Optimal and near-optimal control of a capacitated assemble-to-order system with component commonality and backordered demands

We investigate the optimal policy of a capacitated assemble-to-order (ATO) system with component commonality and backordered demands. Using a Markov decision process framework, we model the problem with the objective of minimising both the expected total discounted cost and the expected average cost rate over an infinite-horizon. To characterise the structure of the optimal policy, we adopt a two-step approach. First, we demonstrate that the value function satisfies a set of preliminary properties, indicating that it is optimal to allocate the common component’s inventory to the product with a larger backorder penalty, if its demand can be immediately fulfilled. This insight simplifies the Bellman optimality equation, allowing for a lower-dimensional state representation, which we then applied to fully characterise the optimal policy. Building on the structure of the optimal policy, we develop four heuristic policies. Extensive numerical experiments demonstrate that these heuristic policies perform well. In particular, heuristics H2 and H3 exhibit, on average, only 2% and 1% performance loss compared to the optimal policy. Our results offer practical implications for addressing larger ATO systems.