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Integer Linear Programming models have been applied to a great
varieties of problems and can be solved by enumeration, branch-
and-bound or cutting plane methods. However, no matter which
method is employed, solving an ILP system is a time-consuming
task. In particular, if the systems are inconsistent they are
noted after complete operations. It is certainly a waste.
Althought, there are some studies proposed the inconsistent
structures of LP systems but there is a solution on LP does not
imply that is consistent on ILP. That is the reason why we must
discuss the inconsistent structure on ILP individually. The
main purposes of this study are to identify the discrete
inconsistent systems and to develop a calibration method for
providing at least one solution. In this study, Chapter 1
introduces the motivation and purposes. Part 1 contains four
chapters. We investigate the inconsistent structure of ILPs and
provide consistent and inconsistent properties for the
Nonnegative ILP systems. In Chapter 2, we introduce the
literature review of this paper, and in Chapter 3, we present
the inconsistent structure of ILP systems which is for the
Nonnegative Integer Linear Programming and in the Chapter 4 we
extend the properties in the Chapter 3 into most general
systems. In Chapter 5, we summarize the properties of the
inconsistent stuctures. Part 2 contains one chapter, Chapter 6.
In Chapter 6, we develop a model and a solution method for
providing at least one solution. Finally, we summarize the
whole study in Chapter 7.
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