TABLE OF CONTENTS

1. Getting Started with Design Structure Matrices
   
2. Types of Design Structure Matrices
   
3. Simplified Methods of Analysis
   
4. DSM Simulation
   
5. Advanced Topics
   
6. References and Web Resources
   

WHAT IS A DESIGN STRUCTURE MATRIX (DSM)?

A design structure matrix (DSM) is a compact, matrix representation of a system or project. The matrix contains a list of all constituent subsystems/activities and the corresponding information exchange and dependency patterns (i.e., what information pieces (parameters) are required to start a certain activity and where does the information generated by the activity feed into).

1. As a systems analysis tool, DSMs provide a compact and clear representation of a complex system and a capture method for the interactions, interdependencies, interfaces between system elements (i.e. sub-systems and modules).

2. As a project management tools, DSMs provide a project representation that allows for feedback and cyclic task dependencies. This is extremely important since most engineering applications exhibit such a cyclic property. This DSM project representation results in an improved and more realistic execution schedule for the corresponding design activities.

A LITTLE BIT OF HISTORY

The use of matrices in system modeling can be traced back to Warfield in the 70s and Steward in the 80s. However, it is not until the 1990s that the method received attention and wide spread. Much of the credit in its current popularity is accredited to MIT's research in the design process modeling arena.

Earlier works started with the use of graphs for system modeling. For example, consider a system that is composed of two elements (or sub-systems): element "A" and element "B". [The two elements  are assumed to completely describe the system and characterize its behavior]. A graph may be developed to represent this system pictorially. The system graph is constructed by allowing a vertex/node on the graph to represent a system element and an edge joining two nodes to represent the relationship between two system elements. The directionality of influence from one element to another is captured by an arrow instead of a simple link. The resultant graph is called a directed graph or simply a digraph.

The use of matrices in system modeling can be traced The matrix representation of a digraph (i.e. directed graph) is a binary (i.e., a matrix populated with only zeros and ones) square (i.e. a matrix with equal number of rows and columns) matrix with m rows and columns, and n non-zero elements, where m is the number of nodes and n is the number of edges in the digraph. The matrix layout is as follows: the system elements names are placed down the side of the matrix as row headings and across the top as column headings in the same order. If there exists an edge from node i to node j, then the value of element ij (column i, row j) is unity (or marked with an X). Otherwise, the value of the element is zero (or left empty). In the binary matrix representation of a system, the diagonal elements of the matrix do not have any interpretation in describing the system, so they are usually either left empty or blacked out.

KEY BENEFITS OF DSM

In a nut shell, binary matrices for system modeling are useful in systems modeling because they can represent the presence or absence of a relationship between pairs of elements of a system. A major advantage of the matrix representation over the digraph is in its compactness and  ability to provide a systematic mapping among system elements that is clear and easy to read regardless of size.

If the system is a project represented by a set of tasks to be performed, then off-diagonal marks in a single row of the DSM represent all of the tasks whose output is required to perform the task corresponding to that row. Similarly, reading down a specific column reveals which task receives information from the task corresponding to that column. Marks below the diagonal represent forward information transfer to later (i.e. downstream) tasks. This kind of mark is called forward mark or forward information link. Marks above the diagonal depict information fed back to earlier listed tasks (i.e. feedback mark) and indicate that an upstream task is dependent on a downstream task.

There are three basic building blocks for describing the relationship amongst system elements: parallel (or concurrent), sequential (or dependent) and coupled (or interdependent).

Three Configurations that Characterize a System
Relationship	Parallel	Sequential	Coupled
Graph Representation
DSM Representation	A B A      B	A B A      B X	A B A   X B X

Points to note are as follows:

• In the parallel configuration, the system elements do not interact with each other. Understanding the behavior of the individual elements allow us to completely understand the behavior of the system. If the system is a project, then system elements would be project tasks to be performed. As such, activity B is said to be independent of activity A and no information exchange is required between the two activities.

• In the sequential configuration, one element influences the behavior or decision of another element is a uni-directional fashion. That is, the design parameters of system element B are selected based on the system element A design parameters. Again, in terms of project tasks, task A has to be performed first before task B can start.

• In the coupled system, the flow of influence or information is intertwined: element A influences B and element B influences A. This would occur if parameter A could not be determined (with certainty) without first knowing parameter B and B could not be determined without knowing A. This cyclic dependency is called "Circuits" or "Information Cycles"

READING THE DSM

The DSM provide insights about how to manage a complex system/project and hilights issues of information needs and requirements, task sequencing, and iterations. A sample DSM is shown below:

The X marks indicate the existence and direction of information flow (or a dependency in a general sense) from one activity in the project (i.e. matrix) to another. Reading across a row reveals the input/dependency flows by an X mark placed at the intersection of that row with the column that bears the name of the input task. Reading across a column reveals the output information flows from that activity to other activities by placing an X in a similar manner described above. For example, consider activity C in the above matrix. Activity C relies on information from activities A and B and delivers information to activities D, E, F and G.

