Disaggregated Benders Decomposition for solving a Network Maintenance Scheduling Problem

TL;DR

This paper introduces a disaggregated Benders decomposition approach with lazy constraints for optimally scheduling network maintenance, significantly improving solution times and proving optimality in complex instances.

Contribution

It develops a novel disaggregated Benders decomposition method with proven Pareto optimal cuts and valid inequalities, enhancing the solution of network maintenance scheduling problems.

Findings

Proves Pareto optimality of Benders cuts.

Achieves optimal solutions in previously unsolved instances.

Reduces solve time using valid inequalities.

Abstract

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.