# Disaggregated Benders decomposition and lazy constraints for solving the budget-constrained dynamic uncapacitated facility location and network design problem

## TL;DR

This paper introduces a novel approach combining disaggregated Benders decomposition and lazy constraints to solve the complex budget-constrained DUFLNDP efficiently, achieving optimal solutions for previously unsolvable instances.

## Contribution

The paper develops a new disaggregated Benders decomposition method with Pareto-optimal cuts and lazy constraints for the DUFLNDP, enabling optimal solutions for larger instances.

## Key findings

- Successfully solved many previously unsolvable instances to optimality.
- Demonstrated the effectiveness of disaggregated Benders with Pareto-optimal cuts.
- Improved solution times and scalability for the DUFLNDP.

## Abstract

We present an approach for solving to optimality the budget-constrained Dynamic Uncapacitated Facility Location and Network Design problem (DUFLNDP). This is a problem where a network must be constructed or expanded and facilities placed in the network, subject to a budget, in order to satisfy a number of demands. With the demands satisfied, the objective is to minimise the running cost of the network and the cost of moving demands to facilities. The problem can be disaggregated over two different sets simultaneously, leading to many smaller models which can be solved more easily. Using disaggregated Benders decomposition and lazy constraints, we solve many instances to optimality that have not previously been solved. We use an analytic procedure to generate Benders optimality cuts which are provably Pareto-optimal.