This paper provides a sensitivity analysis of the judgements used in the Analytic Hierarchy Process in relation to the rank reversal produced in two different situations: the selection of the best alternative (P. α problem), and the ranking of all the alternatives (P. γ problem). In both cases, under the supposition that we employ the row geometric mean method to determine the local priorities, we obtain, in the case of a single criterion, a local stability interval for each judgement, for each alternative and for the paired comparisons matrix which allow us to guarantee the best alternative and the ranking of all of them (the P. α and P. γ problems, respectively). With respect to these three situations (judgement, alternative and matrix) and two problems (P. α and P. γ) we also calculate a local stability index to detect the critical values of the resolution process. Both the local stability intervals and indexes are used as management tools in the final stage of the decision making process, that is to say, the exploitation phase, especially in the negotiation process and the search for consensus between the actors.
