New partial aggregations for multicommodity network flow problems: An application to the fixed-charge network design problem

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in speed at which LP can be solved, as it linear constraints and variables. The conventional approach to improve solve time relaxation Mixed Integer Programming (MIP) model that encodes such instance aggregate all have same origin or destination. However, bound resulting significantly worsen, tempers efficiency aggregating techniques. In this paper, we introduce concept partial aggregation aggregates over subset instead entire underlying network. This offers high level control on trade-off between size aggregated MIP quality its bound. We apply two different models for design problem. Our computational study benchmark instances confirms controlled by aggregation, choosing good allow us original large-scale faster than without with full aggregation. • new commodity representations problems. aggregations fixed-charge design. polyhedra proposed existing formulations. perform extensive instances.