# Skeleton and Infill Housing Construction Delivery Process Optimization Based on the Design Structure Matrix

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## Abstract

**:**

## 1. Introduction

#### 1.1. Definition of SI Housing

#### 1.2. Dilemmas of SI Housing

## 2. Methodology

## 3. Work Items and Dependency Identification in the SI Housing Construction Delivery Process

#### 3.1. Decomposition of the SI Housing Construction Delivery Process

#### 3.2. Identification of the Relationships Among the Main Work Items

- ${W}_{ij}$—the comprehensive relationship strength between the elements in row $i$ and column $j$;
- ${S}_{ij}$—the spatial linkage strength between the elements in row $i$ and column $j$;
- ${E}_{ij}$—the energy linkage strength between the elements in row $i$ and column $j$;
- ${I}_{ij}$—the information linkage strength between the elements in row $i$ and column $j$;
- ${M}_{ij}$—the material linkage strength between the elements in row $i$ and column $j$;
- $\alpha $—the weight of spatial linkage strength in the comprehensive relationship strength;
- $\beta $—the weight of energy linkage strength in the comprehensive relationship strength;
- $\gamma $—the weight of information linkage strength in the comprehensive relationship strength;
- $\kappa $—the weight of material linkage strength in the comprehensive relationship strength.

- (1)
- The weights of the four linkages are made equally important in the initial stage of SI housing development in China: $\alpha $ = $\beta $ = $\gamma $ = $\kappa $ = 1.
- (2)
- The work item ${a}_{1}$ provides guidance and reference information for all subsequent work items, but subsequent work items exert no influence on ${a}_{1}$, thus the row of ${a}_{1}$ is full of different values that represent varying degrees of linkage strength with other elements, and all the column values of ${a}_{1}$ are 0. The work investments, marketing positioning, and product modeling that contribute to ${a}_{1}$ exert a direct influence on the work items ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$ in the research and design system, the linkage strength values for ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$ are higher than the values for ${a}_{5}$, ${a}_{6}$, ${a}_{7}$ in the production and supply system, and ${a}_{8}$, ${a}_{9}$, ${a}_{10}$ in the construction and assembly system, respectively.
- (3)
- The work item ${a}_{11}$ refers to evaluation of the implementation and performance of the whole SI housing construction delivery process, to verify whether it realizes the initial target. All previous work items exert an influence on ${a}_{11}$, but ${a}_{11}$ exerted no influence on previous work items, thus the column of ${a}_{11}$ is full of different values that represent varying degrees of linkage strength with other elements, and all the row values of ${a}_{11}$ are 0. Considering that the work items ${a}_{8}$, ${a}_{9}$, ${a}_{10}$ in the construction and assembly system are the core steps of the whole SI housing construction delivery process and determine the final realization of SI housing, the linkage strength values with the three work items are higher than that with other items. The work items ${a}_{5}$, ${a}_{6}$, ${a}_{7}$ in the production and supply system define material and component production and manufacturing techniques, and have a superior influence on ${a}_{11}$. The work items ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$ in the research and design system provide design guidance for SI housing construction, and exert no direct influence on ${a}_{11}$, thus the linkage strength values for ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$ are smaller than that for other items.
- (4)
- The information communication and feedback among ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$ realize the design of the SI housing together. However, ${a}_{2}$ is superior to ${a}_{3}$ in space from the perspective of housing functions in the S part and I part, as well as the implemented subsequence. A suitable adjustment for ${a}_{2}$ could be conducted in accordance with feedback from ${a}_{3}$. The work items ${a}_{2}$ and ${a}_{3}$ determine the implementation of ${a}_{4}$ together. Simultaneously, subtle adjustments will be conducted in line with the technical level and suitable conditions of ${a}_{4}$. The relationships among ${a}_{8}$, ${a}_{9}$, and ${a}_{10}$ are similar to the relationships among ${a}_{2}$, ${a}_{3}$ and ${a}_{4}$.
- (5)
- From the longitudinal angle of the cooperation process, ${a}_{2}$ determines the implementation of ${a}_{5}$ and ${a}_{8}$, and ${a}_{5}$ and ${a}_{8}$ interact with each other. The production and supply scheme of ${a}_{5}$ is adjusted in accordance with planning, schedule and site construction conditions, and construction and assembly planning of ${a}_{8}$ is adjusted in accordance with production schedules and supply situations of ${a}_{5}$ simultaneously. Moreover, conflicts and low feasibility in the implementation of ${a}_{5}$ and ${a}_{8}$ feed back to ${a}_{2}$, and ${a}_{2}$ is modified in line with the feedback information. The relationship among ${a}_{3}$, ${a}_{6}$ and ${a}_{9}$, as well as ${a}_{4}$, ${a}_{7}$ and ${a}_{10}$, respectively, is equal to the relationships among ${a}_{2}$, ${a}_{5}$ and ${a}_{8}$.

