Order fill rate, leadtime variability, and advance demand information in an assemble-to-order system

We study an assemble-to-order system with stochastic leadtimes for component replenishment. There are multiple product types, of which orders arrive at the system following batch Poisson processes. Base-stock policies are used to control component inventories. We analyze the system as a set of queues driven by a common, multiclass batch Poisson input, and derive the joint queue-length distribution. The result leads to simple, closed-form expressions of the first two moments, in particular the covariances, which capture the dependence structure of the system. Based on the joint distribution and the moments, we derive easy-to-compute approximations and bounds for the order fulfillment performance measures. We also examine the impact of demand and leadtime variability, and investigate the value of advance demand information.