# Cost Control Method and Software in Bidding Process Based on Gray System Forecast

Authors: Xi-Liu Zhou
Journal: Journal of Control Science and Engineering
 (2014)

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## Abstract

With the fast development of social economy, the competition between enterprises in construction projects becomes more and more serious. The cost control method is proposed to the bidding process of enterprises based on the gray system forecast. At the same time, the cost control software is also constructed to the bidding process of enterprises. Experimental results suggest that the proposed approach is feasible and correct.


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## Body

## 1. Introduction

With the fast development of social economy, the competition between enterprises in construction projects becomes more and more fierce. As a result, the low bid has become the major trend and the profit space is smaller and smaller. In this situation, enterprises pay more attention to the cost control of construction projects, regarding the cost control object as an important assessment indicator and improving their core competence through internal management. The coming information era has a revolutionary impact on manufacturing, electronics, and so on. In manufacturing industries, it is a long history since the digital model has acted as a crucial production instrument, and technologies such as numerical control and 3D software have played a prominent role in improving production efficiency.Nowadays, with the construction installation developing toward the low-energy and low-pollution sustainable direction in such a fierce international competitive environment, the operation mode and technologies in traditional CAD era cannot meet various challenges any more, and information technologies have become the main development trend of current construction installation industries in China. The emergence of BIM has just catered for the demand of information technologies, with prominent value advantages in information exchange and sharing, improving the decision-making speed and accuracy, lowering cost and increasing production quality et al.


## 2. Literature Review

Unlike China, western countries pay much attention to the cost control involved in economic development very early. This is mainly determined by their unique social and economic conditions. Similarly, the concept of cost control of construction projects forms gradually as the economy develops [1, 2].Early in the 20th century, the father of production plan progress chart, also the forerunner of scientific management, Henry Lawrence Gantt, founded “Gantt chart” (also called “Bar chart”), which has opened the door of project planning and scientific control and laid a solid foundation for the development of network planning [3–5].In 1955, the US navy established a special project management office (SPO) in their Polaris program, ready to develop new PERT (program evaluation and review technique). Later, the Dupont company combined their planning management technique and the developed PERT and proposed the famous critical path method (CPM). The application of NASA-PERT technique in Apollo missions has made PERT famous all over the world, thus making great contributions to perfecting the CPM [2].In order to balance the progress, expenses (investment and operation cost) and performance (technical parameters or investment benefits), experts proposed the venture evaluation review technique (VERT) in 1973 [6–8]. The book “Accounting Control Method,” designed and formulated by the Business Administration Research Institute of Harvard University, first proposed the concept of cost control. Its connotation is to control and reduce the cost [9].In 1998, Jim first put forward ten principles for cost control and then proposed the cost control system model for a closed cyclic project from the aspect of global cost management [10]. Then in 1999, Frose stressed that an integrated method should be used to manage the project cost. Obviously, the computer software is the best instrument to realize and strengthen the integrated management of project cost [11].In 2003, Peter and Love developed a project management quality cost information system which can help to identify the drawbacks in the project management so that appropriate measures can be taken to avoid mistakes and remedy limitations in future project management [12].In 2006, Lurie developed an engineering tool to control project cost [13]. Later in 2011, Pajares and López-Paredes made improvements and extension on the earned value management and then proposed the Cost Control Index and Schedule Control Index to control project cost [14].Later, more and more countries began to pay attention to the cost control of construction project. Organizations and institutions specialized in relevant researches are set and relevant project contractors also assigned experts for cost control management. For example, the Cost Planning Branch in Japan and the Cost Engineer Association in USA et al. have set special research institutions. Among them, the system cost control method proposed by Harold Kerzner, a famous American project administrator, is comparatively advanced. Nowadays, the widely used methods in western countries are network planning technique, cost optimization, and cost dynamic control.


## 3. Cost Control in Bidding Process

The bidding process is the source where enterprises obtain construction projects. In this stage, cost control is implemented to make a competitive tender offer. First predict and control the target cost before construction projects, then determine the expected cost, and finally determine the tender offer considering proper profits. Decompose the project until processes according to construction drawings and then predict the cost, actually the expected cost of construction enterprises, based on gray prediction theory model. Finally determine the tender offer considering proper profits based on technology, management level, and bidding techniques of competitors. This tender offer has reflected the performance of construction enterprises. If the predicted expected target cost is lower, more flexible space exists in profits, which means stronger competitiveness of the enterprise. Besides, once winning the bid, it will enjoy considerable profits and great economic benefits. Therefore, a good beginning in bidding process is very important. Most of the current vast methods for tender offer are rather general and cannot serve for certain stage specially, while the gray theory can specially predict the bidding cost to make it more approximate to practical work.Bidding decision should be made according to practical project profile and bidding documents. Since loss risks exist in construction projects, full preparations should be made before the bidding decision to manage the cost to guarantee expected profits. The cost control in bidding process should be made based on a serious analysis on the economic development, technology, management level, and feasible project management measures as well as the forecast and judgment for future construction environment. It aims to save labor expenditure, estimate the cost practically, and finally make a realistic target cost. Just as the analysis in the instance does, the bidder tendered without consideration of the complicated reality and made a low estimation on the tender cost, which finally led to the risk of losses. This is very common in construction, so an overall analysis on projects before bidding is definitely necessary.


