Design structure matrix


The design structure matrix is a simple, compact and visual representation of a system or project in the form of a square matrix.
It is the equivalent of an adjacency matrix in graph theory, and is used in systems engineering and project management to model the structure of complex systems or processes, in order to perform system analysis, project planning and organization design. Don Steward coined the term "design structure matrix" in the 1960s, using the matrices to solve mathematical systems of equations.

Overview

A design structure matrix lists all constituent subsystems/activities and the corresponding information exchange, interactions, and dependency patterns. For example, where the matrix elements represent activities, the matrix details what pieces of information are needed to start a particular activity, and shows where the information generated by that activity leads. In this way, one can quickly recognize which other activities are reliant upon information outputs generated by each activity.
The use of DSMs in both research and industrial practice increased greatly in the 1990s. DSMs have been applied in the building construction, real estate development, semiconductor, automotive, photographic, aerospace, telecom, small-scale manufacturing, factory equipment, and electronics industries, to name a few, as well as in many government agencies.
The matrix representation has several strengths.
DSM analysis provides insights into how to manage complex systems or projects, highlighting information flows, task/activities sequences and iteration. It can help teams to streamline their processes based on the optimal flow of information between different interdependent activities.
DSM analysis can also be used to manage the effects of a change. For example, if the specification for a component had to be changed, it would be possible to quickly identify all processes or activities which had been dependent on that specification, reducing the risk that work continues based on out-of-date information.

DSM Structure

A DSM is a square matrix, representing linkages between the system elements. The system elements are often labeled in the rows to the left of the matrix and/or in the columns above the matrix. These elements can represent for example product components, organization teams, or project activities.
The off-diagonal cells are used to indicate relationships between the elements. A marking of the cell indicates a directed link between two elements and can represent design relations or constraints between product components, communication between teams, information flow or precedence relations between activities. In one convention, reading across a row reveals the outputs that the element in that row provides to other elements, and scanning a column reveals the inputs that the element in that column receives from other elements. For example, in the DSM, the marking in row A and column C indicated a link from A to C. Alternatively, the rows and columns may be switched. Both conventions may be found in the literature.
The cells along the diagonal are typically used to represent the system elements. However, the diagonal cells can be used for representing self-iterations. Self-iterations are required when a matrix element represents a block of activities/subsystems that may be further detailed, allowing hierarchical DSM structure.
Two main categories of DSMs have been proposed: static and time-based.
Static DSMs represent systems where all of the elements exist simultaneously, such as components of a machine or groups in an organization. A static DSM is equivalent to an N2 chart or an adjacency matrix. The marking in the off-diagonal cells is often largely symmetrical to the diagonal. Static DSMs are usually analyzed with clustering algorithms.
A time-based DSM is akin to a precedence diagram or the matrix representation of a directed graph. In time-based DSMs, the ordering of the rows and columns indicates a flow through time: earlier activities in a process appear in the upper-left of the DSM and later activities appear in the lower-right. Terms like “feedforward” and “feedback” become meaningful when referring to interfaces. A feedback mark is an above-diagonal mark. Time-based DSMs are typically analyzed using sequencing algorithms, that reorder the matrix elements to minimize the amount of feedback marks, and make them as close as possible to the diagonal.
DSM matrices were categorized to Component-based or Architecture DSM; People-based or Organization DSM, both considered as Static. Activity-based or Schedule DSM and Parameter-based DSM are defined as time-based, as their ordering implies flow.

DSM marking

Initially, the off-diagonal cell markings indicated only the existence/non-existence of an interaction between elements, using a symbol. Such marking is defined as Binary DSM. The marking then has developed to indicate quantitative relation Numeric DSM indicating the "strength" of the linkage, or statistical relations Probability DSM indicating for example the probability of applying new information.

DSM algorithms

The DSM algorithms are used for reordering the matrix elements subject to some criteria. Static DSMs are usually analyzed with clustering algorithms. Clustering results would typically show groups of tightly related elements, and elements that are either not connected or are connected to many other elements and therefore are not part of a group.
Time-based DSMs are typically analyzed using partitioning, tearing and sequencing algorithms.
Sequencing methods try to order the matrix elements such that no feedback marks remain. In case of coupled activities the results is a block diagonal DSM. Partitioning methods include: Path Searching; Reachability Matrix; Triangulation algorithm; and the powers of the Adjacency Matrix.
Tearing is the removal of feedback marks or assignment of lower priority. Tearing of a Component-based DSM may imply modularization or standardization. After tearing a partitioning algorithm is reapplied.
Minimizing feedback loops gets the best results for Binary DSM, but not always for Numeric DSM or Probability DSM. Sequencing algorithms are typically trying to minimize the number of feedback loops and also to reorder coupled activities trying to have the feedback marks close to the diagonal. Yet, sometimes the algorithm just tries to minimize a criterion.

Use and extensions

Interactions between various aspects is done using additional linkage matrices. The Multiple Domain Matrix is an extension of the basic DSM structure. A MDM includes several DSMs that represent the relations between elements of the same domain; and corresponding Domain Mapping Matrices that represent relations between elements of different domains.
The use of DSM has been extended to visualize and optimize the otherwise invisible information flow and interactions associated with office work. This visualization via DSM allows the Lean Body of Knowledge to be applied to office and information intensive flows.
The DSM method was applied as a framework for analyzing the propagation of rework in product development processes, and the related problem of convergence using the theory of linear dynamical systems.
See for a comprehensive, updated survey of DSM extensions and innovations.

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