Editing Integer programming (section)

==Applications==

There are two main reasons for using integer variables when modeling problems as a linear program:
#The integer variables represent quantities that can only be integer. For example, it is not possible to build 3.7 cars.
#The integer variables represent decisions (e.g. whether to include an edge in a [[Graph (discrete mathematics)|graph]]) and so should only take on the value 0 or 1.
These considerations occur frequently in practice and so integer linear programming can be used in many applications areas, some of which are briefly described below.

===Production planning===
Mixed-integer programming has many applications in industrial productions, including job-shop modelling. One important example happens in agricultural [[production planning]] and involves determining production yield for several crops that can share resources (e.g. land, labor, capital, seeds, fertilizer, etc.). A possible objective is to maximize the total production, without exceeding the available resources. In some cases, this can be expressed in terms of a linear program, but the variables must be constrained to be integer.

===Scheduling===

These problems involve service and vehicle scheduling in transportation networks.  For example, a problem may involve assigning buses or subways to individual routes so that a timetable can be met, and also to equip them with drivers. Here binary decision variables indicate whether a bus or subway is assigned to a route and whether a driver is assigned to a particular train or subway. The zero–one programming technique has been successfully applied to solve a project selection problem in which projects are mutually exclusive and/or technologically interdependent.

===Territorial partitioning===

Territorial partitioning or districting problems consist of partitioning a geographical region into districts in order to plan some operations while considering different criteria or constraints. Some requirements for this problem are: contiguity, compactness, balance or equity, respect of natural boundaries, and socio-economic homogeneity. Some applications for this type of problem include: political districting, school districting, health services districting and waste management districting.

===Telecommunications networks===

The goal of these problems is to design a network of lines to install so that a predefined set of communication requirements are met and the total cost of the network is minimal.<ref>{{cite web|last1=Borndörfer|first1=R.|last2=Grötschel|first2=M.|author2-link= Martin Grötschel |title=Designing telecommunication networks by integer programming|url=http://www.zib.de/groetschel/teaching/SS2012/120503Vorlesung-DesigningTelcomNetworks-reduced.pdf|year=2012}}</ref>  This requires optimizing both the topology of the network along with setting the capacities of the various lines.  In many cases, the capacities are constrained to be integer quantities.  Usually there are, depending on the technology used, additional restrictions that can be modeled as linear inequalities with integer or binary variables.

===Cellular networks===
The task of frequency planning in [[GSM]] mobile networks involves distributing available frequencies across the antennas so that users can be served and interference is minimized between the antennas.<ref>{{cite web|last=Sharma|first=Deepak|title=Frequency Planning|url=http://www.slideshare.net/deepakecrbs/gsm-frequency-planning|year= 2010}}</ref>  This problem can be formulated as an integer linear program in which binary variables indicate whether a frequency is assigned to an antenna.

=== Other applications ===

* [[Cashflow matching|Cash flow matching]]
* [[Energy system]] optimization<ref>{{Cite journal|last1=Morais|first1=Hugo|last2=Kádár|first2=Péter|last3=Faria|first3=Pedro|last4=Vale|first4=Zita A.|last5=Khodr|first5=H. M.|date=2010-01-01|title=Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming|url=http://www.sciencedirect.com/science/article/pii/S0960148109001001|journal=Renewable Energy|language=en|volume=35|issue=1|pages=151–156|doi=10.1016/j.renene.2009.02.031|bibcode=2010REne...35..151M |issn=0960-1481|hdl=10400.22/1585|hdl-access=free}}</ref><ref>{{Cite journal|last1=Omu|first1=Akomeno|last2=Choudhary|first2=Ruchi|last3=Boies|first3=Adam|date=2013-10-01|title=Distributed energy resource system optimisation using mixed integer linear programming|url=http://www.sciencedirect.com/science/article/pii/S0301421513003418|journal=Energy Policy|language=en|volume=61|pages=249–266|doi=10.1016/j.enpol.2013.05.009|bibcode=2013EnPol..61..249O |s2cid=29369795 |issn=0301-4215}}</ref>
* [[Unmanned aerial vehicle|UAV]] [[Guidance system|guidance]]<ref>{{Cite book|last1=Schouwenaars|first1=T.|last2=Valenti|first2=M.|last3=Feron|first3=E.|last4=How|first4=J.|title=2005 IEEE Aerospace Conference |chapter=Implementation and Flight Test Results of MILP-based UAV Guidance |date=2005|pages=1–13|doi=10.1109/AERO.2005.1559600|isbn=0-7803-8870-4|s2cid=13447718}}</ref><ref>{{Cite journal|last1=Radmanesh|first1=Mohammadreza|last2=Kumar|first2=Manish|date=2016-03-01|title=Flight formation of UAVs in presence of moving obstacles using fast-dynamic mixed integer linear programming|journal=Aerospace Science and Technology|language=en|volume=50|pages=149–160|doi=10.1016/j.ast.2015.12.021|issn=1270-9638|doi-access=free|bibcode=2016AeST...50..149R }}</ref>
* [[Transit map]] [[Graph drawing|layouting]]<ref>{{cite arXiv |last1=Bast |first1=Hannah |last2=Brosi |first2=Patrick |last3=Storandt |first3=Sabine |date=2017-10-05 |title=Efficient Generation of Geographically Accurate Transit Maps |class=cs.CG |eprint=1710.02226 }}</ref>