We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Applications of Mathematical Modeling | SpringerLink
Skip to main content

Applications of Mathematical Modeling

  • Chapter
  • First Online:
Methods and Models in Mathematical Programming
  • 736 Accesses

Abstract

In this chapter, a set of real-life applications of mathematical programming which are closely related to the methodologies presented in the previous chapters are addressed. For each application, the problem is defined, the model’s components are introduced and then, the model is presented in the general form. Afterward, it is solved on a given set of data with the aid of computer, and the results are analyzed.

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

Access this chapter

eBook
USD 16.99
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

Institutional subscriptions

References

  • Aichele A. Social network interdiction: reducing the capabilities of a terrorist network. Honors Project, U.S. Naval Academy. 2010.

    Google Scholar 

  • Assimakopoulos N. A network interdiction model for hospital infection control. Comput Biol Med 1987;17(6):413–422.

    Article  MathSciNet  Google Scholar 

  • Atkins K, Chen J, Kumar VA, Marathe A. The structure of electrical networks: a graph theory-based analysis. Int J Crit Infrastruct 2009;5(3):265–284.

    Article  Google Scholar 

  • Bisschop J. AIMMS-optimization modeling. Paragon Decision Technology, Harlem. http://www.aimms.com; 2012.

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

    Google Scholar 

  • Burkard RE, Çela E, Pardalos PM, Pitsoulis LS. The quadratic assignment problem. In: Handbook of combinatorial optimization. Springer;New York 1998. p. 1713–1809.

    Chapter  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 

  • Erdoğan S, Miller-Hooks E. A green vehicle routing problem. Transp Res E 2012;48(1):100–114.

    Article  Google Scholar 

  • Ghare PM, Montgomery DC, Turner WC. Optimal interdiction policy for a flow network. Nav Res Logist 1971;18(1):37–45.

    Article  MathSciNet  Google Scholar 

  • Gutfraind AS. New models of interdiction in networked systems. J Mil Oper Res Soc 2011 44 25–27.

    Google Scholar 

  • Hooshmand F, MirHassani SA. An effective bilevel programming approach for the evasive flow capturing location problem. Netw Spat Econ 2018a 18 (https://doi.org/10.1007/s11067-018-9415-0) 1-27.

    Article  MathSciNet  MATH  Google Scholar 

  • Hooshmand F, MirHassani SA. Time dependent green VRP with alternative fuel powered vehicles. Energy Syst 2018b (https://doi.org/10.1007/s12667-018-0283-y) 10 1-36.

    Article  MATH  Google Scholar 

  • Hooshmand F, MirHassani SA, Akhavein A. A scenario-based approach for master surgery scheduling under uncertainty. Int J Healthc Technol Manag 2017;16(3–4):177–203.

    Article  Google Scholar 

  • Hooshmand F, MirHassani SA, Akhavein A. Adapting GA to solve a novel model for operating room scheduling problem with endogenous uncertainty. Oper Res Health Care 2018 19, 26-43.(https://doi.org/10.1016/j.orhc.2018.02.002).

    Article  Google Scholar 

  • Hooshmand F, Mirarabrazi F, MirHassani SA. Efficient Benders decomposition for distance-based critical node detection problem. Omega 2019; https://doi.org/10.1016/j.omega.2019.02.006

  • Hosseini M, MirHassani SA, Hooshmand F. Deviation-flow refueling location problem with capacitated facilities: model and algorithm. Transp Res D 2017;54:269–281.

    Article  Google Scholar 

  • Koç C, Karaoglan I. The green vehicle routing problem: a heuristic based exact solution approach. Appl Soft Comput 2016;39:154–164.

    Article  Google Scholar 

  • Li S, Zhu Y, Li D, Kim D, Huang H. Rumor restriction in online social networks. In: 2013 IEEE 32nd international performance computing and communications conference (IPCCC); 2013; USA.

    Google Scholar 

  • Markowitz HM. Portfolio selection. J Financ 1952;7:77–91.

    Google Scholar 

  • McCollum B, McMullan P, Parkes AJ, Burke EK, Qu R. A new model for automated examination timetabling. Ann Oper Res 2012;194(1):291–315.

