Single-Product Assemble-to-Order Systems with Exogenous Lead Times

We study a single-product assemble-to-order (ATO) system with exogenous lead times operated under a component base stock policy. Both demand and component lead times are random and are assumed to have finite supports. The challenge of evaluating a base stock policy in an ATO system with random lead times lies in the fact that one needs to compute the distribution of the minimum of n correlated random variables, where n is the number of components. The correlation arises because the replenishment quantities of different components are all contingent on the demand for the final product. We tackle this problem by first looking into two special cases, namely, the one with independent and identically distributed (i.i.d.) lead times and the one with sequential lead times. We give two algorithms for the i.i.d. lead time case, but both of them have exponential complexity in some system parameter. Then, we investigate the case of sequential lead times and utilize its particular structure to develop an algorithm with polynomial complexity. This is the first efficient algorithm for the performance evaluation of base stock policies in an assemble-to-order system with random lead times. Furthermore, using the method as an evaluation oracle in a steepest descent algorithm, we also obtain a polynomial time algorithm to optimize base stock for the case of sequential lead times. For the general case of exogenous lead times, we provide efficiently computable upper and lower bounds, which are identified based on the idea of comparing the level of correlation among component orders. Via extensive numerical studies, we test the performance of approximation methods developed from the identified bounds. We find that our proposed methods have advantages over other approximation methods in the literature, and both of them perform well as part of an approximated base stock optimization algorithm.