The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand with Lead Times

We formulate a model of capacity expansion that is relevant to a service provider for whom the cost of capacity shortages would be considerable but difficult to quantify exactly. Due to demand uncertainty and a lead time for adding capacity, not all shortages are avoidable. In addition, technological innovations will reduce the cost of adding capacity but may not be completely predictable. Analytical expressions for the infinite horizon expansion cost and shortages are optimized numerically. Sensitivity analyses allow us to determine the impact of technological change on the optimal timing and sizes of capacity expansions to account for economies of scale, the time value of money and penalties for insufficient capacity.