As complex mathematical models are increasingly adopted for business decision-making, difficulties arise in reusing solvers (i.e., model solving algorithms) against diverse models and data sets and thus the collaboration among users (model/solver builders and decision makers) in multiple departments becomes very difficult. To facilitate the solver reuse, this paper adopts the Web services technologies as the base technologies for linking the solvers to the models, both of which are created on different modeling paradigms and different system platforms, in unified system architecture. Specifically, this paper focuses on designing an ontology that represents the interfacing semantics of the model-solver interactions in a general and standardized form. By referring to the ontology, a model management system(MMS) can autonomously suggest a set of compatible solvers and apply them to individual models even though the decision makers are not knowledgeable enough about all the details of the models and the solvers. Thus, this Web services based MMS would improve the reusability of the solvers by relieving the decision makers from the risk of erroneous application of a solver to syntactically and semantically incompatible models and the burden of considerable understanding of model and solver semantics.