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