### 3.1. Modeling

Gray forecast is the quantitative forecast based on GM (gray model), which can be classified into several types according to its function and features such as sequence forecast, interval forecast, calamity forecast, seasonal calamity forecast, wave forecast, and system forecast. The gray system forecast theory can make up defects of traditional cost forecast theory in forecasting the construction project cost due to its uncertainty with requirements on information and the complicated data in the construction process. It has no requirements on the quantity of forecast data, neither need it get rid of incomparable factors, and the forecast result is reliable as long as the established model has reached the required precision.Establish the mathematical model through gray forecast theory. Suppose that(1)X(0)={X(0)(P)}(P=1~m)
is a set of time sequence collected in the system. Make an accumulation on X(0) and the following sequence forms
(2)X(1)={X(1)(P)}(P=1~n).
Here, X(1)=∑j=1PX(0)(j),  (P=1~n)  which can be solved by the first-order differential equation. It is the GM(1,1) model in gray forecast.Establish the following model throughGM(1,1) model:
(3)dx(1)dt+aX(1)=u.
Here, a is the development gray number and u is the gray action. Solve the equation through a=[a,u]T=(GTG)-1GTYN. Further estimate parameters a and u, get the forecast model of time sequence accumulation and forecast model of original sequence, then substitute the involved data into models, and finally obtain the forecast cost. Here
(4)G=[-12[X(1)(1)+X(1)(2)]1-12[X(1)(2)+X(1)(3)]1⋮-12[X(1)(n-1)+X(1)(n)]1],Xn=[X(0)(2)X(0)(3)⋮X(0)(n)].


### 3.2. Solution Method

(1)
Forecast model of time sequence accumulation:(5)X^(1)(k+1)=(X(0)(1)-ua)e-ak+ua,k=0,1,2,3….
(2)
Forecast model of original sequence:(6)X^(0)(k+1)=X^(1)(k+1)-X^(1)(k)=(X(0)(1)-ua)×(1-ea)e-ak=Ae-ak.
Here,A=(X(0)(1)-(u/a))×(1-ea), X^(0)(1)=X(1)(1), k=1,2,3….
(3)
Accuracy test of the model (construct the variance ratio and small error probability to test the model).
Forecast error:(7)e(k)=X(0)(k)-X^(0)(k).
Forecast error mean:(8)e-=(1n)∑j=1ne(j).
Original data mean:(9)X¯(0)=(1n)∑j=1nx(0)(j).
Standard deviation of original data:(10)S1=1n∑j=1n(X(0)(j)-X¯(0))2.
Standard deviation of forecast error:(11)S2=1n∑j=1n(e(j)-e¯)2.The first posterior indicator: variance ratio M=s2/s1.The second posterior indicator: small error probabilityP=p{|e(k)-e¯|<0.6745S1}.Here,p=m/n (m is the number of errors smaller than the above mentioned). The test shows that, the better the model is, the smaller the grade of accuracy is, and models are incompetent when their accuracy grades are more than four.


## 3.1. Modeling

Gray forecast is the quantitative forecast based on GM (gray model), which can be classified into several types according to its function and features such as sequence forecast, interval forecast, calamity forecast, seasonal calamity forecast, wave forecast, and system forecast. The gray system forecast theory can make up defects of traditional cost forecast theory in forecasting the construction project cost due to its uncertainty with requirements on information and the complicated data in the construction process. It has no requirements on the quantity of forecast data, neither need it get rid of incomparable factors, and the forecast result is reliable as long as the established model has reached the required precision.Establish the mathematical model through gray forecast theory. Suppose that(1)X(0)={X(0)(P)}(P=1~m)
is a set of time sequence collected in the system. Make an accumulation on X(0) and the following sequence forms
(2)X(1)={X(1)(P)}(P=1~n).
Here, X(1)=∑j=1PX(0)(j),  (P=1~n)  which can be solved by the first-order differential equation. It is the GM(1,1) model in gray forecast.Establish the following model throughGM(1,1) model:
(3)dx(1)dt+aX(1)=u.
Here, a is the development gray number and u is the gray action. Solve the equation through a=[a,u]T=(GTG)-1GTYN. Further estimate parameters a and u, get the forecast model of time sequence accumulation and forecast model of original sequence, then substitute the involved data into models, and finally obtain the forecast cost. Here
(4)G=[-12[X(1)(1)+X(1)(2)]1-12[X(1)(2)+X(1)(3)]1⋮-12[X(1)(n-1)+X(1)(n)]1],Xn=[X(0)(2)X(0)(3)⋮X(0)(n)].


