On feasibility cuts for chance-constrained multicommodity network design problems

Abstract: Problem definition: We study efficient exact solution approaches to solve chance-constrained multicommodity network design problems under demand uncertainty, an important class of network design problems. The chance constraint requires us to construct a network that meets future commodity demand sufficiently often, which makes the problem challenging to solve. Methodology/results: We develop a solution approach based on Benders' decomposition, and accelerate the approach with valid inequalities and cut strengthening. We particularly investigate the effects of different subproblem formulations on the strength of the resulting feasibility cuts. We propose a new formulation that we term FlowMIS, and investigate its properties. Additionally, we numerically show that FlowMIS outperforms standard formulations: in our complete solution approach with all enhancements enabled, FlowMIS solves 67 out of 120 solved instances the fastest, with an average speed-up of 2.0x over a basic formulation. Implications: FlowMIS generates strong feasibility cuts tailored to subproblems with a network flow structure. This results in reduced solution times for existing decomposition-based algorithms in the context of network design, and the ability to solve larger problems.