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The classic approach to increasing understanding about a complex system is to model it, typically by 1 decomposing it into subsystems about which we know relatively more; 2 noting the relationships between the integration of the subsystems that give rise to the system's behavior;Manuscript received August 3, Review of this manuscript was arranged by Department Editor C. Publisher Item Identifier S 01 The design structure matrix DSM is becoming a popular representation and analysis tool for system modeling, especially for purposes of decomposition and integration.
A DSM displays the relationships between components of a system in a compact, visual, and analytically advantageous format. A DSM is a square matrix with identical row and column labels. In the example DSM in Fig. An off-diagonal mark signifies the dependency of one element on another. Reading across a row reveals what other elements the element in that row provides to; scanning down a column reveals what other elements the element in that column depends on.
That is, reading down a column reveals input sources, while reading across a row indicates output sinks. Thus, in Fig. There are two main categories of DSMs: static and time-based. Static DSMs represent system elements existing simultaneously, such as components of a product architecture or groups in an organization. Static DSMs are usually analyzed with clustering algorithms. In time-based DSMs, the ordering of the rows and columns indicates a flow through time: upstream activities in a process precede downstream activities, and terms like "feedforward" and "feedback" become meaningful when referring to interfaces.
Time-based DSMs are typically analyzed using sequencing algorithms. DSMs stem from diverse roots. A static DSM is essentially the square matrix called an diagram, long used by systems engineers to represent architectural components and interfaces e.
Organization designers also use matrix-based techniques to document communication networks e. Economists summarize the effects of a change in one product's attributes on other products elasticities in a matrix e. Steward ,  used matrix-based techniques to analyze the structure of the system design process, coining the term "design structure matrix" for a time-based matrix akin to a precedence diagram, which had been used to manage projects since the s e.
This paper refers to all of these techniques broadly as design structure matrices DSMs , although the terms dependency structure matrix, dependency source matrix, dependency map, interaction matrix, incidence matrix, precedence matrix, and others are also used in the literature. The point of the matrix is to illuminate the structure and aid in the design of products, processes, and organizations.
The use of DSMs in both research and industrial practice increased greatly in the s. DSMs have been applied in the building construction - , , , , semiconductor , , automotive , , , , , photographic , aerospace , , , , , , , , , , telecom , small-scale manufacturing , factory equipment , and electronics  industries.
This paper reviews four DSM applications useful to product developers, project planners, project managers, system engineers, and organizational designers . Each of the four applications is applied to a system 2 Lano  extended N charts to include time-sequenced applications. The paper concludes with a summary and a discussion of barriers to DSM use. Relationships between the four types of DSMs are also explored, leading to interesting issues for future research and new DSM applications.
MotivationProduct architecture is the arrangement of functional elements into physical chunks that become the building blocks for a product or family of products . Chunks should implement one or a few functions entirely, and interactions between chunks should be well defined.
Modular system architectures have advantages in simplicity and reusability for a product family or platform , . Research has shown that innovative product architectures can be a source of competitive advantage for product development firms .
Where should one look to achieve innovative product architectures? Rechtin reminds us that the relationships among elements are what give systems their added value, and, furthermore, that the greatest leverage in systems architecting is at the interfaces .
A prerequisite to innovation is understanding, which can be increased through the use of representative models-in this case, preferably ones that highlight the interfaces or interactions between system elements.
A DSM can represent a system architecture in terms of the relationships between its constituent components. Such a model informs system decomposition into subsystems.
Intelligent decomposition or partitioning is important to managing system complexity . The architectural decomposition scheme has ramifications for the ease of system design and integration , . The importance of informed architectural decomposition has led to several matrix-based models e. In general, the system engineering exercise involves the following three steps: 1 decompose the system into elements; 2 understand and document the interactions between the elements i.
Every complex system development project includes these steps, although they are not always approached systematically or innovatively. A component-based DSM facilitates both systemization and innovation. MethodA component-based DSM documents interactions among elements in a system architecture.
An organized taxonomy can help differentiate types of interactions. Pimmler and Eppinger suggest four types, as shown in Table I. The important types of interactions will vary from product to product, and others-such as vibrational or electrical-could also be included.
A single three-dimensional DSM can represent multiple types of interaction data if each off-diagonal cell contains a vector. A quantification scheme facilitates weighting interactions relative to each other.
Off-diagonal square marks in the DSM are  replaced by a number coupling coefficient -e. Alternatively, the weighting scheme could be exponential instead of linear. Weighting information can be obtained by reviewing architectural diagrams and system schematics.
Further clarification comes from interviewing engineers and architectural domain experts. Integration analysis-via the clustering of off-diagonal elements by reordering the rows and columns of the DSM-can provide new insights into system decomposition and integration.
Clustering requires several considerations. The foremost objective is to maximize interactions between elements within clusters chunks while minimizing interactions between clusters , , . It has also been suggested to minimize the size of the clusters .