## 3.2. Solution Method

(1)
Forecast model of time sequence accumulation:(5)X^(1)(k+1)=(X(0)(1)-ua)e-ak+ua,k=0,1,2,3….
(2)
Forecast model of original sequence:(6)X^(0)(k+1)=X^(1)(k+1)-X^(1)(k)=(X(0)(1)-ua)×(1-ea)e-ak=Ae-ak.
Here,A=(X(0)(1)-(u/a))×(1-ea), X^(0)(1)=X(1)(1), k=1,2,3….
(3)
Accuracy test of the model (construct the variance ratio and small error probability to test the model).
Forecast error:(7)e(k)=X(0)(k)-X^(0)(k).
Forecast error mean:(8)e-=(1n)∑j=1ne(j).
Original data mean:(9)X¯(0)=(1n)∑j=1nx(0)(j).
Standard deviation of original data:(10)S1=1n∑j=1n(X(0)(j)-X¯(0))2.
Standard deviation of forecast error:(11)S2=1n∑j=1n(e(j)-e¯)2.The first posterior indicator: variance ratio M=s2/s1.The second posterior indicator: small error probabilityP=p{|e(k)-e¯|<0.6745S1}.Here,p=m/n (m is the number of errors smaller than the above mentioned). The test shows that, the better the model is, the smaller the grade of accuracy is, and models are incompetent when their accuracy grades are more than four.


