  We study a general class of quadratic capacitated $p$-location problems
facility location problems with single assignment where a non-separable,
non-convex, quadratic term is introduced in the objective function to account
for the interaction cost between facilities and customer assignments. This
problem has many applications in the field of transportation and logistics
where its most well-known special case is the single-allocation hub location
problem and its many variants. The non-convex, binary quadratic program is
linearized by applying a reformulation-linearization technique and the
resulting continuous auxiliary variables are projected out using Benders
decomposition. The obtained Benders reformulation is then solved using an exact
branch-and-cut algorithm that exploits the underlying network flow structure of
the decomposed separation subproblems to efficiently generate strong
Pareto-optimal Benders cuts. Additional enhancements such as a matheuristic, a
partial enumeration procedure, and variable elimination tests are also embedded
in the proposed algorithmic framework. Extensive computational experiments on
benchmark instances (with up to 500 nodes) and on a new set of instances (with
up to 1,000 nodes) of four variants of single-allocation hub location problems
confirm the algorithm's ability to scale to large-scale instances.
