Department of Mathematics

The "multi-type" or "modular" capacitated facility location problem is a discrete location model that addresses non-convex piecewise linear production costs as, for instance, staircase cost functions. The literature basically distinguishes three different ways to formulate non-convex piecewise linear cost minimization problems: the convex combination model, the incremental model and the multiple choice model. All three models are generally equivalent, but in case of the MCFLP, the latter one allows to include additional variable upper bounds (implied bounds) that strengthen the LP relaxation. We show that the latter formulation, with these inequalities included, strictly dominates the other two ways of formulating the problem. We additionally investigate different strategies of including these variable upper bounds within the model using a common MIP solver.