John N. Warfield

Binary Matrices in System Modeling

This primarily tutorial paper on the use of binary matrices in system modeling also includes new material related to the initial development of such matrices. The decomposition of binary matrices into levels such that all feedback is contained within the levels is illustrated. A method for developing a binary matrix en route to a structural model of a system is outlined. The development procedure partitions the matrix on the basis of supplied data entries. Then the interconnections between subsystems are added. This procedure permits transitivity to be used in developing the matrix.

Toward Interpretation of Complex Structural Models

The interpretation of complex structural models is facilitated by a variety of operations that can be carried out by a computer. Several of these involve partitions on a reachability matrix, which describes a contextual relation among the elements of the system under study. When partitioning of the reachability matrix in various ways does not permit adequate interpretation, cycles are usually the source of difficulty. A weighting matrix applied to the elements of a maximal cycle set permits a set of digraphs to be developed, which allows for more detailed interpretation of a cycle. When still further development is needed, the maximal cycle sets can be identified and placed in a hierarchy based on an inclusion relation. This hierarchy suggests a natural order of study of the system proceeding from the least complex maximal cycle sets to the most complex sets.

Developing Interconnection Matrices in Structural Modeling

A procedure is described for developing an interconnection matrix that specifies a cascade connection of two known digraphs to form a digraph. The solution of this form of the interconnection problem can be applied to complete the process of description of a binary relation initiated by the process of partitioning on elements described in a companion paper [3]. It is assumed that the contextual relation being modeled is transitive. Based on this assumption, it is shown that the possibilities of interconnection can be completely prescribed in a characteristic logic equation. This equation can be used as the complete basis for development of an interconnection matrix. An example of its use is given. Much of the burden of structural modeling is assigned to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.

Crossing Theory and Hierarchy Mapping

Techniques are introduced which are applicable to machine construction of digraph maps. These techniques are oriented toward reduction of the number of crossings in a map as a means of improving the readability of hierarchical structures. Permuting, psi-factoring, rotating, twirling, and absorbing are among the techniques considered. Examples are given to illustrate these techniques. When these and related procedures are fully developed for use with machine-interactive processes, they will facilitate group modeling efforts.

On Arranging Elements of a Hierarchy in Graphic Form

Hierarchies are fundamental in the study of many kinds of complex systems. Methods are presented that assist in the development of a hierarchy or a set of hierarchies. Once the element set and the relations among the elements are established, the rationalizing procedure presented allows computer determination of how many separate hierarchies are represented by the relations among the elements. An example of the rationalization process is given. Two methods?the element method and the level method?are given for developing a hierarchy for a connected subordination matrix. Each method is illustrated with an example.

Developing Subsystem Matrices in Structural Modeling

A major requirement for structural modeling is that the necessary data be acquired and organized into a form from which a structural model can be developed. A reachability matrix is one such form. It is very useful when the contextual relation being modeled is transitive and multilevel. A significant step in the development of a reachability matrix consists of the ordering of elements of the system in such a way that much of the data required can be computed from supplied data, using the transitivity condition. The process described for orderimg the element set suffices to define a set of subsystems and reduces the problem of developing a reachability matrix to one of developing a set of its component interconnection matrices that join these subsystems. The process described assigns much of the burden of structural modeling to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.

Unified Program Planning

Program planning begins with problem definition and ends with planning for action. The key products that result from the problem definition, value system design, and system synthesis steps are discussed and interrelated through the use of interaction matrices. Particular emphasis is given to defining objectives and to defining a set of measures on the objectives by which to determine their attainment. Interaction matrices relate objectives measures to objectives and link activities and measures of their accomplishment to the attainment of objectives. A major consequence of program planning is the choice of a program to pursue, and identification of the projects that will be carried out as a part of a selected program. Selecting the set of projects is discussed in terms of consistency with corporate or agency policy, and the economics, risk, and potential benefits associated with each project. A criterion function that incorporates the latter three factors is described and proposed as a practical way of evaluating the relative merits of projects.

Systems science serves enterprise integration: a tutorial

Enterprise integration is a major global challenge of these times. It is now possible for a new generation of practitioners to engage this challenge selectively by applying a recently articulated version of systems science (WSS). This tutorial paper argues that a half-century of disarray of the systems field can be seen as ending; and that the distillation of WSS to support a wide variety of application areas (in this instance, enterprise integration) can occupy practitioners as they harness the work program of complexity (WPOC) selectively. Carrying out the WPOC yields predictable portfolio components, consisting of a well-defined mix of tangible and intangible products. The three causes of poor intellectual productivity identified by Kenneth Boulding are nullified when appropriate role matching is achieved between WSS and enterprise integration.

Twenty laws of complexity: science applicable in organizations

The ‘LTI Set’, consisting of 20 Laws of Complexity, a Taxonomy of the Laws of Complexity, and five Indexes of Complexity, is proposed as the core of a developing science of complexity that is applicable to resolving complexity in organizations. The LTI Set links to these included topics: Alternative Science-Free Organizational Practices; Educational Practices Appropriate to Complexity; Quality Control of Science; Applications of the Science of Complexity in Organizations; Enabling Conditions for Effective Organizational Practice. A critical condition for significant advances in resolving complexity is that the organization recognize the strong, even dominant, behavioral aspects of complexity, as reflected in the Laws; and take account of these in redefining the main role of top management. That role is to set up and administer a responsive corporate infrastructure to meet the demands of complexity, along the lines set forth here. Further advances in behavior can be made through new educational programs that reflect older scientific values applied to the challenges of today, in contrast to reliance on unwarranted assumptions that undermine organizations. Appropriately remodeled to reflect the relentless demands of complexity, the university can become a model for other institutions in society. Copyright

Perspectives on quality coordination and assurance in global supply chains

The 2007 recall of Berko Electric Toe-Space Heaters made in the US, the recall of backpack blowers made in Japan, the recalls of toys and pet food produced in China have exposed the potential of global supply chain disruptions. This product recall storm leads to the issue of quality assurance in global supply chain management. Product recalls indicate that manufacturing companies are particularly vulnerable to ensure quality when they source via a global supply chain with poor visibility. Obviously, a supply chain cannot afford this kind of sourcing and supply structure that threatens the supply-chain integrity. This special issue on quality assurance in global supply chains intends to offer a few useful concepts, methods, and approaches to ensure quality in global supply chains. The 14 articles presented here identified common themes and indicate increased emphasis on supply chain quality assurance.