Intern, City of Stillwater, Transportation Department, Stillwater, OK, from June 2010 to May 2011.
Junior Engineer, Nagarjuna Construction Company Ltd, Bangalore, India, from August 2008 to June 2009.
Graduate Engineer Trainee, Nagarjuna Construction Company Ltd, Bangalore, India, from August 2007 to July 2008.
Publications:
Vinay Mekki Basavaraj, Phil Lewis. “Factors Affecting the Unit Bid Price of Asphalt Mix Designs”.ASCE Texas Section Fall 2011 Meeting Amarillo, October 2011.
Professional Memberships:
American Society of Civil Engineers ADVISER’S APPROVAL:
Dr. M. Phil Lewis
Name: VINAY MEKKI BASAVARAJ Date of Degree: December, 2011
Institution: Oklahoma State University Location: Stillwater, Oklahoma
Title of Study: INFLUENCE OF BID QUANTITY ON ASPHALT UNIT PRICES IN THE STATE OF OKLAHOMA
Pages in Study: 43 Candidate for the Degree of Master of Science
Major Field: Civil Engineering
It is a general belief in the construction industry that the unit Price of construction bid items decrease as the quantities increase; however, this inverse relationship should be examined to determine its true nature. This paper tries to find the relationship between unit price and bid quantity for commonly used asphalt mix designs in the state of Oklahoma. Over 500 observations were observed for S3 (PG 64-22) and S4 (PG64-22). These two mix designs were analyzed to assess the relationship between unit price and bid quantity. Results indicate that there is a moderate negative relationship between unit price and bid quantity for S3 (PG 64-22) and a weak negative relationship for S4 (PG 64-22). Since the unit price of S4 (PG64-22) is more sensitive to increases in bid quantity than S3 (PG 64-22). Although this study does not address the cause for sudden sharp variation in the peaks in the unit price for both the mix designs, it is recommended that more research be performed to address this issue of sudden changes in the unit prices of each mix design.