  The Analytic Hierarchy Process (AHP) is widely used for decision making
involving multiple criteria. Elsner and van den Driessche introduced a
max-algebraic approach to the single criterion AHP. We extend this to the
multi-criteria AHP, by considering multi-objective generalisations of the
single objective optimisation problem solved in these earlier papers. We relate
the existence of globally optimal solutions to the commutativity properties of
the associated matrices; we relate min-max optimal solutions to the generalised
spectral radius; and we prove that Pareto optimal solutions are guaranteed to
exist.
