Mathematical Foundations of Input–Output Models

  • Raymond R. TanEmail author
  • Kathleen B. Aviso
  • Michael Angelo B. Promentilla
  • Krista Danielle S. Yu
  • Joost R. Santos
Part of the Lecture Notes in Management and Industrial Engineering book series (LNMIE)


A detailed discussion of the mathematical foundations of input–output analysis is given in this chapter. The basic data format used in economic input–output models is discussed first, leading to the basic formulation and its solution using the matrix inversion approach. The use of the basic input–output model for key sector analysis is illustrated with the aid of an example. Applications of the input–output equations are depicted using spreadsheets, which provide an ideal foundation to understand the LINGO codes in subsequent chapters. Then, extensions involving mathematical programming, regional input–output models, and physical input–output models are considered; these variants are also illustrated with examples.


Leontief inverse Key sector Optimization Mathematical programming Regional input–output model Physical input–output model 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Raymond R. Tan
    • 1
    Email author
  • Kathleen B. Aviso
    • 1
  • Michael Angelo B. Promentilla
    • 1
  • Krista Danielle S. Yu
    • 2
  • Joost R. Santos
    • 3
  1. 1.Chemical Engineering DepartmentDe La Salle UniversityManilaPhilippines
  2. 2.School of EconomicsDe La Salle UniversityManilaPhilippines
  3. 3.Department of Engineering Management and SystemsGeorge Washington UniversityWashingtonUSA

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