Performance Evaluation of Lattice-Dependent Base-Stock and Rationing Policies for 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, 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 optimal for a special case of the ATO model presented here (the M-system).

In this paper, we conduct numerical experiments to evaluate the use of an LBLR policy for our general 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 1800 instances, outperforming SBSR and FBFR by up to 2.7% and 4.8%, respectively. 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.

We then modify our optimization criterion to total expected discounted cost over an infinite horizon, and show that submodularity and supermodularity, which have been used to ensure the optimality of LBLR for the M-system, need not hold for our general model. Thus, if LBLR is to be shown to be optimal for general ATO systems, a different methodology will likely be required.