## 4. SI Housing Construction Delivery Process Optimization

#### 4.1. Optimization Methods of the DSM

- (1)
- $V=\left\{{v}_{1},{v}_{2}\cdots ,{v}_{n}\right\}$ is a finite and nonempty set of knots, called the knots set. ${v}_{i}$ is a knot.
- (2)
- $E=\left\{{e}_{12},{e}_{13},\cdots ,{e}_{ij}\right\}$ is a set of finite edges, called the edge set. ${e}_{ij}$ is an edge.
- (3)
- Element ${e}_{ij}$ in $E$ corresponds to the knot $\left({v}_{i},{v}_{j}\right)$ in $V$.
- (4)
- If there is an access from knot ${v}_{i}$ to knot ${v}_{j}$, it is considered reachable between ${v}_{i}$ and ${v}_{j}$. Graph $G$ is considered a strongly connected graph when any knot is reachable by other knots in it [43].

- (1)
- $i$ =1, 2, …, $n$; $j$ =1, 2, …, $n$;
- (2)
- If $\left({v}_{i},{v}_{j}\right)\in E$, ${a}_{ij}$ = 1; otherwise ${a}_{ij}$ = 0.
- (3)
- If there is at least one non-zero access from ${v}_{i}$ to ${v}_{j}$, ${p}_{ij}$ = 1; otherwise ${p}_{ij}$ = 0.

#### 4.2. Optimization Result of the DSM

- In the DSM, if all elements in one row are zero, it indicates that the work in this row will not output information to other works, thus it will be executed last.
- In the DSM, if all elements in one column are zero, it indicates that the work in this column has no need for inputting information from other activities, thus it will be executed at the beginning.
- The work items in a coupling work set mean that relationships among these works are close. Therefore, the work items in a coupling work set should operate as a single holistic work.

- Coupling work sets in the reachable matrix $P$ are normalized as single holistic works respectively. Matrix ${P}^{\prime}$ is the reduced matrix of matrix $P$ after reducing the dimension of matrix $P$.
- ${P}^{\prime}{E}_{m-1}={\left({p}_{1},{p}_{2},\cdots ,{p}_{n}\right)}^{T}(m\ge 1)$; n-dimensional column vector ${E}_{0}={\left(1,1,\cdots ,1\right)}^{T}$, ${E}_{m}={\left({e}_{1},{e}_{2},\cdots ,{e}_{n}\right)}^{T}$; When ${p}_{i}\in \left\{0,1\right\}$, ${e}_{i}$ = 0; When ${p}_{i}\notin $ {0,1}, ${e}_{i}$ = 1. Therefore, the necessary and sufficient condition for work ${a}_{i}$ to be an m-level element is ${p}_{i}$ = 1.

