Optimal Control of a Nested-Multiple-Product Assemble-to-Order System

In this paper, we study an assemble-to-order system consisting of n products assembled from a subset of m distinct components where the products have a modular nested design. i.e., product i has only one additional component more than product i-1. In particular, we study the optimal production and inventory allocation policies of such systems. Components are produced on independent production facilities one unit at a time, each with a finite production rate and exponentially distributed production times. The components are stocked ahead of demand and therefore incur a holding cost per unit per unit of time. Demand from each product occurs continuously over time according to a Poisson process. The demand for a particular product can be either satisfied (provided all its components are available in stock) or rejected. In the latter case, a product-dependent lost sale cost is incurred. In this situation, a manager is confronted with two decisions: when to produce a component and whether or not to satisfy an incoming product order from on-hand inventory. We show that, for the production of a component, the optimal policy is a base-stock type where the base-stock level depends on all other components' inventory. We also show that, for inventory allocation, the optimal policy is a multi-level rationing policy where the rationing levels depend on all other components' inventory. We propose a simple heuristic that we numerically compare against the optimal policy and show that, when carefully designed, it can be very effective