The capacity expansion problems involve determination of the optimum timing and sizing of the capacity for the facilities that have to meet a given demand function. There are various versions of the problem in the literature. In this thesis, a mathematical model for the expansion of a facility producing a single commodity is formulated. This formulation is then used for solving the capacity expansion problem for an optical disc manufacturing system, producing two types of products by the use of two different capacity types. The effects of the technological improvements and economies of scale are considered. The dynamic programming approach is used and a forward recursion algorithm is devised and coded on a personal computer.