A Matching Model for Construction Subcontractor Selection in Engineering Bid Decisions Using Ordinal Priority Approach

Figures & data

Table 1. Summary of indicators for subcontractor selection.

First level indicator	Second level indicator indicators	Reference
Control and management capabilities	Price	Zou and Lim (2006); Hartmann et al. (2009); El-Kholy (2022)
	Quality management level	Hartmann et al. (2009); Hu (2021); El-khalek et al. (2019)
	Safety management level	Hu (2021)
Professional technical ability	Mechanical resource level	Polat et al. (2015)
	Construction design	Chen et al. (2016)
	Technical staff level	Zou and Lim (2006); Hartmann et al. (2009); El-khalek et al. (2019)
Enterprise status and experience	Number of similar projects undertaken	Zou and Lim (2006)
	Corporate reputation	Hartmann et al. (2009)
	Enterprise financial level	Hu (2021)
Risk management and control capabilities	Risk management level	Hartmann et al. (2009)
	Organizational flexibility level	Mbachu (2008)

Table 2. Summary of subcontractor’s bidding decision index.

First level indicator	Secondary indicators
Subcontractor’s own factors	Technical management level
	Economic status
	Similar engineering experience
	Relationship with the owner
Contractor factors	Reputation status
	Financial capability
	Management ability
Project factors	Project income
	Project type
	Project conditions
External factors	Environmental conditions
	Social conditions

Table 3. Sets, parameters, and variables of the two-sided matching model.

Symbol	Representation
$A_i$	Represents the $\mathit{i}$^th member of Party A of the matching party
$\mathit{A}=\left\{A_1,A_2,\dots ,A_{\mathrm{m}}\right\}$	Represents the collection of all $\mathit{m}$ objects of the members of Party A
${\omega }_{A_i}=\left\{{\omega }_{A_1},{\omega }_{A_2},\dots ,{\omega }_{A_i}\right\}$	Represents the weight set of the members of Party A
$B_j$	Represents the $\mathit{j}$^th member of Party B of the matching party
$\mathit{B}=\left\{B_1,B_2,\dots ,B_{\mathrm{n}}\right\}$	Represents the collection of all $\mathit{n}$ objects of the members of Party B
${\omega }_{B_j}=\left\{{\omega }_{B_1},{\omega }_{B_2},\dots ,{\omega }_{B_j}\right\}$	Represents the weight set of the members of Party B
$T_{\mathrm{x}}$	Represents the $\mathit{x}$^th evaluation index of $A_i$ evaluating $B_j\mathrm{while}\mathit{X}=1,2\dots \mathit{u}$
$\mathit{T}=\left\{1,\mathit{\hspace{0.17em}}2,\dots ,\mathit{u}\right\}$	Represents the set of evaluation indicators of $A_i$ to $B_j$
$S_{\begin{array}{c}\mathrm{y}\\ \mathit{\hspace{0.17em}}\end{array}}$	Represents the $\mathit{y}$^th evaluation index of $B_j$ evaluating $A_i\mathrm{where}\mathit{y}=1,2\dots \mathrm{k}$
$\mathit{S}=\left\{1,\mathit{\hspace{0.17em}}2,\dots ,\mathrm{k}\right\}$	Represents the set of evaluation indicators of $B_j$ to $A_i$
${\omega }_{\mathrm{ixj}}^{r_j}$	Weight (importance) of $B_j$ based on $T_{\mathrm{x}}$ by $A_i$ at rank $r_j$
$F_{\mathrm{j}\mathrm{y}\mathrm{i}}^w$	Represents $A_i$ based on $S_{\begin{array}{c}\mathrm{y}\\ \mathit{\hspace{0.17em}}\end{array}}$ by $B_j$ at rank $\mathit{w}$
${\omega }_{\mathrm{j}\mathrm{y}\mathrm{i}}^w$	Weight (importance) of $A_i$ based on $S_{\begin{array}{c}\mathrm{y}\\ \mathit{\hspace{0.17em}}\end{array}}$ by $B_j$ at rank $\mathit{w}$
$q_{\mathrm{ij}}$	Represents $A_i$ ranks $B_j$ in $q_{\mathrm{ij}}$ place based on $T_{\mathrm{x}}$
$Q_{\mathrm{i}}^x=\left\{q_{\mathit{i}1},q_{\mathit{i}2},\dots ,q_{\mathit{in}}\right\}$	Represents the ordered vector of $A_i$ preference to $B_j$ based on $\mathit{T}=\left\{1,\mathit{\hspace{0.17em}}2,\dots ,\mathit{u}\right\}$
$P_{\mathrm{ij}}$	Represents $B_j$ ranks $A_i$ in $P_{\mathrm{ij}}$ place based on $S_{\begin{array}{c}\mathrm{y}\\ \mathit{\hspace{0.17em}}\end{array}}$
$P_{\mathrm{j}}^y=\left\{p_{1\mathit{j}},p_{2\mathit{j}},\dots ,p_{\mathit{mj}}\right\}$	Represents the ordered vector of $B_j$ preference to $A_i$ based on $\mathit{S}=\left\{1,\mathit{\hspace{0.17em}}2,\dots ,\mathrm{k}\right\}$
${\alpha }_{\mathrm{ij}}$	Indicates the satisfaction of $A_i$ to $B_j$
${\beta }_{\mathrm{ij}}$	Indicates the satisfaction of $B_j$ to $A_i$

Figure 1. The flowchart of the proposed framework.

