Abstract
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.
Highlights
It is common knowledge that assemble-to-order (ATO) systems are notoriously difficult to analyze: Despite the popularity of ATO systems in practice, the structure of the optimal inventory replenishment and allocation policy is still unknown for general ATO systems
We develop a Linear Programming (LP) formulation to find the globally optimal stationary randomized policy, and Mixed Integer Programming (MIP) formulations to find the optimal stationary deterministic policy within each heuristic class (LBLR, SBSR, and fixed base-stock and fixed rationing (FBFR))
We find that lattice-dependent base-stock and lattice-dependent rationing (LBLR) performs better than SBSR by up to 2.6% of the globally optimal cost on a test bed constructed from 350 instances. (The average distances from the optimal cost are 0.5% and 1.4%, respectively.) LBLR has a notable computational advantage; the computation times of LBLR are shorter by up to three orders and one order of magnitude, respectively
Summary
It is common knowledge that assemble-to-order (ATO) systems are notoriously difficult to analyze: Despite the popularity of ATO systems in practice, the structure of the optimal inventory replenishment and allocation policy is still unknown for general ATO systems. Simple heuristic control policies for general ATO systems are attracting widespread interest in practice (Lu et al 2010). In a recent study, Nadar et al (2014) consider a Markovian ATO “generalized M-system.” This system involves a single master product which uses multiple units from each component, and multiple individual products each of which uses multiple units from a single unique component. We adapt the lattice-dependent basestock and lattice-dependent rationing (LBLR) policy introduced by Nadar et al (2014) to ATO systems with general product structures, evaluating its use as a heuristic replenishment and allocation policy. The MIP formulations of SBSR and FBFR, additional numerical results, and the structural counter examples to Nadar et al (2014) are contained in the online appendix
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