Model management is the task of selecting and applying appropriate analytical models by a Decision Support System. The selection of a model in current model management systems requires definitive boundaries or explicit rules and reasoning. Selection of a model, however, often requires examining choice attributes that have no clear definitions or that overlap in their applicability. The selection of a single model from among various alternative models may thus require components of fuzzy reasoning. In this paper, we examine the use of belief graphs, a fuzzy technique, to select an appropriate integer programming solution methodology based upon several problem formulation characteristics. Our prototype shows that belief graphs are effective at selecting model methodologies within the scope of the decision setting