## 4. Cost Control Instance in Bidding Process

In bidding process, the cost of mechanical and electrical installation projects is mainly labor cost. Final account materials of four similar recent projects have been collected in this paper and the labor cost worked out is shown in Table1.Table 1
Cost statistics of similar projects.
Project number
1
2
3
4
Cost of each work day
150
130
130
140
Unit: yuan.Suppose that the original sequence is(12)X(0)={X(0)(1),X(0)(2),X(0)(3)}={150,130,130,140}.Step
1. Make an accumulation on X(0) and get X(1)={150,280,410,550}.Step
2. Take a test on X(0) about its accurate smoothness: P(k)=X(0)(k)/X(1)(k-1) and obtainP(2)=130/150=0.867;P(3)=130/280=0.464<0.5;P(4)=140/410=0.341<0.5.WhenK>2, the accurate smoothness condition can be satisfied.Step
3. Verify whether X(1) obeys the accurate index law Q(1)(k)=X(1)(k)/X(1)(k-1) or not and obtainQ(1)(2)=280/150=1.867;Q(1)(3)=410/280=1.464;Q(1)(4)=550/410=1.341.∀
k, Q(1)(k)[a,b], d=b-a, when d<0.5, Q[1,1.5], and X(1) obeys the accurate index law, so a model can be established for X(1).Step
4. Mean generation with consecutive neighbor for X(1): let Z(1)(k)=0.5X(1)(k)+0.5X(1)(k-1) and obtain
(13)Z(1)=[Z(2),Z(3),Z(4)]=(0.5×280+0.5×150,0.5×410+0.5hh×280,0.5×550+0.5×410)=(215,345,480)B=[-Z(1)(2)1-Z(1)(3)1-Z(1)(4)1]=[-2151-3451-4801],Y=[X(0)(2)X(0)(3)X(0)(4)]=[130130140].Step
5. Make a least square estimation on a^=[a,u] and obtain
(14)a^=(BTB)-1BTY=[-0.04120.17].Step
6. Finalize model. Consider the following:
(15)dX(1)dt-0.04X(1)=120.17.
The time response equation is
(16)X^(1)(k+1)=(X(1)(0)-ua)e0.04k+ua.
Here, a=-0.04 and u=120.17. Consider the following:
(17)X^(1)(k+1)=(150+3004.25)e0.04k-3004.25=3154.25e0.04k-3004.25.Step
7. Solve the simulation value of X(1)(18)X^=(X^(1)(1),X^(1)(2),X^(1)(3),X^(1)(4))=(150,278.3,409.6,548.0).Step
8. Restore X(0), solve its simulation value according to X^(0)(k)=X^(1)(k)-X^(1)(k-1), and obtain
(19)X^(0)=(X^(0)(1),X^(0)(2),X^(0)(3),X^(0)(4))=(150,128.3,131.3,138.4).
The comparison between the original value and the forecast value is shown in Table 2.Table 2
Comparison between the original value and the forecast value.
Project number
1
2
3
4
Cost of each work day(X(0))
150
130
130
140
Gray forecast cost(X^(0))
150
128.3
131.3
138.4
Unit: yuan.Step
9. Accuracy test. Make calculations according to residual equation e(i)=X(0)-X^(0) and obtain Table 3.Mean value of residual:e¯=(1/4)∑i=14e(i)=0.5.Variance of residual:S22=(1/4)∑i=14[e(i)-e¯]2=1.5.Practical mean value:x¯=(1/4)∑i=14X(0)=137.8.Practical variance:S12=(1/4)∑i=14[X(0)-x¯]2=68.8.Posterior error ratio:M=(S2/S1)=(1.5/68.8)=0.15.Table 3
Result of accuracy test.
Project number
1
2
3
4
Cost of each work day(X(0))
150
130
130
140
Gray forecast cost(X^(0))
150
128.3
131.3
138.4
e
(
i
)
0
1.7
−1.3
1.6
Unit: yuan.The second posterior indicator: small error probabilityP=p{|e(k)-e¯|<0.6745S1} in which 0.6745S1=5.59, P1=|e(1)-e¯|=0.5<0.6745S1. Similarly, P2=|e(2)-e¯|<0.6745S1, P3=|e(3)-e¯|<0.6745S1, P4=|e(4)-e¯|<0.6745S1, and P=(3/4)=0.75. According to the accuracy table, we know that this model belongs to ones with the third grade of accuracy, so the corresponding forecast result is reliable.Step
10. Make forecast according to the forecast model
(20)X^(1)(k+1)=3154.25e0.04k-3004.25.
When k=4, X^(1)(5)=693.7; when k=3, X^(1)(4)=550(21)X^(0)(5)=X^(1)(5)-X^(1)(4)=143.7,
namely, that the forecast cost of each work day is 143.7 yuan. The expected project duration is 12 months (each month contains 22 work days) and 150 operators are in need each day, so the total expected labor cost is 5.69 billion yuan. Other costs can also be forecasted in this way. The forecast results are shown in Table 4.Table 4
Forecast costs of mechanical and electrical installation project in SN Insecticide Factory.
Number
Project
Cost (billion yuan)
1
Labor cost
569
2
Materials cost
2582
3
Expense of using construction machinery
619
4
Measure fee
357
5
Required fees
236
6
Business management expense
198
7
Profits
403
8
Taxes
386
Total
5350The forecast cost of the project is 53.5 billion yuan; so it is reasonable to set the tender price to about 53.5 billion yuan.


## 5. Cost Control Software in Bidding Process

The system contains the following ten modules: login, user management, file, tool, view, construction component management, basic information management, knowledge management, maintenance management, and contingency plan management. Its functional structure is shown in Figure1. The user main interface, composed of tool bar, build tree, and main window, will pop up once the system is being logged in. With a component-based open architecture, the system enjoys good reusability and maintainability, which can satisfy different demands and provide individualized service. It also provides IFC file parser and IFC standard data interface engines, so information exchange and sharing between the design, construction, operation, and maintenance stage of the system and other application systems are allowed, which makes contributions to avoiding the information fault between different stages in the current construction cycle and other application systems. Besides, the system has provided a multidimensional visual work platform based on BIM technique and network environment, which makes the information exchange between different operation maintenance departments and participants possible, thus achieving network maintenance management.Figure 1
Mechanical and electrical equipment installation management system based on BIM.As to the BIM-based mechanical and electrical equipment installation management system, the author has designed a cost control software module in bidding process through the mentioned cost control method based on gray forecast.During the cost control in bidding process, relevant data of some familiar recent projects are used to forecast the corresponding data of the mentioned project. The data that needs forecasting include labor cost, material cost, expense of using construction machinery, measure fee, required fees, business management expense, profits, and taxes. The corresponding calculation interface is shown in Figure2.Figure 2
Calculation interface of the cost control software module in bidding process.


## 6. Conclusion

This paper has adopted the gray system forecast method to explore the cost control problem in bidding process in installation enterprises and its main contents were as follows: proposed a cost control method in bidding process based on the gray system forecast, then provided the corresponding cost control instance of an enterprise, and finally showed the BIM software results of the installation project cost control in a factory.



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*Source: 296241-2014-07-17.xml*