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Application of Graph Theory and Matrices of Relations in Modeling Complex Systems

Saber Kivaj, Ali | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40459 (44)
  4. University: Sharif University of Technology
  5. Department: Management and Economics
  6. Advisor(s): Malaek, Mohammad Bagher
  7. Abstract:
  8. Design of complex systems requires different challenges to be met simultaneously. Yet the current methods lack a sound theoretic framework and thus designers normally rely on heuristic or empirical methods; based on available experiences. Such approaches to the system design entail both technical and business risks and subsequently increase the probability of long-term problems. In this research, along with the theoretical framework of the systems design concepts, we discuss number of important models. The main concentration of the work, however, is to; somehow, correlate Axiomatic Design Matrix (ADM) with Design Structure Matrix (DSM). Here we exploit mathematical model based on sets and by means of them, we redefine both ADM as well as DSM representations of mathematical relations. Once, we have the algorithms to obtain DSM models; we make use of ADM model to decouple the desired tasks. In addition, we introduce a generalized ADM model to show relations of the system’s functions. The efficiency of the proposed methods is then investigated thru two different case studies for both small and large systems. The resulting Block-Triangular Matrix and optimum sequence of functions show the efficiency of the proposed methods to decrease the complexity of large systems
  9. Keywords:
  10. Complex System ; Decoupling ; Axiomatic Design ; Design Structure Matrix ; Block Triangular Matrix ; Functions Optimum Sequence

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