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Minimizing Material Waste in Additive Manufacturing through Online Reel Assignment

Ilayda Celenk, Willem van Jaarsveld, Ivo J. B. F. Adan, Alp Akcay

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.

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.
Paper Structure (15 sections, 7 theorems, 47 equations, 6 figures, 6 tables)

This paper contains 15 sections, 7 theorems, 47 equations, 6 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. The Online Allocation Model
  4. Industrial context
  5. Operator model
  6. MDP formulation
  7. Methods
  8. Analytical Policies
  9. Random Policy
  10. Index Policy
  11. Deep Reinforcement Learning Policy
  12. Results
  13. Numerical Results
  14. Case Study
  15. Conclusion and Discussion

Key Result

Lemma 4.1

Consider the random policy $\pi(R)$ under which each reel is selected with equal probability of $\frac{1}{N}$. Let $\hat{g}_N^{\pi(R)}$ and $g_N^{\pi(R)}$ denote the long-run average costs of the augmented and naive $N$-reel MRPs under $\pi(R)$, respectively, with Bellman equations given by eq:bellm

Figures (6)

  • Figure 1: Reel of Filament
  • Figure 2: Example component-to-reel assignment.
  • Figure 3: MDP Model
  • Figure 4: Comparison of average filament waste under different policies for $N = 2$ reels.
  • Figure 5: Average filament loss as a function of number of reels $N$ in Case 4.
  • ...and 1 more figures

Theorems & Definitions (17)

  • Definition 4.1
  • Definition 4.2
  • Lemma 4.1
  • proof
  • Definition 4.3
  • Lemma 4.2
  • proof
  • Theorem 4.3
  • proof
  • Theorem 4.4
  • ...and 7 more