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[[File:A sample Design Structure Matrix (DSM).png|273x193px|framed|right|A sample DSM with 7 elements and 11 dependency marks.]]
The '''Design Structure Matrix (DSM)''' (also referred to as '''dependency structure matrix''', '''dependency structure method''', '''dependency source matrix''', '''problem solving matrix (PSM)''', '''incidence matrix''', '''''N<sup>2</sup>'' matrix''', '''interaction matrix''', '''dependency map''' or '''design precedence matrix''') is a simple, compact and visual representation of a system or project in the form of a square [[matrix (mathematics)|matrix]].<ref name="DSMbook">S.D. Eppinger and T.R. Browning
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,<ref>D. V. Steward: ''The Design Structure System: A Method for Managing the Design of Complex Systems.'' In: ''IEEE Transactions on Engineering Management.'' 28(3), 1981, S. 71-74.</ref> using the matrices to solve mathematical systems of equations.
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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 (output from A, input to C). Alternatively, the rows and columns may be switched (without a change of meaning). Both conventions may be found in the literature.<ref name="DSMbook"/>
The cells along the diagonal are typically used to represent the system elements. However, the diagonal cells can be used for representing self-iterations (e.g., rework of a code that did not pass its unit testing). Self-iterations are required when a matrix element represents a block of activities/subsystems that may be further detailed, allowing hierarchical DSM structure.<ref>A. Karniel and Y. Reich, [http://www.researchgate.net/publication/4255493_Simulating_Design_Processes_with_self-iteration_activities_based_on_DSM_planning “Simulating Design Processes with self-iteration activities based on DSM planning,”] in Proceedings of the International Conference on Systems Engineering and Modeling - ICSEM'07, Haifa, 2007.
Two main categories of DSMs have been proposed: static and time-based.<ref name="DSMreview">T. Browning: [http://dx.doi.org/10.1109/17.946528 "Applying the Design Structure Matrix to System Decomposition and Integration Problems: A Review and New Directions."] In: ''IEEE Transactions on Engineering Management.'' 48(3):292-306, 2001.</ref>
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The DSM algorithms are used for reordering the matrix elements subject to some criteria. Static DSMs are usually analyzed with [[Cluster analysis|clustering algorithms]] (i.e., reordering the matrix elements in order to group together related elements). Clustering results would typically show groups (clusters) 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.<ref name="DSMbook"/>
Time-based DSMs are typically analyzed using partitioning, tearing and sequencing algorithms.<ref name="DSMbook"/><ref name="complex"/><ref>A. Karniel and Y. Reich, [http://link.springer.com/chapter/10.1007%2F978-0-85729-570-5_3 "Design process planning using DSM"], in Managing the Dynamics of New Product Development Processes: A New Product Lifecycle Management Paradigm, Springer, 2011
'''Sequencing''' methods try to order the matrix elements such that no feedback marks remain.<ref name="DSMbook"/><ref name="complex"/> In case of coupled activities (activities that have cyclic links, e.g., activity A is linked to B, which is linked to C, which is linked to A) the results is a block diagonal DSM (i.e., blocks or groups of coupled activities along the diagonal). Partitioning methods include: Path Searching; Reachability Matrix; Triangulation algorithm; and the powers of the Adjacency Matrix.
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*Web-Portal of DSM Community: http://www.dsmweb.org
*International Design Structure Matrix Conference: http://www.dsm-conference.org
== Further reading ==
*DSM book: http://mitpress.mit.edu/books/design-structure-matrix-methods-and-applications
*[http://www.theserverside.net/tt/articles/showarticle.tss?id=ControllingDependencies Control Component Dependencies, TheServerSide.net article]
*[http://hbswk.hbs.edu/archive/1979.html Innovation at the Speed of Information]
*[http://www.lattix.com/files/dl/wp/oopsla05.pdf Using Dependency Models to Manage Complex Software Architecture]
*{{cite book
| last = Karniel
| first = Arie
| last2 = Reich
| first2 = Yoram
| authorlink =
| year =2011
| title = Managing the Dynamics of New Product Development Processes: A New Product Lifecycle Management Paradigm
| publisher = Springer
| isbn = 978-0-85729-569-9}}
[[Category:Systems theory]]
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