  We address the exact resolution of a MINLP model where resources can be
activated in order to satisfy a demand (a partitioning constraint) while
minimizing total cost. Cost functions are convex latency functions plus a fixed
activation cost. A branch and bound algorithm is devised, featuring three
important characteristics. First, the lower bound (therefore each subproblem)
can be computed in O(nlog n). Second, to break symmetries resulting in improved
efficiency, the branching scheme is n-ary (instead of the "classical" binary).
Third, a very affective heuristic is used to compute a good upper bound at the
root node of the enumeration tree. All three features lead to a successful
comparison against CPLEX MIPQ, which is the fastest among several commercial
and open-source solvers: computational results showing this fact are provided.
