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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chernikov SN (1953). Systems of linear inequalities. Uspekhi Matematicheskikh Nauk 8(2): 7–13.
Kohler DA (1967). Projections of Convex Polyhedral Sets. Operations Research Center, University of California: Berkeley.
Langford CH (1927). Some theorems of deducibility. Annals of Mathematics I 28: 16–40.
Williams HP (1976). Fourier-Motzkin Elimination extended to integer programming problems. Journal of Combinatorial Theory 21: 118–123.
Williams HP (2013). The general solution of a mixed integer linear programme over a cone. Working paper LSEOR 13.139. Management Science Group, London School of Economics.
Williams HP (2016). The dependency diagram of a linear programme. Journal of the Operational Research Society 67(3): 450–456.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Williams, H. The dependency diagram of a mixed integer linear programme. J Oper Res Soc 68, 829–833 (2017). https://doi.org/10.1057/jors.2016.45
Published:
Issue Date:
DOI: https://doi.org/10.1057/jors.2016.45