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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aichele A. Social network interdiction: reducing the capabilities of a terrorist network. Honors Project, U.S. Naval Academy. 2010.
Assimakopoulos N. A network interdiction model for hospital infection control. Comput Biol Med 1987;17(6):413–422.
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.
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.
Burkard RE, Çela E, Pardalos PM, Pitsoulis LS. The quadratic assignment problem. In: Handbook of combinatorial optimization. Springer;New York 1998. p. 1713–1809.
Castillo E, Gonejo AJ, Pedregal P, Garcia R, Alguacil N. Building and solving mathematical programming models in engineering and science. Wiley; Hoboken, NJ 2002.
Erdoğan S, Miller-Hooks E. A green vehicle routing problem. Transp Res E 2012;48(1):100–114.
Ghare PM, Montgomery DC, Turner WC. Optimal interdiction policy for a flow network. Nav Res Logist 1971;18(1):37–45.
Gutfraind AS. New models of interdiction in networked systems. J Mil Oper Res Soc 2011 44 25–27.
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.
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.
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.
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).
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.
Koç C, Karaoglan I. The green vehicle routing problem: a heuristic based exact solution approach. Appl Soft Comput 2016;39:154–164.
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.
Markowitz HM. Portfolio selection. J Financ 1952;7:77–91.
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.
MirHassani SA. Improving paper spread in examination timetables using integer programming. Appl Math Comput 2006;179(2):702–706.
MirHassani SA, Abolghasemi N. A particle swarm optimization algorithm for open vehicle routing problem. Expert Syst Appl 2011;38(9):11547–11551.
MirHassani SA, Ebrazi R. A flexible reformulation of the refueling station location problem. Transp Sci 2012;47(4):617–628.
MirHassani SA, Ghorbanalizadeh M. The multi-product pipeline scheduling system. Comput Math Appl 2008;56(4):891–897.
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.
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.
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.
Moradi S, MirHassani SA. Transportation planning of petroleum products and integrated inventory management. Appl Math Model 2015;39(23–24):7630–7642.
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.
Rahmani A, MirHassani SA. Lagrangean relaxation-based algorithm for bi-level problems. Optim Methods Softw 2015;30(1):1–14.
Ribeiro CC. Sports scheduling: problems and applications. Int Trans Oper Res 2012;19:201–226.
Salmeron J, Wood K, Baldick R. Analysis of electric grid security under terrorist threat. IEEE Trans Power Syst 2004;19(2):905–912.
Shen S, Smith JC, Goli R. Exact interdiction models and algorithms for disconnecting networks via node deletions. Discret Optim 2012;9:172–188.
Sherali HD, Smith JC. Two-stage stochastic hierarchical multiple risk problems: models and algorithms. Math Program 2009;120:403–427.
Steinrauf R. A network interdiction model. MSc Thesis, Naval Postgraduate School; 1991.
Teles JP, Castro PM, Matos HA. Global optimization of water networks design using multiparametric disaggregation. Comput Chem Eng 2012;40:132–147.
Teles JP, Teles PM, Matos HA. Multi-parametric disaggregation technique for global optimization of polynomial programming problems. J Glob Optim 2013;55:227–251.
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
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
DOI: https://doi.org/10.1007/978-3-030-27045-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27044-5
Online ISBN: 978-3-030-27045-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)