    Article  MathSciNet  Google Scholar 

  • MirHassani SA. Improving paper spread in examination timetables using integer programming. Appl Math Comput 2006;179(2):702–706.

    Article  MathSciNet  Google Scholar 

  • MirHassani SA, Abolghasemi N. A particle swarm optimization algorithm for open vehicle routing problem. Expert Syst Appl 2011;38(9):11547–11551.

    Article  Google Scholar 

  • MirHassani SA, Ebrazi R. A flexible reformulation of the refueling station location problem. Transp Sci 2012;47(4):617–628.

    Article  Google Scholar 

  • MirHassani SA, Ghorbanalizadeh M. The multi-product pipeline scheduling system. Comput Math Appl 2008;56(4):891–897.

    Article  MathSciNet  Google Scholar 

  • MirHassani SA, Jalaeian Bashirzadeh A. A GRASP meta-heuristic for two-dimensional irregular cutting stock problem. Int J Adv Manuf Technol 2015;81(1–4):455–464.

    Article  Google Scholar 

  • MirHassani SA, Mirhadi SM, Rahmani A. A computational approach to convex hull of zero-one MIP problems with special structure. J Inf Optim Sci 2015a;36(3):197–230.

    MathSciNet  Google Scholar 

  • MirHassani SA, Raeisi S, Rahmani A. Quantum binary particle swarm optimization-based algorithm for solving a class of bi-level competitive facility location problems. Optim Methods Softw 2015b;30(4):756–768.

    Article  MathSciNet  Google Scholar 

  • Moradi S, MirHassani SA. Transportation planning of petroleum products and integrated inventory management. Appl Math Model 2015;39(23–24):7630–7642.

    Article  MathSciNet  Google Scholar 

  • Moradi S, MirHassani SA, Hooshmand F. Efficient decomposition-based algorithm to solve long-term pipeline scheduling problem. Petroleum Science https://doi.org/10.1007/s12182-019-00359-3

  • Öncan T, Altınel IK, Laporte G. A comparative analysis of several asymmetric traveling salesman problem formulations. Comput Oper Res 2009;36(3):637–654.

    Article  MathSciNet  Google Scholar 

  • Rahmani A, MirHassani SA. Lagrangean relaxation-based algorithm for bi-level problems. Optim Methods Softw 2015;30(1):1–14.

    Article  MathSciNet  Google Scholar 

  • Ribeiro CC. Sports scheduling: problems and applications. Int Trans Oper Res 2012;19:201–226.

    Article  Google Scholar 

  • Salmeron J, Wood K, Baldick R. Analysis of electric grid security under terrorist threat. IEEE Trans Power Syst 2004;19(2):905–912.

    Article  Google Scholar 

  • Shen S, Smith JC, Goli R. Exact interdiction models and algorithms for disconnecting networks via node deletions. Discret Optim 2012;9:172–188.

    Article  MathSciNet  Google Scholar 

  • Sherali HD, Smith JC. Two-stage stochastic hierarchical multiple risk problems: models and algorithms. Math Program 2009;120:403–427.

    Article  MathSciNet  Google Scholar 

  • Steinrauf R. A network interdiction model. MSc Thesis, Naval Postgraduate School; 1991.

    Google Scholar 

  • Teles JP, Castro PM, Matos HA. Global optimization of water networks design using multiparametric disaggregation. Comput Chem Eng 2012;40:132–147.

    Article  Google Scholar 

  • Teles JP, Teles PM, Matos HA. Multi-parametric disaggregation technique for global optimization of polynomial programming problems. J Glob Optim 2013;55:227–251.

    Article  MathSciNet  Google Scholar 

  • Trick M. Formulations and reformulations in integer programming. In: International conference on integration of artificial intelligence (AI) and operations research (OR) techniques in constraint programming; 2004. New York : Springer p. 366–379.

    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). Applications of Mathematical Modeling. In: Methods and Models in Mathematical Programming. Springer, Cham. https://doi.org/10.1007/978-3-030-27045-2_6

Download citation

Publish with us

Policies and ethics