In this dissertation, we conduct both theoretical and computational research on dynamic decision-making problems under uncertainty involving discrete choices. First, we study a multiechelon uncapacitated lot-sizing problem in series with intermediate demands. For the two-echelon case, we give a polynomial-time dynamic programming algorithm and establish a hierarchy between the alternative formulations. For the general multiechelon case, we present a family of valid inequalities and show its strength. Our computational results show that the multicommodity formulation is very effective in solving uncapacitated multi-item two-echelon lot-sizing problem, and the branch-and-cut algorithm is very effective in solving capacitated multi-item multiechelon lot-sizing problem. Second, we study a finite-horizon stochastic decision-making problem involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a joint chance-constrained program and develop a branch-and-cut method. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. In the final part, we investigate a class of two-stage stochastic pure integer programs with finitely many realizations of the uncertain parameters. Based on Benders' method, we propose decomposition algorithms with parametric Gomory cuts, and demonstrate our algorithms by examples and prove the finite convergence of the proposed algorithms.