Mathematical Model of the Assembly Robot Performance in Automated Manufacturing

Kizito Paul Mubiru; Nalubowa Maureen Ssempijja

doi:doi:10.11648/j.mma.20251003.12

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Mathematical Model of the Assembly Robot Performance in Automated Manufacturing

Kizito Paul Mubiru^*

, Nalubowa Maureen Ssempijja

Published in Mathematical Modelling and Applications (Volume 10, Issue 3)

Received: 23 September 2025 Accepted: 5 October 2025 Published: 30 October 2025

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Abstract

Robot performance in automated manufacturing supports the competitive edge in manufacturing industries, enhancing customer sustainability and reducing operational costs. The robot cell controller must therefore optimize the operational tasks in the assembly of components or parts of the product to support automated manufacturing strategies for the manufacturing plant. This study proposes a Markov decision process model for robot performance in a steel assembly plant. The performance of the robot is characterized as a Markov chain, and its operational cost matrix represents the expected reward for the Markov decision process problem. This study utilized hourly data for two consecutive weeks. The principal challenge addressed focused on determining the best product assembly option to reduce the assembly expenses of the robot cell. We considered a multi-period planning horizon, where the optimal decision was determined for assembling or not assembling additional products based on the demand and availability of finished assembled products. The model was tested, and the results demonstrated the existence of an optimal state-dependent decision and assembly expenditure of managing the robot cell of the steel assembly plant. As a cost optimization strategy for managing robot cells, improved efficiency and resource utilization for assembled products were realized, supporting automated manufacturing initiatives of the steel assembly plant used in the case study.

Published in	Mathematical Modelling and Applications (Volume 10, Issue 3)
DOI	10.11648/j.mma.20251003.12
Page(s)	49-58
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Automation, Manufacturing, Mathematical Model, Performance, Robot

References

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APA Style

Mubiru, K. P., Ssempijja, N. M. (2025). Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Mathematical Modelling and Applications, 10(3), 49-58. https://doi.org/10.11648/j.mma.20251003.12

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ACS Style

Mubiru, K. P.; Ssempijja, N. M. Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Math. Model. Appl. 2025, 10(3), 49-58. doi: 10.11648/j.mma.20251003.12

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AMA Style

Mubiru KP, Ssempijja NM. Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Math Model Appl. 2025;10(3):49-58. doi: 10.11648/j.mma.20251003.12

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@article{10.11648/j.mma.20251003.12,
  author = {Kizito Paul Mubiru and Nalubowa Maureen Ssempijja},
  title = {Mathematical Model of the Assembly Robot Performance in Automated Manufacturing
},
  journal = {Mathematical Modelling and Applications},
  volume = {10},
  number = {3},
  pages = {49-58},
  doi = {10.11648/j.mma.20251003.12},
  url = {https://doi.org/10.11648/j.mma.20251003.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20251003.12},
  abstract = {Robot performance in automated manufacturing supports the competitive edge in manufacturing industries, enhancing customer sustainability and reducing operational costs. The robot cell controller must therefore optimize the operational tasks in the assembly of components or parts of the product to support automated manufacturing strategies for the manufacturing plant. This study proposes a Markov decision process model for robot performance in a steel assembly plant. The performance of the robot is characterized as a Markov chain, and its operational cost matrix represents the expected reward for the Markov decision process problem. This study utilized hourly data for two consecutive weeks. The principal challenge addressed focused on determining the best product assembly option to reduce the assembly expenses of the robot cell. We considered a multi-period planning horizon, where the optimal decision was determined for assembling or not assembling additional products based on the demand and availability of finished assembled products. The model was tested, and the results demonstrated the existence of an optimal state-dependent decision and assembly expenditure of managing the robot cell of the steel assembly plant. As a cost optimization strategy for managing robot cells, improved efficiency and resource utilization for assembled products were realized, supporting automated manufacturing initiatives of the steel assembly plant used in the case study.
},
 year = {2025}
}

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TY  - JOUR
T1  - Mathematical Model of the Assembly Robot Performance in Automated Manufacturing

AU  - Kizito Paul Mubiru
AU  - Nalubowa Maureen Ssempijja
Y1  - 2025/10/30
PY  - 2025
N1  - https://doi.org/10.11648/j.mma.20251003.12
DO  - 10.11648/j.mma.20251003.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 49
EP  - 58
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20251003.12
AB  - Robot performance in automated manufacturing supports the competitive edge in manufacturing industries, enhancing customer sustainability and reducing operational costs. The robot cell controller must therefore optimize the operational tasks in the assembly of components or parts of the product to support automated manufacturing strategies for the manufacturing plant. This study proposes a Markov decision process model for robot performance in a steel assembly plant. The performance of the robot is characterized as a Markov chain, and its operational cost matrix represents the expected reward for the Markov decision process problem. This study utilized hourly data for two consecutive weeks. The principal challenge addressed focused on determining the best product assembly option to reduce the assembly expenses of the robot cell. We considered a multi-period planning horizon, where the optimal decision was determined for assembling or not assembling additional products based on the demand and availability of finished assembled products. The model was tested, and the results demonstrated the existence of an optimal state-dependent decision and assembly expenditure of managing the robot cell of the steel assembly plant. As a cost optimization strategy for managing robot cells, improved efficiency and resource utilization for assembled products were realized, supporting automated manufacturing initiatives of the steel assembly plant used in the case study.

