Backorder Minimization in Multiproduct Assemble-to-Order Systems

We consider a multiproduct assemble-to-order system. Components are built to stock with inventory controlled by base-stock rules, but final products are assembled to customer orders only. There are multiple types of orders, which arrive at the system following batch Poisson processes. The leadtimes for replenishing component inventory are stochastic. We study the optimal allocation of a given budget among component inventories so as to minimize a weighted average of backorders over product types (or, alternatively, the average response time among orders). We derive several easy-to-compute bounds and approximations for the expected number of backorders, and use them to formulate surrogate optimization problems. Efficient algorithms are developed to solve these problems, and numerical examples illustrate the effectiveness of the bounds and approximations. Our study also generates new insights on several design issues, both analytically and numerically. ∗Part of this author’s research was conducted at the Graduate School of Management, University of California, Irvine, as a post-doctoral researcher, and supported in part by NSF grants DMI-9896339 and DMI-0084922. †Supported in part by NSF grants DMI-9896339 and DMI0084922. ‡Supported in part by NSF grant DMI-0085124, and by HK/RGC grant CUHK4376/99E.