Stochastic Programming Based Inventory Control for the M System

The M system is a representative assemble-to-order inventory system with two components and three products. We apply a previously-developed stochastic programming (SP) based approach to this case, focusing on complexity reduction and numerical testing. We show that the general procedure of the SP-based approach can be simplified. The base stock levels are determined by solving a non-linear optimization problem and the allocation policy can 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, as the SP-based approach has been proven to do, represents significant progress since this optimality criterion is generally not satisfiable by other common approaches. Moreover, 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.