Assemble-to-Order Inventory Management via Stochastic Programming: Chained BOMs and the M-System

We study an inventory management mechanism that uses two stochastic programs (SPs), the customary one-period Assemble-to-Order (ATO) model and its relaxation, to conceive control policies for dynamic ATO systems. We introduce a class of ATO systems, those that possess what we call a ‘chained BOM’. We prove that having a chained BOM is a sufficient condition for both SPs to be L convex in the first-stage decision variables. We show by examples the necessity of the condition. For ATO systems with a chained BOM, our result implies that the optimal integer solutions of the SP models can be found efficiently, and thus expedites the calculation of control parameters. The M system is a representative chained BOM system with two components and three products. We show that in this special case, the SPs can be solved as a one-stage optimization problem. The allocation policy can also be reduced to simple, intuitive instructions, of which there are four distinct sets, one for each of four different parameter regions. We highlight the need for component reservation in one of these four regions. Our numerical studies demonstrate that achieving asymptotic optimality represents a significant advantage of the SP-based approach over alternative approaches. Our numerical comparisons also show that outside of the asymptotic regime, the SP-based approach has a commanding lead over the alternative policies. Our findings indicate that the SP-based approach is a promising inventory management strategy that warrants further development for more general systems and practical implementations.