Skip to main content

Main Components of Mathematical Models

  • Chapter
  • First Online:
  • 867 Accesses

Abstract

In the previous chapter, the main components of a mathematical model (decision variables, constraints, objective function, and parameters) were described. This chapter provides more details about the types of variables, constraints, and objective functions and categorizes mathematical models. Also, a brief reference to the solution methods of mathematical models is provided.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Appa GM, Pitsoulis LS, Williams HP, editors. Handbook on modelling for discrete optimization. Springer;Boston, MA 2006.

    MATH  Google Scholar 

  • Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming: theory and algorithms.Chichester Wiley; 2006.

    Book  Google Scholar 

  • Beale EM, Tomlin JA. Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Proceedings of the 5th international conference on operations research; 1969; London.

    Google Scholar 

  • Beck A. Introduction to nonlinear optimization: theory, algorithms, and applications with MATLAB. Siam;Philadelphia, PA 2014.

    Book  Google Scholar 

  • Bertsimas D, Tsitsiklis JN. Introduction to linear optimization. Athena Scientific;Belmont, MA 1997.

    Google Scholar 

  • Bertsimas D, Weismantel R. Optimization over integers. Dynamic Ideas; Belmont, MA 2005.

    Google Scholar 

  • Birge JR, Louveaux F. Introduction to stochastic programming. Springer;New York 2015.

    MATH  Google Scholar 

  • Boyd S, Vandenberghe L. Convex optimization. Cambridge University Press;Philadelphia, PA 2004.

    Book  Google Scholar 

  • Bradley SP, Hax AC, Magnanti TL. Applied mathematical programming. Addison-Wesley;Reading, MA 1977.

    Google Scholar 

  • Castillo E, Gonejo AJ, Pedregal P, Garcia R, Alguacil N. Building and solving mathematical programming models in engineering and science. Wiley; Hoboken, NJ 2002.

    MATH  Google Scholar 

  • Chen DS, Batson RG, Dang Y. Applied integer programming: modeling and solution. Wiley;Hoboken, NJ 2010.

    MATH  Google Scholar 

  • Chinneck JW, Ramadan K. Linear programming with interval coefficients. J Oper Res Soc 2000;51(2):209–220.

    Article  Google Scholar 

  • Colson P, Marcotte P, Savard G. An overview of bilevel optimization. Ann Oper Res 2007;153(1):235–256.

    Article  MathSciNet  Google Scholar 

  • Conforti M, Cornuéjols G, Zambelli G. Integer programming. Springer;New York 2014.

    MATH  Google Scholar 

  • Dempe S. Foundations of bilevel programming. New York: Springer; 2002.

    MATH  Google Scholar 

  • Ehrgott M. Multicriteria optimization. Springer;Berlin 2005.

    MATH  Google Scholar 

  • Jeroslow RG. The polynomial hierarchy and a simple model for competitive analysis. Math Program 1985;32(2):146–164.

    Article  MathSciNet  Google Scholar 

  • Lew A, Mauch H. Dynamic programming: a computational tool. New York: Springer; 2006.

    MATH  Google Scholar 

  • Lu J, Han J, Hu Y, Zhang G. Multilevel decision-making: a survey. Inf Sci 2016;346–347(10):463–487.

    Article  MathSciNet  Google Scholar 

  • Marcotte P, Savard G, Semet F. A bilevel programming approach to the travelling salesman problem. Oper Res Lett 2004;32:240–248.

    Article  MathSciNet  Google Scholar 

  • Ramadan K. Linear programming with interval coefficients. MSc Thesis-Carleton University; 1996.

    Google Scholar 

  • Rao SS. Optimization theory and applications.New Delhi : New Age International 1978.

    Google Scholar 

  • Sarker RA, Newton CS. Optimization modelling: a practical approach. Taylor & Francis;Boca Raton, FL 2007.

    Book  Google Scholar 

  • Schrijver A. Theory of linear and integer programming. Wiley;Chichester 1998.

    MATH  Google Scholar 

  • Straffin PD. Game theory and strategy. Providence, RI: American Mathematical Society; 1993.

    MATH  Google Scholar 

  • Taha HA. Integer programming: theory, applications, and computations. Academic;Cambridge, MA 1975.

    MATH  Google Scholar 

  • Winston WL. Operations research: applications and algorithms. Cengage Boston, MA; 2003.

    MATH  Google Scholar 

  • Wolsey LA, Nemhauser GL. Integer and combinatorial optimization. Wiley;Hoboken, NJ 1999.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

MirHassani, S.A., Hooshmand, F. (2019). Main Components of Mathematical Models. In: Methods and Models in Mathematical Programming. Springer, Cham. https://doi.org/10.1007/978-3-030-27045-2_2

Download citation

Publish with us

Policies and ethics