Experimental Results Indicating Lattice-Dependent Policies May Be Optimal for General Assemble-To-Order Systems

We consider an assemble-to-order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice-dependent base-stock and lattice-dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M-system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state-dependent base-stock and state-dependent rationing (SBSR) policy, and a fixed base-stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.