Proceedings of the 8th Mechanical and Industrial Engineering Symposium (MIE 2025)

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A Robust MILP Model for Energy-Efficient Unrelated Parallel Machines Under Uncertainty to Minimize Makespan, Energy Consumption and Total Tardiness

Authors
Aldi P. Nurrachman1, *, Jatinder N. D. Gupta2, Vincent F. Yu3, Yun Prihantina Mulyani1
1Universitas Gadjah Mada, Yogyakarta, Indonesia
2University of Alabama Huntsville, Alabama, United States
3National Taiwan University of Science and Technology, Taipei, Taiwan, ROC
*Corresponding author. Email: aldipascagamanurrachman@mail.ugm.ac.id
Corresponding Author
Aldi P. Nurrachman
Available Online 24 May 2026.
DOI
10.2991/978-94-6239-687-6_11How to use a DOI?
Keywords
Energy consumption; Unrelated parallel machine scheduling; multi scenario uncertainty; setup time
Abstract

In sustainable manufacturing, scheduling models must address both operational efficiency and energy consumption under realistic conditions. This paper presents a robust Mixed Integer Linear Programming (MILP) model for the Unrelated Parallel Machine Scheduling Problem with Sequence-Dependent Setup Times (UPMS-SDST), incorporating uncertain processing times. The model simultaneously optimizes three objectives: minimizing makespan, total energy consumption, and total tardiness. Adopting an absolute robustness framework, we model worst-case scenario behaviour to ensure schedule reliability. A new benchmark suite is introduced, reflecting real-world uncertainty through job-machine variability and due-date tightness. Experimental evaluations on small instances demonstrate the MILP model’s effectiveness and highlight the computational trade-offs involved in exact optimization.

Copyright
© 2026 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 8th Mechanical and Industrial Engineering Symposium (MIE 2025)
Series
Atlantis Highlights in Engineering
Publication Date
24 May 2026
ISBN
978-94-6239-687-6
ISSN
2589-4943
DOI
10.2991/978-94-6239-687-6_11How to use a DOI?
Copyright
© 2026 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Aldi P. Nurrachman
AU  - Jatinder N. D. Gupta
AU  - Vincent F. Yu
AU  - Yun Prihantina Mulyani
PY  - 2026
DA  - 2026/05/24
TI  - A Robust MILP Model for Energy-Efficient Unrelated Parallel Machines Under Uncertainty to Minimize Makespan, Energy Consumption and Total Tardiness
BT  - Proceedings of the 8th Mechanical and Industrial Engineering Symposium (MIE 2025)
PB  - Atlantis Press
SP  - 145
EP  - 157
SN  - 2589-4943
UR  - https://doi.org/10.2991/978-94-6239-687-6_11
DO  - 10.2991/978-94-6239-687-6_11
ID  - Nurrachman2026
ER  -