**3. Research Methodology**

#### *3.1. The Primary thought of the Study*

This study aimed to establish a framework model and method based on the interaction between activities for selecting a project delivery method for construction projects. Therefore, the activity-based DSMs are selected to identify the order and correlation of execution of the main activities and to analyze the likelihood and feasibility of their portfolios to optimize the project delivery process. At the same time, partitioning is chosen as an optimization and analysis tool because it needs to consider the combination of activities.

An example is taken from literature by [48] to explain the basic idea of the framework and then propose the specific steps of the framework in Figure 2. Firstly, the system activities are decomposed, and the spaghetti graph is drawn in Figure 2a. The arrow represents the information relationship between the activities; for example, the arrow B to C means C needs to receive output information from B before it can start. The original DSM is drawn in Figure 2b, and finally, the partitioned DSM is shown in Figure 2c.

**Figure 2.** The DSM Method Framework.

Based on the representation of the DSM activity relationship, we can sort out this study's basic ideas and work. The project delivery method can be associated with the representation of three activity relationships in partitioned DSM.


uncertainty gradually decrease or converge only after E-D-H iterations occur. If multiple contractors perform separately, this iteration will not be accurately predicted and adequately controlled. There are similar but more complicated relationships among I, L, J, and F, and more upfront planning is required. It is difficult for owners to coordinate different contractors effectively, so they are more suitable for one contractor to conduct integrated management.

#### *3.2. The Procedure of the Selection Model*

The selection model for PDM using DSM includes four steps: Identify Requirements or Objectives, Building/Creating the Design Structure Matrix, Project Redesign/Optimization, and Design/Select Project Delivery Method. The model is shown in Figure 3.

Step 1. Identify requirements or objectives. This step consists of three main tasks, including asking the owner and environmental requirements or limitations, identifying project characteristics, and determining project goals. Identifying the environment of the project and clarifying the project owner's needs is the primary task of choosing a suitable project delivery method [4,56,57]. The sequence of activities, the responsibilities of the organization, and the corresponding contract structure are all based on meeting the owner's needs. Project characteristics define the technical nature of the work [58] which will affect the rationality and feasibility of redesigning the process. Project objectives need to be defined broadly in terms of scope, schedule, budget, and project complexity [4].

Step 2. Building/Creating the Design Structure Matrix. Appropriate structural decomposition and accuracy of activity dependencies determine the effectiveness of the DSM approach [48]. This step, therefore, consists of four activities. First, the project manager should fully decompose the project and forms a list of activities whose outputs constitute the entirety of the project entity. The list of activities can be determined by converting existing documents or structured expert interviews [48]. Second, the inputs and outputs of each activity should be determined, which reflect the dependencies between the activities. After the activities and their dependencies are entered into the matrix, an activity-based DSM can be formed. Finally, the marks in the DSM should be checked to confirm whether the relationships between the activities are correct and whether there are activity conflicts. It is worth noting that even if the activities are decomposed the same in different projects, the relationship between activities may still change with the owner's goals and requirements. When schedules are tight, identifying requirements may no longer be an absolute priority activity, but instead needs to be developed gradually through constant feedback during design and construction.

Step 3. Project Redesign/Optimization. After representing the process in the matrix, the project can be redesigned using partitioning, tearing, banding, and clustering. As mentioned previously, this framework focuses on the relationship and regrouping of activities, so partitioning is the main analysis tool.

Step 4. Design/Select Project Delivery Method. In this step, the strength of the relationship and the sequence of activities in the same partition should be checked first from a technical, regulatory, or management perspective. A partition represents the least amount of feedback between activities within it but may be technical, regulatory, or have weak dependencies that are not worth management action. Once it is confirmed that there is no unreasonableness or error, the activities in the partition can be packaged as a basis for assigning responsible persons. Likewise, relationships between activity packages should be examined and combined where feasible. Team activities can be assigned when all activities and activity packages have no relationship conflicts. Finally, a suitable PDM is selected or designed.

**Figure 3.** The Framework Model Using DSM to Select the PDM.

#### **4. Case Study**

This article uses a case study to describe the feasibility of this method in actual project implementation and uses surveys for verification. The survey asks practitioners their views on the project's activity relationship and inputs the feedback into the model to obtain the simulation results. The feasibility of the method is verified by comparing the simulation results with the actual delivery method.

#### *4.1. Background of the Project*

The project is a post-earthquake hospital reconstruction project in China with a total investment of 73.55 million yuan (US\$11.37 million) and a total construction area of

13,918 m2. The project was publicly tendered on 16 January 2018. The winning bidder was determined on 14 February 2018 and the construction of the project began in April 2018 and was finally finished on 7 August 2019. The funding for the project is fiscal funds, which can remain stable and sufficient.
