The objective of this thesis is to develop and analyse two stochastic control problems arising in the context of investment capacity expansion. In both problems the underlying market fluctuations are modelled by a geometric Brownian motion. The decision maker’s aim is to determine admissible capacity expansion strategies that maximise appropriate expected present-value performance criteria. In the first model, capacity expansion has price/demand impact and involves proportional costs. The resulting optimisation problem takes the form of a singular stochastic control problem. In the second model, capacity expansion has no impact on price/demand but is associated with fixed as well as proportional costs, thus resulting in an impulse control problem. Both problems are completely solved and the optimal strategies are fully characterised. In particular, the value functions are constructed explicitly as suitable classical solutions to the associated Hamilton-Jacobi-Bellman equations