Optimal Capacity Expansion Over an Infinite Horizon

The problem of choosing an optimal initial capacity expansion from a finite number of durable facility sizes is affected by potential future expansion decisions. As we consider such expansions over longer and longer study horizons, the optimal initial facility choice can fluctuate due to end-of-study effects. We discuss an algorithm that will determine, for arbitrary deterministic demand profiles, how long a horizon is sufficient to reach stability in the first facility choice. Moreover, it is shown that this first choice is the optimal first choice for the infinite horizon problem. We also establish an explicit analytical formula for a study horizon guaranteed to provide a first facility size that, followed by an infinite horizon expansion strategy, will attain a discounted cost within a predetermined maximal error of the optimal infinite horizon cost.