Bicriteria Fixed-Charge Network Flow – Separating Fixed Costs and Flow Costs

Bicriteria Fixed-Charge Network Flow – Separating Fixed Costs and Flow Costs

Michael Stiglmayr,

University of Wuppertal


The fixed-charge network design problem is one of the classical network design problems. From a multiobjectve perspective its objective function is the weighted-sum of a network flow objective and the sum of the fixed costs (i.e. design costs). Flow can only be routed through those edges for which the respective binary design variable equals one. The single criteria flow problem is well studied in literature; a lot of different solution approaches have been developed and applied, including branch and cut, Lagrangian relaxation as well as heuristic methods like dynamic cost scaling. However, from an application point of view design costs and flow costs are not directly comparable. Usually the design costs are due a-priori, whereas the flow costs correspond to maintenance or operation costs which incur on a regular basis. In this talk we will present heuristic and exact solution approaches based on the two-phase method and ranking algorithms.


Michael Stiglmayr graduated with a diploma in technical mathematics at the University of Erlangen-Nuremberg in 2004 and received a PhD at the University of Wuppertal in 2010. His thesis examines discrete and continuous optimization problems in medical imaging applications.
Since 2010 Michael is an assistant professor at the University of Wuppertal. He is currently a visiting professor in mathematics at the University of Koblenz.
The focus of his research are different aspects of multiobjective optimization such as multiobjective combinatorial problems, computational complexity, representation of the non-dominated set and applications of multiobjective programming.

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