Bounds for aggregating nodes in network problems

It is often necessary or desirable in practice to replace a large, detailed optimization model with a smaller, approximate model. It would be useful to have bounds on the error resulting from this process of aggregation. This paper develops such bounds for a class of linear minimum-cost network-flow problems, where groups of nodes in a large problem are replaced by aggregate nodes. Two types of bounds are derived: A priori bounds are available before solving the aggregated problem; a posteriori bounds, which are generally tighter, may be computed afterwards.