VL  - 10
IS  - 3
ER  -

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Author Information

Kizito Paul Mubiru

Mechanical and Production Engineering, Kyambogo University, Kyambogo, Uganda

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http://orcid.org/0009-0007-8289-0324
Nalubowa Maureen Ssempijja

Mechanical and Production Engineering, Kyambogo University, Kyambogo, Uganda

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Plain Text BibTeX RIS

APA Style

Mubiru, K. P., Ssempijja, N. M. (2025). Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Mathematical Modelling and Applications, 10(3), 49-58. https://doi.org/10.11648/j.mma.20251003.12

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ACS Style

Mubiru, K. P.; Ssempijja, N. M. Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Math. Model. Appl. 2025, 10(3), 49-58. doi: 10.11648/j.mma.20251003.12

Copy | Download

AMA Style

Mubiru KP, Ssempijja NM. Mathematical Model of the Assembly Robot Performance in Automated Manufacturing. Math Model Appl. 2025;10(3):49-58. doi: 10.11648/j.mma.20251003.12

Copy | Download

@article{10.11648/j.mma.20251003.12,
  author = {Kizito Paul Mubiru and Nalubowa Maureen Ssempijja},
  title = {Mathematical Model of the Assembly Robot Performance in Automated Manufacturing
},
  journal = {Mathematical Modelling and Applications},
  volume = {10},
  number = {3},
  pages = {49-58},
  doi = {10.11648/j.mma.20251003.12},
  url = {https://doi.org/10.11648/j.mma.20251003.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20251003.12},
  abstract = {Robot performance in automated manufacturing supports the competitive edge in manufacturing industries, enhancing customer sustainability and reducing operational costs. The robot cell controller must therefore optimize the operational tasks in the assembly of components or parts of the product to support automated manufacturing strategies for the manufacturing plant. This study proposes a Markov decision process model for robot performance in a steel assembly plant. The performance of the robot is characterized as a Markov chain, and its operational cost matrix represents the expected reward for the Markov decision process problem. This study utilized hourly data for two consecutive weeks. The principal challenge addressed focused on determining the best product assembly option to reduce the assembly expenses of the robot cell. We considered a multi-period planning horizon, where the optimal decision was determined for assembling or not assembling additional products based on the demand and availability of finished assembled products. The model was tested, and the results demonstrated the existence of an optimal state-dependent decision and assembly expenditure of managing the robot cell of the steel assembly plant. As a cost optimization strategy for managing robot cells, improved efficiency and resource utilization for assembled products were realized, supporting automated manufacturing initiatives of the steel assembly plant used in the case study.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model of the Assembly Robot Performance in Automated Manufacturing

AU  - Kizito Paul Mubiru
AU  - Nalubowa Maureen Ssempijja
Y1  - 2025/10/30
PY  - 2025
N1  - https://doi.org/10.11648/j.mma.20251003.12
DO  - 10.11648/j.mma.20251003.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 49
EP  - 58
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20251003.12
AB  - Robot performance in automated manufacturing supports the competitive edge in manufacturing industries, enhancing customer sustainability and reducing operational costs. The robot cell controller must therefore optimize the operational tasks in the assembly of components or parts of the product to support automated manufacturing strategies for the manufacturing plant. This study proposes a Markov decision process model for robot performance in a steel assembly plant. The performance of the robot is characterized as a Markov chain, and its operational cost matrix represents the expected reward for the Markov decision process problem. This study utilized hourly data for two consecutive weeks. The principal challenge addressed focused on determining the best product assembly option to reduce the assembly expenses of the robot cell. We considered a multi-period planning horizon, where the optimal decision was determined for assembling or not assembling additional products based on the demand and availability of finished assembled products. The model was tested, and the results demonstrated the existence of an optimal state-dependent decision and assembly expenditure of managing the robot cell of the steel assembly plant. As a cost optimization strategy for managing robot cells, improved efficiency and resource utilization for assembled products were realized, supporting automated manufacturing initiatives of the steel assembly plant used in the case study.

VL  - 10
IS  - 3
ER  -

Copy | Download