Sequential Capacity Expansion Options

We consider a firm expanding its production capacity in stages under uncertainty. The firm decides on the investment times and the size of the investment lumps. This setting gives rise to an impulse control problem for which we derive a quasi-variational inequality that involves two state variables: a stochastic price process and a controlled capacity process. We provide a general verification theorem and construct an optimal two-dimensional (s,S)-type policy for a specific case. The firm “waits and sees” before investing until the perpetuity value of newly installed capacity exceeds the total opportunity cost by a sufficient margin. Our model generalizes extant models dealing with “the option to expand” capacity and makes predictions of both the optimal investment timing and the optimal scale of production.