Second, it may be useful to allow for some overlapping of clusters-i. Third, if using a three-dimensional 3-D DSM, one must decide whether to slice it into several two-dimensional 2-D matrices and work with each separately, or to perform a composite analysis by weighting the various types of interactions based on their relative importance.
For example, spatial relationships may be more important than data flow associations, since wiring can often be repositioned more easily than larger hardware. Both procedures have advantages and can reveal significant relationships. However, analyzing 2-D matrices is much simpler, and a composite analysis, while conceptually attractive, might obscure some of the basic insights. Finally, it may be useful to keep integrative elements such as data buses outside of the clusters, noting that these elements must interact substantially with all of the clusters.
In some cases, highly interactive components are assigned to a "controls cluster" that interacts with all clusters. While it is not yet possible to optimize all of these objectives, clustering algorithms are very helpful in integration analysis.
By reordering rows and columns, a clustering algorithm seeks a DSM configuration that optimizes an objective function. For example, the objective could be to minimize the coupling between the clusters while minimizing the size of the largest cluster.
In this case, the reordered DSM will have clusters of elements along the diagonal. Several algorithms and heuristics have been offered to aid in determining appropriate objective functions and optimization e. Altus et al. Pimmler and Eppinger  use a distance from the diagonal penalty computed for each interaction.
Yager  discusses advanced clustering algorithms for general applications. A clustering algorithm should account for the importance of both precluding negative relationships and ensuring positive ones.
After clustering analysis, any interactions exogenous to the clusters should be noticed as interfaces where special attention and verification may be required.
No single clustering approach is a panacea. Fortunately, visual inspection and manipulation are often adequate for small or sparse matrices. ExamplePimmler and Eppinger  use a component-based DSM to reveal and explore alternative architectures "to improve the quality of the resulting product design and to ease the substantial coordination demands that are required when subsystems interact" at Ford Motor Company.
Numerical entries correspond to a quantification scheme like the one in Table II. Not every element of the climate control system interacts with every other element on a materials basis, but all of the materials interactions that do exist are essential to achieve desired functionality. Using a distance penalty algorithm or by examination, the climate controls system can be clustered into subsystems on the basis of materials interactions as shown in Fig.
The front-end cluster represents the set of components at the fore of the engine compartment involved with heat transfer to the exterior air. The refrigerant cluster consists of the air conditioner components; the interior air cluster represents the components at the front of the passenger compartment involved in modifying interior air temperature.
Assigning two of the elements, evaporator core and condenser, to two clusters each forces the clusters to overlap, highlighting areas requiring integration across clusters.
Remaining components are assigned to the three existing clusters and a new controls cluster based on spatial, energy, and information interactions which are not covered here since the materials perspective suffices to illustrate the application. Even this simple analysis revealed to Ford the utility of overlapping what were previously mutually exclusive architectural clusters. InsightsWhile the above example is simple, the underlying methodology is powerful.
When other types of interactions are included, conducting the decomposition and integration analysis with respect to varied objective functions provides alternative architectural perspectives. Integration analysis with a DSM promotes architectural innovation by demonstrating the rationale behind architecting decisions [63, pp. Integration analysis also supports modularization , , , , which, in turn, enables product platforms and other advantageous approaches to product development.
DSM has advantages like simplicity and it can organize the flow of data. Therefore, an area that DSM brings some important benefits is in project management. This tool can identify the cycle that iteration occurs, it also can minimize some revisions that are unnecessary, which accelerates the deliveries. The objective of this paper is to do a bibliometric analysis that focuses on identifying the most co-cited papers about DSM literature only journals that is connected with project management. The result shows that DSM can be used with different approaches like traditional, hybrid or agile project management. Gephi: an open source software for exploring and manipulating networks. Bibliometrics and citation analysis.
Show all documents This results in performance degradation concerning the throughput and successful handovers. To address this problem, this paper proposes proactive algorithms for balancing the load across the small-cell clusters and compares their balancing results to the previous reactive algorithms. The proactive algorithms distribute the new UEs, one by one, to the small cells, while the reactive algorithms are only triggered when the load of the chosen cluster reaches a predefined threshold. In addition, this paper employs the design structure matrix DSM method in order to balance the load across the small cells and to reduce the inter-communications between the access points APs as well.
It seems that you're in Germany. We have a dedicated site for Germany. This book introduces state-of-the-art models and methods based on the matrix in the field of product design and change management. It develops several types of matrix models for a broad range of applications, with the goal of efficiently finding product design solutions and proactively analyzing design change propagation. The book offers readers an extensive introduction to design automation, highlighting fundamental and innovative concepts, as well as cutting-edge technologies. Further, it familiarizes them with the latest advances in design change propagation and prediction. Lastly, the book puts forward design change-oriented matrix models and includes a proactive analysis of change propagation.
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 2 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. 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 s,  using the matrices to solve mathematical systems of equations. 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.
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