The feasibility determination problem involves deciding whether a design meets certain criteria based on a performance measure estimated through Monte Carlo simulation. It typically comes into play when the decision-maker faces the problem of selecting a subset of designs according to some prescribed standards. Feasibility determination of a finite set of alternative designs is a special case of the classical multiple comparisons with a control problem, in the sense that the control that we compare with here is modeled as known. Ranking and selection procedure focuses on intelligently allocating the total simulation budget to each design to better support the decisions when comparing a set of alternative designs. It is an issue of critical importance when the decision-maker faces a limited simulation budget. The ranking and selection procedure for feasibility determination provides the potential for significant simulation budget reduction while obtaining decisions with greater accuracy. In this thesis, we first investigate the performance of current asymptotically optimal allocation methods. We prove that under certain conditions, current methods perform no better than the naive equal allocation method. To achieve better performance when the total simulation budget is limited, we propose a new allocation method that is based on a finite simulation budget perspective. We prove that the simulation budget allocated by our method converges to the optimal value. We also provide a proof that our method always performs no worse than current asymptotically optimal allocation methods. Numerical experiments of three illustrative examples, a facility-sizing problem, and an emergency department setup problem are conducted to demonstrate the effectiveness of our method. The majority of the research in ranking and selection formulate the budget allocation problem as a static optimization problem. We demonstrate the inadequacy of this formulation. In Bayesian setting, we formulate the budget allocation as a stochastic control problem and provide a one-step lookahead policy. We also illustrate the stochastic control implementation of previous proposed finite budget allocation method. Numerical examples are provided to demonstrate the differences between static and dynamic methods. In simulation practice, different designs with close parameters often have similar performances. In this situation, we propose a new allocation method that takes the relationships between different designs into consideration. We use the kriging metamodel to capture the inter-design relationships and incorporate the information obtained from kriging into our allocation procedure based on the Bayesian framework. Computational results demonstrate the efficacy of this methodology.