Optimal Dynamic Substitution Policy for Components in an Assemble-to-Order System

In assemble-to-order system, the substitution of higher-class components for lower-class components is often applied when the latter are stock-out. But the decision for substitution should be made in advance in practice. How to manage the substitution in such a system is of managerial interest. We model this scenario as a two-stage mathematical programming where the first step is to determine how many to order for each product at the beginning of the selling season, and the second step is to explore the substitution rule. We exploit the structural properties of the substitution rule and present a dynamic substitution policy. Then we show that our substitution policy is a threshold policy and present the upper bound of the threshold.