Table 4. Ranking evaluation indicators.

Evaluation index	A1	A2	A3	A4
Control and management capabilities
Price	5	6	11	2
Quality management level	1	1	9	11
Safety management level	6	7	10	10
Professional technical ability
Mechanical resource level	4	8	3	6
Technical staff level	3	3	2	8
Construction design	2	4	1	7
Enterprise status and experience
Undertake similar projects	8	2	5	9
Corporate reputation	7	5	4	3
Enterprise financial level	11	10	6	1
Risk control level
Risk management level	9	9	8	4
Organizational flexibility level	10	11	7	5

Table 5. The contractor rankings of the subcontractors under plot $A_1$ according to the evaluation indicators.

Evaluation index	B1	B2	B3	B4	B5	B6	B7
Price	6	2	1	5	4	3	7
Quality management level	3	1	5	2	1	4	7
Safety management level	2	1	7	3	4	5	6
Mechanical resource level	4	3	6	1	7	6	5
Technical staff level	3	1	5	2	4	7	6
Construction design	1	3	2	4	5	6	7
Undertake similar projects	1	5	4	2	6	7	3
Corporate reputation	4	3	1	5	7	6	2
Enterprise financial level	4	3	5	7	6	2	1
Risk management level	7	2	6	4	5	1	3
Organizational flexibility level	5	3	4	2	6	1	7

Note: The ranking of the evaluation index $T_1,T_2,T_3,T_4$ changes due to different bids, and the ranking of the rest of the evaluation indicators is constantly changing.

Table 6. The contractor rankings of the subcontractors under plot $A_2$ according to the evaluation indicators.

Evaluation index	B1	B2	B3	B4	B5	B6	B7
Price	3	1	2	7	5	6	4
Quality management level	3	1	5	2	1	4	7
Safety management level	2	1	7	3	4	5	6
Mechanical resource level	3	4	2	5	1	7	6
Technical staff level	3	1	5	2	4	7	6
Construction design	2	5	3	1	6	7	4
Undertake similar projects	2	4	3	5	7	6	1
Corporate reputation	4	3	1	5	7	6	2
Enterprise financial level	4	3	5	7	6	2	1
Risk management level	7	2	6	4	5	1	3
Organizational flexibility level	5	3	4	2	6	1	7

Note: The ranking of the evaluation index $T_1,T_2,T_3,T_4$ changes due to different bids, and the ranking of the rest of the evaluation indicators is constantly changing.

Table 7. The contractor rankings of the subcontractors under plot $A_3$ according to the evaluation indicators.

Evaluation index	B1	B2	B3	B4	B5	B6	B7
Price	3	2	4	6	7	1	5
Quality management level	3	1	5	2	1	4	7
Safety management level	2	1	7	3	4	5	6
Mechanical resource level	5	3	6	1	7	2	4
Technical staff level	3	1	5	2	4	7	6
Construction design	2	7	4	6	1	3	5
Undertake similar projects	1	3	6	2	7	5	4
Corporate reputation	4	3	1	5	7	6	2
Enterprise financial level	4	3	5	7	6	2	1
Risk management level	7	2	6	4	5	1	3
Organizational flexibility level	5	3	4	2	6	1	7

Note: The ranking of the evaluation index $T_1,T_2,T_3,T_4$ changes due to different bids, and the ranking of the rest of the evaluation indicators is constantly changing.

Table 8. The contractor ranking of the subcontractors under plot $A_4$ according to the evaluation indicators.

Evaluation index	B1	B2	B3	B4	B5	B6	B7
Price	1	3	5	6	2	4	7
Quality management level	3	1	5	2	1	4	7
Safety management level	2	1	7	3	4	5	6
Mechanical resource level	5	4	1	3	6	2	7
Technical staff level	3	1	5	2	4	7	6
Construction design	3	6	5	1	2	4	7
Undertake similar projects	2	4	7	3	6	1	5
Corporate reputation	4	3	1	5	7	6	2
Enterprise financial level	4	3	5	7	6	2	1
Risk management level	7	2	6	4	5	1	3
Organizational flexibility level	5	3	4	2	6	1	7

Note: The ranking of the evaluation index $T_1,T_2,T_3,T_4$ changes due to different bids, and the ranking of the rest of the evaluation indicators is constantly changing.

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