A compact formulation of a mixed-integer set

作者：Agra Agostinho^*; Constantino Miguel

来源：Optimization, 2010, 59(5): 729-745.

DOI：10.1080/02331930802434914

• polyhedral characterization
• mixed-integer programming
• compact formulation

We consider mixed-integer sets of the form X {(s, y) is an element of R(+) x Z(n) : s + a(j)y(j) >= b(j), for all j is an element of N}. A polyhedral characterization for the case where X is defined by two inequalities is provided. From that characterization we give a compact formulation for the particular case where the coefficients of the integer variables can take only two possible integer values a(1), a(2) is an element of Z(+) : X(n,m) = {(s, y) is an element of R(+) x Z(n+m) : s + a(1)y(j) >= b(j), for all j is an element of N(1), s + a(2)y(j) >= b(j), j is an element of N(2)} where N(1) = {1, ... , n}, N(2) = {n + 1, ... , n + m}. In addition, we discuss families of facet-defining inequalities for the convex hull of X(n,m).

• 出版日期2010