This paper presents a method to support the identification of the cause-effect relationships of strategic objectives of a strategy map of a balanced scorecard. A strategy map contains the strategic objectives of an organization, grouped into four perspectives (a) finances, (b) clients, (c) internal processes and (d) growth and learning, all of them linked through cause-effect relationships. The issue addressed in this paper is the identification of those relationships, topic in which the existing literature is scarce. A previous work was revisited, which uses the Analytic Hierarchy Process (AHP) to establish the "importance" of the arcs (relationships) of a strategy map. That work then deletes those arcs with an importance lower than a given threshold level defined by the authors. This paper goes beyond by selecting the arcs using a multi-objective linear programming model (LP). The model has two objectives (a) to minimize the number of selected relationships and (b) to maximize the total importance of the selected relationships. It is interested to see that a trade-off between both objectives is produced, so a control variable is used to incorporate the importance given to both objectives by managers. The paper also shows some applications of the method and their analysis. (C) 2014 Elsevier B.V. All rights reserved.