The Construction Project Bid Evaluation Based on Gray Relational Model

(1)

Procedia

Engineering

Procedia Engineering 00 (2011) 000–000 www.elsevier.com/locate/procedia

Advanced in Control Engineeringand Information Science

The Construction Project Bid Evaluation Based on Gray

Relational Model

Yan Hong-yan

∗

Department of Engineering Management Hunan University of Finance and Economics,Changsha, 410000,China Abstract

The construction project bid evaluation is a typical multi-objective decision-making problem. Considering the content of the construction project bid evaluation, an appraisal index system of the construction project bid evaluation was established; The reasonable range of index values which can reflect the tenderer preference was utilized to perform standardization of evaluation indicators; The optimal grey relational grades for bidder were determined by gray relational model, and the optimal decision-making conclusion for bid evaluation was made after comparison of the optimal grey relational grades. The model had the advantages of complementary of theory and experience, strong operability and scientific quantify, therefore popularized the grey correlation model application in construction project.

1. Introduction

Construction project tendering and bidding is the trading method internationally recognized and widely adopted in assigning or undertaking engineering tasks. Bid evaluation is not only the key link of bidding, but also the soul of the entire bidding activity. This thesis attempts to establish and analyze the index involved in the process of bid evaluation and establish a kind of scientific and reasonable evaluation method, so as to achieve the purpose of selecting the best solution ultimately and help to create a good environment for fair competition.

Construction project bid evaluation is a typical multi-objective decision-making problem. There have been a lot of researches [1-3] on determination of construction project bid evaluation model, index system and the weights of each indicator. However, the current evaluation methods of construction projects are still lack of scientificity and rationality. For example, the expert evaluation method only considers project

∗_{Corresponding author. Tel.:+8613637428467}

E-mail address: [email protected]

Open access under CC BY-NC-ND license.

(2)

evaluation index; low-bidding price method conducts quantitative evaluation on the tenders simply depending on project bidding and offer [4]; the entropy method can effectively avoid the impact of the subjective judgment errors of experts on weight distribution. However, the most disorder index is not necessarily the index that exerts the most impact on project benefits, or the most important index for the tender. Therefore, the most reasonable results cannot certainly be achieved using the entropy method to calculate weights and evaluate bidding [5]. With adequate consideration to the rational requirements of the tenders for index information, this thesis integrated overall assessment of gray relation with interval of index value, and established construction project evaluation model.

2. Construction Of The Decision-Making Evaluation Index System For Construction Project Bid Evaluation

Currently, the specific indicators of construction project bid evaluation have many classification methods [6-7]. In short, the construction project bid evaluation mainly includes two aspects of contents: Technical bid and business bid evaluation. Technical bid evaluation is the scorings of the technical part of tender documents (construction planning and design, etc.); Business bid evaluation focuses on the economic part of the tender documents, mainly the rationality of the tender’s offer and its grades. Therefore, on the basis of the evaluation principles and contents, the decision-making evaluation index system for construction project bid evaluation was established, as shown in Table 1.

Table 1 Decision-making evaluation index system for construction project bid evaluation

Objective W Criteria level Ui Index level Uij

Comprehensive evaluation of construction project bid evaluation decision-making

Technical bid evaluation U1

Organizational structure U11 Technical strength U12

Construction organization solution U13 Quality security measures U14 Enterprise credit and performance U15 Business bid evaluation U2

Tender responsiveness U21 Rationality of the offer U22

Closeness of the offer and target price U23 Other additional conditions U24

3. Gray relational model for decision-making of construction project bid evaluation

3.1. Preparation of gray relational model for decision-making of construction project bid evaluation

For a construction project bid evaluation decision-making problem, it is supposed that there are n qualified bidders in total, which are respectively as ₁ _n，

(

_{, and the property set for} evaluation of bidders is . As the importance of each evaluation index varies, a weight

m j

p

,L

,

)

}

i

=

,1 L

2 ,

,

n

{

u

,

u

m

U

=

1

L

)

(

ω

=

1

,

2

,

L

,

is given to each indicator, and

ω

j satisfies the conditions: 1 =

j j

, which represents its degree of importance in overall evaluation. Property value of property can be

∑

ω

=

u

1

j

m ij

x

(3)

achieved through the evaluation of the bidders by property , so as to establish a decision-making

matrix of bidding unit

p

_i:

p

i

u

j

( )

n nm n n m m n x x x x x x x x x p p p x X × = = L M L M M L L M 1 1 2 22 21 1 12 11 2 1 m n ij × = (1) m

3.2. Steps for construction of gray relational model of construction project bid evaluation decision-making

3.2.1. Construction of the optimal decision-making matrix

The selection of bidders has comparative relativity, so the final decision-making is only for m indicators of n solutions. For the purpose of analysis and comparison, the ideal bidding solution ₀ is supposed as the reference sequence. The solution is objectively the best possible solution, which selects the optimal value of each index from m indicators of n bidding solutions. The evaluation index of is set.

p

j

p

₀ Therefore, _g the optimal gray relational decision-making matrix with (n +1) solutions consisting of initial decision-making matrix X and

X

p

₀is:

m n nm n n x x x x x x 1 11 01 M M m m n g x x x p p X × + = = ) 1 ( 1 1 12 0 02 1 L M L L L M p0 (2)

3.2.2. Index standardization based on the reasonable interval of index value.

Construction project bid evaluation should not only dependent on information bidders provided, but also take the requirements of proprietors for construction project into consideration. In order to reasonably introduce the preference of tenderers and make best use of the data of the original bidding data, a reasonable interval of index value should be used in the standardization of data.