## 5. Discussion

- The housing design work of cast-in-site housing construction is divided according to specialties, such as building design, structural design, water and electricity supply design, and equipment design. However, that of the SI housing construction delivery process is divided according to different parts, including design of the S part, design of the I part, and design of the connections between the S part and I part. Designers with different specialties participate in each part of the design, which increases the communication and cooperation between designers. Meanwhile, the traditional serial design mode of building design → structural design → water and electricity supply design → equipment design is changed into the concurrent design mode in SI housing, in which the S part and I part can be designed simultaneously by the collaboration of designers with different specialties, significantly promoting design efficiency. In addition, the S part, I part and connections between them could be produced independently without disturbing each other, which reduces the waiting time between different works and improves production efficiency and supply efficiency.
- In the traditional serial construction mode, works in different specialties are implemented in a rigorous precedence order of main structure construction → secondary structure construction → refined decoration construction, with water and electricity supply construction and equipment construction inserted within this chain. Contractors with different specialties seldom collaborate together. Contractors in pre-works generally ignore their influence on follow-up works. When the follow-up workers encounter problems inhibiting their works arising from the pre-works, they have to do some repair or even rework on the pre-works, which is hugely wasteful because the pre-workers have possibly already left the construction site when their work finished and could not communicate with the follow-up workers in the parallel construction mode. In the SI housing construction delivery process, different parts of the housing are constructed and assembled in a parallel mode. Constructors for the S part, I part and connections between them create an integrated construction and assembly by planning together in a way that adequately considers the works in every part before starting. During the construction and assembly process, workers for different parts communicate with each other and solve the problems together whenever necessary. The parallel mode could reduce waste caused by conflicts and rework, and improve constructive efficiency.

## 6. Conclusions

- (1)
- Constructing a comprehensive DSM that covers the components and their complex inner logic relationships in different layers considering for system design, service life, adaptability and stakeholders in line with the characteristics of SI housing.
- (2)
- Upgrading the DSM optimization based on intelligent methods to provide greater clarity of components organization and to optimize the parallel works and cross works in a more efficient way.
- (3)
- Exploring the underlying cause as well as the transmission mechanism of iterations to predict rework risk and minimize building delivery duration and construction cost.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The diagrammatic sketch of SI housing system [4].

Job Category | Amount of Interviewees | Average Working Experience in Construction Industry | Average Working Experience in SI Housing System (Years) | ||
---|---|---|---|---|---|

<5 Years | 5–10 Years | >10 Years | |||

Researchers | 8 | 2 | 4 | 2 | 2.7 |

Designers | 5 | 2 | 2 | 1 | 2.2 |

Developers | 5 | 2 | 2 | 1 | 2.0 |

Contractors | 4 | 0 | 2 | 2 | 1.5 |

Manufacturers/suppliers | 6 | 2 | 3 | 1 | 2.5 |

Total | 28 | 8 | 13 | 7 | 2.3 |

Optimization Methods | Feature |

Optimization based on graph theory | Matrix operates using mature mathematical tools. This optimization method is generally applied to small or medium-sized projects. |

Optimization based on fuzzy relations | This optimization method is generally applied to the optimization of a DSM based on fuzzy relations |

Optimization based on intelligent methods | Matrix is optimized using a genetic algorithm or simulated annealing algorithm. This optimization method is generally applied to the optimization of complex, multi-objective and multi-constraint DSMs. |

Algorithm of ∨ | ∨ | 0 | 1 | Algorithm of ∧ | ∧ | 0 | 0 |

0 | 0 | 1 | 0 | 0 | 0 | ||

1 | 1 | 1 | 1 | 0 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Cao, X.; Li, X.; Yan, Y.; Yuan, X. Skeleton and Infill Housing Construction Delivery Process Optimization Based on the Design Structure Matrix. *Sustainability* **2018**, *10*, 4570.
https://doi.org/10.3390/su10124570

**AMA Style**

Cao X, Li X, Yan Y, Yuan X. Skeleton and Infill Housing Construction Delivery Process Optimization Based on the Design Structure Matrix. *Sustainability*. 2018; 10(12):4570.
https://doi.org/10.3390/su10124570

**Chicago/Turabian Style**

Cao, Xinying, Xiaodong Li, Yangzhi Yan, and Xiang Yuan. 2018. "Skeleton and Infill Housing Construction Delivery Process Optimization Based on the Design Structure Matrix" *Sustainability* 10, no. 12: 4570.
https://doi.org/10.3390/su10124570