Compact MILP models for the Discrete Cost Multicommodity Network Design Problem

We investigate a challenging NP-hard variant of Network Design Problems called the Discrete Cost Multicommodity Network Design Problem (DCMNDP), which arises in a wide range of real-life situations such as telecommunication settings, multicast routing and aircraft assignment. In graph theory terms, the DCMNDP requires designing a minimum cost network by installing at most one facility on each edge while the installed capacities permit the routing of a prescribed multi-commodity flow value. We focus on investigating polynomial-sized Mixed Integer Linear Programming (MILP) formulations. Besides a basic arc-flow formulation, two new overflow and flow aggregation based formulations are proposed. To improve the performance of the proposed formulations, valid cuts/constraints are appended. Preliminary computational results are conducted on real-world networks and randomly generated instances using a general-purpose MIP solver.