Minimizing Material Waste in Additive Manufacturing through Online Reel Assignment

Abstract: We study a variant of the online bin packing problem that arises in filament-based 3D printing systems operating in make-to-order settings, where only a limited number of filament reels of finite capacity can be handled at once. Components are assigned to reels upon arrival and insufficient reels are discarded to be replaced with new ones, resulting in material waste. To minimize the long-run average discarded filament through an online assignment policy, we formulate this problem as an infinite-horizon average-cost Markov Decision Process and analyze the structure of policies under stochastic, sequential demand. We first show that under a random allocation policy, the system decomposes into a collection of identical single-reel processes, allowing us to derive a closed-form expression for the average waste and enabling a tractable baseline analysis. Building on this decomposition, we construct a theoretically grounded index policy that assigns each reel a score reflecting the marginal cost of assignment and prove that it constitutes a one-step policy improvement over random allocation. We embed the index-based structure within a Deep Reinforcement Learning framework using approximate policy iteration. The resulting method achieves near-optimal performance across a range of simulated and real-world scenarios. Our results demonstrate that Reinforcement Learning policy significantly reduces material waste while maintaining real-time feasibility and interpretability.