Capacity Expansion with Lead Times and Autocorrelated Random Demand

The combination of uncertain demand and lead times for installing capacity creates the risk of shortage during the lead time, which may have serious consequences for a service provider with dependent customers. This paper analyzes a model of capacity expansion with autocorrelated random demand and a fixed lead time for adding capacity. To provide a specified level of service, a discrete time expansion timing policy uses a forecast error-adjusted minimum threshold level of excess capacity position to trigger an expansion. Under this timing policy, the expansion cost can be minimized by solving a deterministic dynamic program. We study the effects of demand characteristics and the lead time length on the capacity threshold. Autocorrelation acts similarly to randomness in hastening expansions but has a smaller impact, especially when lead times are short. However, the failure either to recognize autocorrelation or to accurately estimate its extent can cause substantial policy errors.