The green marks (below the diagonal) represent forward flow of information. The red marks (above the diagonal) are of special significance. Such a mark reveal a feedback from a later (i.e. downstream) activity to an earlier (i.e. upstream) one. This means that the earlier activity has to be repeated in light of the late arrival of new information.

This iterative process in common in most engineering design and development projects. Design iterations create rework and require extra comunication and negotiation which result in a prolonged development process. In order to speed up this iterative design process, the DSM methodology suggests the manipulation of the matrix elements such that iterative behavior is removed from the matrix, or at least minimized (a process called partitioning -- see details below.

It is worth noting that some DSM researchers and practitioners use an opposite convention for the feedforward and feedback marks, as discussed above. That is, the DSM can be built in such a way that sub-diagonal marks represent feedback (MIT DSM Lab).

Design structure matrices can be used to represent four different types of data:

COMPONENT-BASED DESIGN MATRICES

A component-based DSM documents interactions between elements in a complex system architecture. Different types of interactions can be displayed in the DSM. Types of interactions will vary from project to project.
Some representative interaction types are shown in the table below (Pimmler and Eppinger, 1994).

As an example, consider the material interaction between components for an automobile Climate Control System.

Clustering the "X" marks along the diagonal of the DSM resulted in the creation of three "chunks" for the Climate Control System. The "chunks" are (Pimmler and Eppinger, 1994): (1) Front End Air Chunk; (2) Refrigerant Chunk; (3) Interior Air Chunk.

TEAM-BASED DESIGN MATRICES

This approach is used for organizational analysis and design based on information flow among various organizational entities.  Individuals and groups participating in a project are the elements being analyzed (rows and columns in the matrix).  A Team-based DSM is constructed by identifying the required communication flows and representing them as connections between organizational entities in the matrix.  For the modeling exercise it is important to specify what is meant by information flow among teams. The table, below, presents several possible ways information flow can be characterized. 

The matrix can be manipulated in order to obtain clusters of highly interacting teams and individuals while attempting to minimize inter-cluster interactions. The obtained groupings represent a useful framework for organizational design by focusing on the predicted communication needs of different players.

For an application example, refer to McCord and Eppinger (1993). They propose a team-based DSM to analyze the organizational structure necessary for an improved automobile engine development process.

ACTIVITY-BASED DESIGN MATRICES

Three types of task interactions can be observed from the matrix. In the figure, below, tasks 1 and 2 are "independent" since no information is exchanged between them. These tasks can be executed simultaneously (in parallel). Tasks 3, 4, and 5 are engaged in a sequential information transfer and are considered "dependent". These tasks would typically be performed in series. Tasks 7 and 8, however, are mutually dependent on information. These are "interdependent" or "coupled" tasks often requiring multiple iterations for completion.

A Sample Task-Based DSM

1 2 3 4 5 6 7 8 9 1 1                 2   2               3   X 3             4   X   X X 4           5   X   X 5         6   X       6 X     7         X   7 X X 8      X       X 8   9            X     9

Marked cells above the diagonal represent iterations in the process. This occurs when an activity is dependent on information from a task scheduled for a later execution. Such scenarios often lead to rework and are undesirable. A number of algorithms have been developed (Warfield, 1973; Steward, 1981) to minimize such instances of iteration (above diagonal marked cells) by re-arranging the sequence of tasks in the process. Methods are also available on how to handle iterations in the process that cannot be eliminated through re-sequencing.

DSM models using simple binary representations strictly display the existence of a dependency between two tasks without providing additional information on the nature of the interaction. Further studies have extended the basic DSM configuration by capturing additional facts on the development process. For example, the numerical DSM adds task duration in the diagonal elements, and replaces marks with numbers in the off-diagonal cells each representing the degree of dependency between two tasks (Browning, 1998; Yassine, 1999).

PARAMETER-BASED DESIGN MATRICES

This type of modeling is used to analyze system architecture based on parameter interrelationships. A parameter-based DSM is constructed through explicit definition of a system's decomposed elements and their interactions. A systematic taxonomy and a quantification scheme assist in the analysis by categorizing types of interactions among system elements and associating an appropriate weight to each. Table 1 and Table 2, below, present the classification of interactions and an example of a quantification scheme proposed by Pimmler and Eppinger (1994).

Black (1990)applied a parameter-based DSM to an automobile brake system design, using the DSM to describe the current practices of a brake system component supplier. The DSM shown below is extracted from the original DSM which was (103 X 103). After sequencing the parameters, the resultant DSM (also shown below) two blocks of coupled, low level parameter determinations become apparent.

Parameter-Based DSM for Brake System (Black, 1990)