*2.3. Design Structure Matrix*

The design structure matrix (DSM), also known as the dependency structure matrix, has become a widely used modeling framework in research and practice. The DSM is a network modeling tool that reflects the interaction of the system's elements, thereby highlighting the system's architecture (or designed structure) [40]. According to the type of system being modeled, DSM can represent various types of architectures. For example, to model a process architecture, the DSM elements would be the activities in the process, and the interactions would be the flow of information and/or materials between them [41]. The DSM approach allows the project or engineering manager to represent meaningful task relationships to determine a reasonable sequence for the modeled activities [42]. The DSM has been identified as a potential tool to simulate interdependent activities, identify suitable assumptions, and formulate and evaluate the result [43].

The activity-based DSM is basically an N-square matrix that contains an activity list of rows and columns arranged in the same order. The order of activities in a row or column indicates the order of execution. In DSM, the relationship between activities is represented by the "X" mark in off-diagonal cells, which reflects the information flow between activities. The "X" mark above the diagonal indicates the information assumption or premise needed to start an activity. DSM is an N-square graph matrix representation of a process that is especially suitable for modeling the sequence and iterative information relationship between activities in the product development process [44–46].

Three possible relationship types between activities and corresponding DSM expressions are shown in Figure 1.


**Figure 1.** Three Configurations in DSM Analysis.

The DSM can be divided into four categories: component-based DSM, team-based DSM, activity-based DSM, and parameter-based DSM. The former two DSMs can also be called static DSM, and the last two can be called time-based DSM [47]. They correspond to the four DSM structural directions, as suggested by Yassine, and demonstrate the corresponding analysis methods as shown in Table 1.

**Table 1.** Four Different Types of Data in DSM (adapted from Yassine 2004).


Partitioning eliminates or reduces feedback marks [46]. This process reorders activities so that dependencies are below or close to diagonals. When this is completed, we can see which activities are sequential, which can be completed in parallel, and which are coupled or iterative [48].

Tearing is the process of selecting the set of feedback marks that, if removed from the matrix (and then the matrix is re-partitioned), it will make the matrix a lower triangle [48]. Once the hypothesis is made through tearing, the matrix is subdivided to determine the preferred execution sequence [42].

Banding is to add alternating light and dark bands in DSM to show independent (i.e., parallel or concurrent) activities (or system elements) [49]. The collection of bands or levels constitutes the critical path of the system/project [48].

Although DSM is considered an effective tool for planning and sequencing, it is rarely used in construction projects. DSM is mostly used for optimizing activities during the planning and design phases [50–55]. These studies have improved the integration of activities in planning and design, helping engineers and managers to control work more precisely and improve work efficiency. However, research on project delivery method selection based on activity optimization has not been seen.
