Fraud detection is a key activity with serious socio-economical impact. Inspection activities associated with this task are usually constrained by limited available resources. Data analysis methods can provide help in the task of deciding where to allocate these limited resources in order to optimise the outcome of the inspection activities. This paper presents a multi-strategy learning method to address the question of which cases to inspect first. The proposed methodology is based on the utility theory and provides a ranking ordered by decreasing expected outcome of inspecting the candidate cases. This outcome is a function not only of the probability of the case being fraudulent but also of the inspection costs and expected payoff if the case is confirmed as a fraud. The proposed methodology is general and can be useful on fraud detection activities with limited inspection resources. We experimentally evaluate our proposal on both an artificial domain and on a real world task.