A decomposition approach to solve a bilevel capacitated facility location problem with equity constraints

In this paper, we study a capacitated facility location problem 1 with two decision makers. One (say, the leader) decides on which subset of facilities to open and the capacity to be installed in each facility with the goal of minimizing the overall costs; the second decision maker (say, the follower), once the facilities have been designed, aims at maximizing the profit deriving from satisfying the demands of a given set of clients beyond a certain threshold imposed by the leader. The leader can foresee but cannot control the follower’s behavior. The resulting mathematical formulation is a discrete–continuous bilevel optimization problem. We propose a decomposition approach to cope with the bilevel structure of the problem and the integrality of a subset of variables under the control of the leader. Such a proposal has been tested on a set of benchmark instances available in the literature.