Analysis and evaluation of an Assemble-to-Order system with batch ordering policy and compound Poisson demand

We consider a multi-product and multi-component Assemble-to-Order (ATO) system where the external demand follows compound Poisson processes and component inventories are controlled by continuous-time batch ordering policies. The replenishment lead-times of components are stochastic, sequential and exogenous. Each element of the bill of material (BOM) matrix can be any non-negative integer. Components are committed to demand on a first-come-first-serve basis. We derive exact expressions for key performance metrics under either the assumption that each demand must be satisfied in full (non-split orders), or the assumption that each unit of demand can be satisfied separately (split orders). We also develop an efficient sampling method to estimate these metrics, e.g., the expected delivery lead-times and the order-based fill-rates. Based on the analysis and a numerical study of an example motivated by a real world application, we characterize the impact of the component interaction on system performance, demonstrate the efficiency of the numerical method and quantify the impact of order splitting.