Disaggregated Benders Decomposition for solving a Network Maintenance Scheduling Problem

We consider a problem concerning a network and a set of maintenance requests to be undertaken. We wish to schedule the maintenance in such a way as to minimise the impact on the total throughput of the network. We apply disaggregated Benders cuts and lazy constraints to solve the problem to optimality, as well as exploring the strengths and weaknesses of the technique. We prove that our Benders cuts are pareto optimal. Solutions to the LP relaxation also provide further valid inequalities to reduce total solve time. We implement these techniques on simulated data presented in previous papers, and compare our solution technique to previous methods and a direct MIP formulation. We prove optimality in many problem instances that have not previously been proven.