Complex mathematical models are often built to describe a physical process that would otherwise be extremely difficult, too costly or sometimes impossible to analyze. Generally, these models require solutions to many partial differential equations. As a result, the computer codes may take a considerable amount of time to complete a single evaluation. A time tested method of analysis for such models is Monte Carlo simulation. These simulations, however, often require many model evaluations, making this approach too computationally expensive. To limit the number of experimental runs, it is common practice to model the departure as a Gaussian stochastic process (GaSP) to develop an emulator of the computer model. One advantage for using an emulator is that once a GaSP is fit to realized outcomes, the computer model is easy to predict in unsampled regions of the input space. This is an attempt to 'characterize' the overall model of the computer code. Most of the historical work on design and analysis of computer experiments focus on the characterization of the computer model over a large region of interest. However, many practitioners seek other objectives, such as input screening (Welch et al., 1992), mapping a response surface, or optimization (Jones et al., 1998). Only recently have researchers begun to consider these topics in the design and analysis of computer experiments. In this dissertation, we explore a more traditional response surface approach (Myers, Montgomery and Anderson-Cook, 2009) in conjunction with traditional computer experiment methods to search for the optimum response of a process. For global optimization, Jones, Schonlau, and Welch's (1998) Efficient Global Optimization (EGO) algorithm remains a benchmark for subsequent research of computer experiments. We compare the proposed method in this paper to this leading benchmark. Our goal is to show that response surface methods can be effective means towards estimating an optimum response in the computer experiment framework.