Three-partition Inequalities for Constant Capacity Capacitated Fixed-charge Network Flow Problems

Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled by collapsing the corresponding subset of nodes defining the cut into a single node. In this work we give new valid inequalities for the capacitated fixed-charge network flow problem by exploiting additional information of the network. In particular, the new inequalities are based on a three-partitioning of the nodes and they can be modeled by collapsing the each partition into a single node. The three-partitions inequalities include the flow cover inequalities as a special case. We discuss the constant capacity case and give a polynomial separation algorithm for the inequalities. Finally, we report computational results with the new inequalities for networks with different characteristics.