The effectiveness of several performance bounds for capacitated production, partial-order-service, assemble-to-order systems

We consider an assemble-to-order (ATO) system: Components are made to stock by production facilities with finite capacities, and final products are assembled only in response to customers' orders. The key performance measures in this system, such as order fill rates, involve evaluation of multivariate probability distributions, which is computationally demanding if not intractable. The purpose of this paper is to develop computationally efficient performance estimates. We examine several ideas scattered in diverse literatures on approximations for multivariate probability distributions, and determine which approach is most effective in the ATO application. To do so, we first tailor different approximation ideas to the ATO setting to derive performance bounds, and then compare these bounds theoretically and numerically. The bounds also allow us to make connections between capacitated and uncapacitated ATO systems and gain various insights.