The follower competitive facility location problem under the nested logit choice rule.

•The competitive facility location problem under the nested logit rule is studied.•Proof of the concavity of the objective function is presented.•A branch and cut approach over a generalized linear reformulation is implemented.•Two new inequalities are introduced: improved submodular cuts and one-opt cuts.•Locations with nested logit are closer to reality than with multinomial logit.