Editing Integer programming (section)

==Variants==
'''Mixed-integer linear programming''' ('''MILP''') involves problems in which only some of the variables, <math>x_i</math>, are constrained to be integers, while other variables are allowed to be non-integers.

'''Zero–one linear programming''' (or '''binary integer programming''') involves problems in which the variables are restricted to be either 0 or 1. Any bounded integer variable can be expressed as a combination of [[binary data|binary variables]].<ref>{{cite book|last=Williams|first=H.P.|title=Logic and integer programming|series=International Series in Operations Research & Management Science|year=2009|volume=130|isbn= 978-0-387-92280-5}}</ref> For example, given an integer variable, <math>0\le x\le U</math>, the variable can be expressed using <math>\lfloor \log_2U\rfloor+1</math> binary variables:
:<math display=block>
x = x_1+2x_2+4x_3+\cdots+2^{\lfloor \log_2U\rfloor}x_{\lfloor \log_2U\rfloor+1}.
</math>