Multi-Objective MILP Models for Optimizing Makespan and Energy Consumption in Additive Manufacturing Systems
Saaad, Safae ; Touil, Achraf and Oucheikh, Rachid LU
(2025)
In Engineering Proceedings
97(1).
- Abstract
Additive manufacturing (AM) is revolutionizing industrial production by enabling the fabrication of complex, customized components with reduced material waste. However, the scheduling of AM machines presents significant challenges in terms of optimizing both time-related performance and energy consumption. This paper introduces a novel multi-objective mixed-integer linear programming (MILP) model for scheduling AM machines with the dual objectives of minimizing makespan and energy consumption. We address the single-machine environment with detailed mathematical formulation that accounts for machine-specific parameters such as power consumption rates during different operational states, including printing, setup, and idle modes.... (More)
Additive manufacturing (AM) is revolutionizing industrial production by enabling the fabrication of complex, customized components with reduced material waste. However, the scheduling of AM machines presents significant challenges in terms of optimizing both time-related performance and energy consumption. This paper introduces a novel multi-objective mixed-integer linear programming (MILP) model for scheduling AM machines with the dual objectives of minimizing makespan and energy consumption. We address the single-machine environment with detailed mathematical formulation that accounts for machine-specific parameters such as power consumption rates during different operational states, including printing, setup, and idle modes. Additionally, we consider part-specific characteristics including height, area requirements, and volume, ensuring practical feasibility constraints are met. The proposed model is validated using a comprehensive set of test problems, with optimal solutions reported for small to medium-sized instances. For larger problem instances, where computational complexity prevents finding optimal solutions within reasonable time limits, we report the best solutions obtained under specified time constraints. Computational experiments demonstrate that our approach effectively balances the trade-off between makespan and energy consumption, providing valuable insights for production planning in AM facilities. The results indicate potential energy savings of up to 18% compared to makespan-only optimization approaches, with minimal impact on overall completion times.
(Less)
- author
- Saaad, Safae
; Touil, Achraf
and Oucheikh, Rachid
LU
- organization
- publishing date
- 2025
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- 3D printing, additive manufacturing, energy optimization, makespan, mathematical modeling, MILP, multi-objective optimization, scheduling, sustainable manufacturing
- in
- Engineering Proceedings
- volume
- 97
- issue
- 1
- article number
- 28
- publisher
- MDPI AG
- external identifiers
-
- scopus:105023691914
- ISSN
- 2673-4591
- DOI
- 10.3390/engproc2025097028
- language
- English
- LU publication?
- yes
- id
- 27593988-85b9-4f06-8d7c-e5894d1a2693
- date added to LUP
- 2026-02-03 15:38:20
- date last changed
- 2026-05-27 07:05:18
@article{27593988-85b9-4f06-8d7c-e5894d1a2693,
abstract = {{<p>Additive manufacturing (AM) is revolutionizing industrial production by enabling the fabrication of complex, customized components with reduced material waste. However, the scheduling of AM machines presents significant challenges in terms of optimizing both time-related performance and energy consumption. This paper introduces a novel multi-objective mixed-integer linear programming (MILP) model for scheduling AM machines with the dual objectives of minimizing makespan and energy consumption. We address the single-machine environment with detailed mathematical formulation that accounts for machine-specific parameters such as power consumption rates during different operational states, including printing, setup, and idle modes. Additionally, we consider part-specific characteristics including height, area requirements, and volume, ensuring practical feasibility constraints are met. The proposed model is validated using a comprehensive set of test problems, with optimal solutions reported for small to medium-sized instances. For larger problem instances, where computational complexity prevents finding optimal solutions within reasonable time limits, we report the best solutions obtained under specified time constraints. Computational experiments demonstrate that our approach effectively balances the trade-off between makespan and energy consumption, providing valuable insights for production planning in AM facilities. The results indicate potential energy savings of up to 18% compared to makespan-only optimization approaches, with minimal impact on overall completion times.</p>}},
author = {{Saaad, Safae and Touil, Achraf and Oucheikh, Rachid}},
issn = {{2673-4591}},
keywords = {{3D printing; additive manufacturing; energy optimization; makespan; mathematical modeling; MILP; multi-objective optimization; scheduling; sustainable manufacturing}},
language = {{eng}},
number = {{1}},
publisher = {{MDPI AG}},
series = {{Engineering Proceedings}},
title = {{Multi-Objective MILP Models for Optimizing Makespan and Energy Consumption in Additive Manufacturing Systems}},
url = {{http://dx.doi.org/10.3390/engproc2025097028}},
doi = {{10.3390/engproc2025097028}},
volume = {{97}},
year = {{2025}},
}