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Embedding Economic Input-Output Models in Systems of Systems: An MBSE and Hetero-functional Graph Theory Approach

Mohammad Mhadi Naderi, Megan S. Harris, John C. Little, Amro M. Farid

Abstract

Characterizing the interdependent nature of Anthropocene systems of systems is fundamental to making informed decisions to address challenges across complex ecological, environmental, and coupled human-natural systems. This paper presents the first application of Model-Based Systems Engineering (MBSE) and Hetero-functional Graph Theory (HFGT) to economic systems, establishing a scalable and extensible methodology for integrating economic input-output (EIO) models within a unified system-of-systems modeling framework. Integrating EIO models into the MBSE-HFGT workflow demonstrates how the structural form and function of economic systems can be expressed through SysML's graphical ontology and subsequently translated into the computational structure of HFGT. Using a synthetic Rectangular Choice of Technology (RCOT) example as a pedagogical foundation, the study confirms that the dynamics captured by basic EIO models, as well as other complex economic models grounded in EIO theory, can be equivalently reproduced within the MBSE-HFGT framework. The integration with MBSE and HFGT thus preserves analytical precision while offering enhanced graphical clarity and system-level insight through a shared ontological structure. By integrating modeling languages and mathematical frameworks, the proposed methodology establishes a foundation for knowledge co-production and integrated decision-making to address the multifaceted sustainability challenges associated with Anthropocene systems of systems.

Embedding Economic Input-Output Models in Systems of Systems: An MBSE and Hetero-functional Graph Theory Approach

Abstract

Characterizing the interdependent nature of Anthropocene systems of systems is fundamental to making informed decisions to address challenges across complex ecological, environmental, and coupled human-natural systems. This paper presents the first application of Model-Based Systems Engineering (MBSE) and Hetero-functional Graph Theory (HFGT) to economic systems, establishing a scalable and extensible methodology for integrating economic input-output (EIO) models within a unified system-of-systems modeling framework. Integrating EIO models into the MBSE-HFGT workflow demonstrates how the structural form and function of economic systems can be expressed through SysML's graphical ontology and subsequently translated into the computational structure of HFGT. Using a synthetic Rectangular Choice of Technology (RCOT) example as a pedagogical foundation, the study confirms that the dynamics captured by basic EIO models, as well as other complex economic models grounded in EIO theory, can be equivalently reproduced within the MBSE-HFGT framework. The integration with MBSE and HFGT thus preserves analytical precision while offering enhanced graphical clarity and system-level insight through a shared ontological structure. By integrating modeling languages and mathematical frameworks, the proposed methodology establishes a foundation for knowledge co-production and integrated decision-making to address the multifaceted sustainability challenges associated with Anthropocene systems of systems.
Paper Structure (15 sections, 21 equations, 4 figures, 1 table)

This paper contains 15 sections, 21 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: Inter-industrial relationships of economic sectors in terms of technical coefficients
  • Figure 2: Block Definition Diagram that defines the EIO model form.
  • Figure 3: Activity Diagram that defines the EIO model function.
  • Figure 4: Colored Petri Net representation of the EIO model

Theorems & Definitions (11)

  • Definition 1: System Operand SE-Handbook-Working-Group:2015:00
  • Definition 2: System Process Hoyle:1998:00SE-Handbook-Working-Group:2015:00
  • Definition 3: System Resource SE-Handbook-Working-Group:2015:00
  • Definition 4: Buffer Schoonenberg:2019:ISC-BK04Farid:2022:ISC-J51
  • Definition 5: CapabilitySchoonenberg:2019:ISC-BK04Farid:2022:ISC-J51Farid:2016:ISC-BC06
  • Definition 6: The Negative 3$^{rd}$ Order Hetero-functional Incidence Tensor (HFIT) $\widetilde{\cal M}_\rho^-$ Farid:2022:ISC-J51
  • Definition 7: The Positive 3$^{rd}$ Order Hetero-functional Incidence Tensor (HFIT) $\widetilde{\cal M}_\rho^+$ Farid:2022:ISC-J51
  • Definition 8: Engineering System Net Schoonenberg:2022:ISC-J50
  • Definition 9: Engineering System Net State Transition Function Schoonenberg:2022:ISC-J50
  • Definition 10: Operand NetFarid:2008:IEM-J04Schoonenberg:2019:ISC-BK04Khayal:2017:ISC-J35Schoonenberg:2017:IEM-J34
  • ...and 1 more