The dependency diagram of a mixed integer linear programme

Abstract

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier-Motzkin Elimination. This is explained in a paper referenced below. The paper, given here, extends the results to the Mixed Integer case (MILP). It is shown how projection of a MILP leads to a finite disjunction of polytopes. This is expressed as a set of inequalities (mirroring those in the LP case) augmented by correction terms with finite domains which are subject to linear congruences.

Keywords:

• integer programming
• elimination of variables
• projection
• linear congruences
• generalised Chinese remainder theorem