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. Subject classifications: Inventory/production: multi-item; operating characteristics; stochastic models. Queues: approximations; batch; multichannel; correlation. ∗Most of this research was carried out while the author was a post doctoral researcher at the Graduate School of Management of UC Irvine, supported in part by NSF grants DMI-9896339 and DMI-0084922. †Supported in part by NSF grants DMI-9896339 and DMI-0084922. ‡Supported in part by NSF grants ECS-9705392 and DMI-0085124. Part of this author’s research was undertaken while he was on leave at the Chinese University of Hong Kong, Dept. of Systems Engineering and Engineering Management, and supported by a Direct Grant from CUHK and by HK/RGC grant CUHK4376/99E.