We consider designing a service system in which the service provider performs an operation on incoming transactions from a client. In the design process it is critical to balance the cost invested in provisioning the system capacity against the benefit of satisfying the system performance requirements specified in service level agreements with clients. The service capacity decision is based on information on parameters such as transaction arrival rate, service level required by the client, and fixed/variable cost rates. In most cases, some input parameters such as demand/transaction arrival rate are uncertain at design time and values used are estimates. Nonetheless, violating the service level requirement during actual operation may result in a penalty cost. We identify alternative approaches suitable for analyzing this design problem by surveying the literature on service system design and related areas. To compare several selected approaches, we develop a model using each approach to determine the optimal system capacity of a single-server service system. We conclude by presenting our thoughts on when to use what approach.