Capacity Expansion for Random Exponential Demand Growth with Lead Times
针对需求不确定且产能建设有提前期的情况，建立了一个产能扩张模型，通过设定服务水平和时机规则，将问题转化为无提前期的确定性模型，并分析了需求参数和提前期长度对扩张时机的影响。
The combination of demand uncertainty and a lead time for adding capacity creates the risk of capacity shortage during the lead time. We formulate a model of capacity expansion for uncertain exponential demand growth and deterministic expansion lead times when there is an obligation to provide a specified level of service. The service level, defined in terms of the ratio of expected lead-time shortage to installed capacity, is guaranteed by timing each expansion to begin when demand reaches a fixed proportion of the capacity position. Under this timing rule, the optimal facilities to install can be determined by solving an equivalent deterministic problem without lead times. Numerical results show the effects of the demand parameters and lead-time length on the expansion timing. The interaction of timing with expansion size is explored for the case when continuous facility sizes are available with economies of scale.