Various investment and operational practices, such as investing in flexible manufacturing systems and writing contracts to hedge the future risks, increasingly require tools for the valuation of contingent claims whose values depend on multiple underlying stochastic variables. These contingent claims incorporate advanced features, such as the early exercise of options, intermediate decisions, optimal policies, and possible causes of the dynamic behavior of the economic and operational environments. It would be impractical to utilize single-regime models, which specify a given mean and volatility to represent the evolution of an underlying variable, to describe the uncertainties from those economic and operational environments. Therefore, regime-switching models, which allow changes in the mean and volatility of the underlying stochastic variables over time, emerge as an alternative approach. Since the current literature on the regime-switching models mainly focuses on modeling and valuing an option on a single stochastic variable, the existing regime-switching models can not be applied to value options on several financial and non-financial regime-switching variables. Those options are complicated and require the development of a lattice approach, which is a discrete representation of a continuous process. Thus, one of the primary goals of this research is to develop a lattice approach that can be applied to value options on multiple underlying stochastic processes with multiple regimes. In this thesis, the existing lattice approach is extended in two major directions:​ lattice for a single stochastic process with multiple regimes, and lattice for multiple stochastic processes with multiple regimes. We then present three applications for the proposed lattices. The first application prices swing options under price uncertainty. The second application incorporates the product life cycle in valuing the flexibility of a manufacturing system that has three capacity options:​ expansion, contraction, and switching. The third application prices European and American rainbow options on correlated multiple regime-switching stochastic processes. We show that when compared with the Monte Carlo simulation, the proposed lattice for multiple stochastic processes with multiple regimes is computationally efficient and converged to the actual value of the options within a smaller number of steps.