The reasonable interval of index values in multi-objective decision-making is what decision-makers determine according to the relevant knowledge, experience. Indicators can be divided into benefit-based index (the greater, the better), cost-based index (the smaller the better) and interval index (one intermediate value will be better). Tenderers should first determine the reasonable interval

[

S ,

_j

U

_j

]

of each index based on the engineering needs. For interval index, the optimal intermediate value needs to be determined and standardized according to standardized function. The standardized functions established are as follows respectively:

a. Cost-based subordinate function

(3) ⎪ ⎪ ⎩ ⎪⎪ ⎨ ⎧ ≤ ≤ ≤ ij j j x x S U − − ≤ = j j ij j j ij j ij ij S U S U x U x y 1 0

In which : refers to the maximum index； refers to the minimum index； is the data

standardized.

S

j

U

j

y

ij

b. Benefit-based subordinate function

(4) ⎪ ⎪ ⎩ ⎪⎪ ⎨ ⎧ ≤ ≤ ≤ − − j j S S 0 1 ≤ = j ij j ij j j ij ij j ij S x U x S U x U x y

(4)

c. Moderate subordinate function ⎪ ⎪ ⎩ ≤ − j ij j ij j j j S x S MID 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ ≤ ≤ − = ≤ ≤ − − ≤ = j ij ij j j ij j j j ij j ij j ij MID x S S x MID x U x MID MID U x U U x y 1 0 (5)

In which： _j is the optimal intermediate value of the index. Thus, the optimal gray relational matrix

X

_gcan be standardized as

MID

Y

_g：

m n nm n n m m n g y y y y y y y y y p p p0 Y × + = = ) 1 ( 1 1 1 12 11 0 02 01 1 L M L M M L M L (6)

3.2.3. Calculation of gray relational coefficient[8]

ij j ij = y −y Δ 0 (7) max max min Δ + Δ Δ + Δ = ρ ρ ς ij ij (8) In which： _ij j i

Δ

； i j ij；

=

Δ

min

Δ

max

=

max

Δ

ρ

refers to resolution coefficient，

normally as

ρ

=0.5。The relational coefficient calculated can be shown in matrix as follows：

m n nm n n m m ij × = ς ς ς ς ς ς ς ς ς ς L M L M M L L 1 1 2 22 21 1 12 11 (9)

3.2.4. Calculation of optimal gray relational grade

As the measurement criteria for similarity of index sequence，the relational grade refers to the variation value within [0，1] interval.

ω

j

=

(

ω

1

,

ω

2

,

L

,

ω

m

)

, the weight vector of the index, can be obtained through the Delphi method to calculate the optimal gray relational grade of the various solutions

γ

gi_:

∑

= = m j j ij gi 1ως γ (10)

Obviously, the bidder with the optimal gray relational grade should be determined as the bid winner. 4. Conclusion

In this thesis, the construction project bid evaluation model was established by combining the gray relational overall evaluation with the reasonable interval of index value. The main conclusions were as follows:

（_{1）In order to introduce the preference of the tenderee as reasonable as possible and make full use of} the information of the original bidding data, the reasonable interval of index value was introduced into the process of data standardization. In this way, the preference of the tenderee was reasonably introduced in the thesis, and the reasonable requirements of the tenderee for index information were adequately

(5)

considered. Meanwhile, the information of the original bidding data was fully used to enhance the scientificity of bid evaluation decision-making.

（_{2）The application of gray making model in construction project bid evaluation} decision-making is a new area. With its clear and definite method, this model can be used in the process of evaluation and analysis of bid evaluation decision-making simplified by computer software, so as to improve the bid evaluation efficiency. By using this evaluation model, a number of tenders can be easily sorted according to their advantages and disadvantages. Therefore, the model has some popularization value in the decision-making of construction project bid evaluation.

（_{3）Evaluation of construction project bid evaluation decision-making is not mature in China.} Particularly speaking, further study and discussion must be made on the interaction and mutual influence relationship between the indexes of the evaluation index system.

References

[1]Gou-Qi, Tian-Zhichao, Zeng-Lu. Application of AGA-FAHP in Bids Evaluation of Construction Projects. Water-saving Irrigation, 2010, pp. 62-64 (In Chinese).,.

[2]Liu-Xing, Zhao-Jikun. Improved Entropy Method in the Project Bid Evaluation. Manufacture Information Engineering of China, 2010, Vol 39.pp. 60-62 (In Chinese).,.

[3]Qi-Longliang, Liu-Kaiyun. Intelligence Evaluation Model Based on Improved SVR Algorithm for Construction Project Bidding. Shanxi Architecture, 2010, Vol 36.pp. 254-255 (In Chinese).,.

[4]Sheng-Songtao, Mao-Jianping, Shu-Chenan. Application of fuzzy comprehensive evaluation method in evaluation of water conservancy project bid evaluation. Yangtze River, 2008, Vol 39.pp. 104-106 (In Chinese).,.

[5]Whang-Zhoupu, Zhang-Yi. The Project Bid Evaluation Model Based on Entropy Method. Science and Technology Management Research, 2010, pp. 47-48 (In Chinese).,.

[6]Liyan-Cang, Suo-JUuanjuan, Zhou-Shujing. New safety assessment model for civil engineering structure. Proceedings 2008 International Workshop on Modeling, Simulation and Optimization, WMSO, 2008, pp. 143-145

[7]Mohamedm, Ahmed E-D, Moheeb E-S. New safety assessment model for civil engineering structure. Journal of Professional Issues in Engineering Education and Practice, 2008, Vol 134.pp. 315-326

[8]Zhang-Xichun, Ma-Weihua, Jiang-Xinghua. Empirical Study on the Evaluation of the University’s Scientific and Technological Innovation Ability Based on Grey Correlation Grade Evaluation Method. Science and Technology Management Research, 2010, pp. 66-70 (In Chinese)