MIP presolve techniques for a PDE-based supply chain model

Authors:
Agnes Dittel;Armin Fugenschuh;Simone Gottlich;Michael Herty
Affiliations:
Fachbereich Mathematik, Technische Universitat Darmstadt, Darmstadt, Germany;Fachbereich Mathematik, Technische Universitat Darmstadt, Darmstadt, Germany;Fachbereich Mathematik, Technische Universitat Kaiserslautern, Kaiserslautern, Germany;Department of Mathematics, RWTH Aachen University, Aachen, Germany
Venue:
Optimization Methods & Software
Year:
2009

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Abstract

We consider a mixed-integer linear program (MIP) for supply chains that has been derived in [A. Fugenschuh, S. Gottlich, M. Herty, A. Klar, and A. Martin, A discrete optimization approach to large scale supply networks based on partial differential equations, SIAM J. Sci. Comput. 30(3) (2008), pp. 1490-1507] from a continuous supply chain model based on partial differential equations (PDEs). We develop new presolve techniques where knowledge about the continuous framework is involved. For this purpose, several presolve levels are introduced and compared numerically. The presented methods reduce the size of the MIP in terms of number of variables and constraints, accelerate the solution process of the MIP when using numerical solvers, and finally assure that such solvers are able to find feasible solutions at all, where in some cases they would fail without.