An aggressive reduction scheme for the simple plant location problem

Pisinger et al. introduced the concept of ‘aggressive reduction’ for large-scale combinatorial optimisation problems. The idea is to spend much time and effort in reducing the size of the instance, using information obtained from a sequence of fast lowerand upper-bounding procedures. The hope is that the reduced instance will then be small enough to be solved by an exact algorithm. We present an aggressive reduction scheme for the simple plant location problem, also known as the uncapacitated facility location problem. The scheme involves a pre-processing phase, a dual ascent phase, a Lagrangian phase, and a Linear Programming phase. Using this scheme, in conjunction with the CPLEX MIP solver, we are able to solve to proven optimality larger instances than any previously solved in the literature.