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The goals of resource management fall within the overall aims of autonomic and grid computing, namely the sharing of resources automatically, and the allocation of resources depending on both application and business needs. Resource allocation can be guided by policies which encapsulate decisions made by the management system. Policies can be used to encapsulate many different types of management decisions including possible corrective actions when a performance requirement of an application is not being satisfied and actions to take place when there is more demand then supply. System policy is derived from the interactions between Service Level Agreements (contractual agreements between businesses) and locally specified management rules. This paper explores the potential use of mathematical models (e.g., optimisation models) for relating the various types of policies. It describes the current and proposed work in applying policies to resource management in the context of autonomic and grid computing systems.