Joint inventory replenishment and component allocation optimization in an assemble-to-order system

This paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses an independent base-stock policy for inventory replenishment. Product demands in each period are integer-valued correlated random variables, with each product being assembled from multiple units of a subset of components. The system quotes a prespecified response time window for each product and receives a reward if the demand for that product is filled within its response time window. We formulate a two-stage stochastic integer program with recourse to determine the optimal base-stock policy and the optimal component allocation policy for the ATO system. We show that the component allocation problem is a general multidimensional knapsack problem (MDKP) and is NP-hard. We propose a simple, order-based component allocation rule and show that it can be solved in either polynomial or pseudopolynomial time. We also use the sample average approximation method to determine the optimal base-stock levels and compare it with two variations of the equal fractile heuristic. Intensive testing indicates that our solution method for each stage of the stochastic program is robust, effective, and that it significantly outperforms existing methods. Finally, we discuss several managerial implications of our findings.