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A compact formulation of a mixed-integer set
- DOI:
- 10.1080/02331930802434914
pages 729-745
Available online: 15 Oct 2008Abstract
We consider mixed-integer sets of the form X = {(s, y) 
+ × 
n : s + a j y j ≥ b j , 
j 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 + : X n,m = {(s, y) + × n+m : s + a 1 y j ≥ b j , j N 1, s + a 2 y j ≥ b j , j 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 .
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- Available online: 15 Oct 2008
Author affiliations
- a DMat and CEOC, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
- b DEIO and CIO, University of Lisbon, Edifício C6, Campo Grande, 1749-016 Lisboa, Portugal
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