Abstract The paper presents a real-world decision-making problem in the context of the Brazilian Federal Police (BFP), which consists of establishing priorities for Police Operations. This study deals with allocating resources to trigger police operations that, while demanding more resources and specialized techniques, also promote the effectiveness of police actions more conspicuously and directly. Driven by the Value Focused Thinking methodology, the objectives and values of the Federal Police were structured and represented by criteria, which let police operations be evaluated and prioritized. The FITradeoff method was applied to rank the operations, with an innovative methodological perspective, which integrates two different paradigms for preference modelling: elicitation by decomposition and holistic evaluations. A mathematical modelling approach is presented to deal with the combination of both types of information obtained by the Decision Maker (DM), in order to search for dominance relations between alternatives. This study shows how incorporating holistic judgments in the process can be useful for tightening the decision process, since the inequalities obtained with holistic judgments have a high impact on the space of weights compatible with the DM’s preferences. A clear conceptual framework is presented for the analysis, showing how the application of such a combined approach to prioritizing special police operations adds a step to the decision-making processes and policies of the BFP, thereby broadening the managerial implications of tackling public security issues by seeking to solve them using management mathematics.