Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead Times

We consider the multiproduct and multicomponent assemble-to-order (ATO) systems where the replenishment lead times of the components are stochastic, sequential, and independent of the system state. The component inventories are either controlled by the continuous-time base-stock policies, namely, a base-stock ATO system, or by the continuous-time batchordering policies, namely, a batch-ordering ATO system. This paper develops the following results: First, for a base-stock ATO system with a single end product and renewal demand arrivals, we characterize the probability distribution of the delivery lead time, i.e., the time it takes to satisfy a demand. The exact analysis allows us to provide simple proofs for the important system properties. Second, for a base-stock ATO system with multiple end products and demand following independent Poisson processes, we characterize the dependence among the stockout delays of the components. We show that a multiproduct ATO system can be decomposed into multiple single-product subsystems with each subsystem corresponding to one product. The analysis allows us to develop two numerical methods to evaluate the performance of the base-stock ATO systems of medium to large sizes. A hypothetical example inspired by a real-world problem is presented. Third, for a batch-ordering ATO system, we develop efficient numerical methods for performance evaluation based on Monte Carlo simulation. Given the sample size, the number of products, and the reorder points, the computational complexity of the methods is no more than that of sorting a set of real numbers, where the set size equals to the sum of the batch sizes of all components. Finally, we characterize the impact of the dependence among the components on various ATO systems, and discuss the limits of the approach.