A Mixed Integer Linear Programming Approach to Production Optimization in a Surface Treatment Area of the Aerospace Industry
Abstract
Production scheduling, especially in intricate sectors like aerospace, is essential. This study presents a Mixed Integer Linear Programming (MILP) model to optimize production in the surface treatment area of an aerospace company. The complex task involves several constraints, including raw material alloy type, tank capacity, and fixture design for parts. The goal is to find the optimal combination to maximize production, efficiency, and safety. Unique to this problem is the integration of factors such as different tanks, fixtures, scheduling, and geometric constraints. Technical requirements have been integrated as constraints to satisfy aircraft manufacturing certifications. Experiments with thirty real and thirty simulated scenarios showed that the proposed model significantly outperformed the company's existing methods. In the best case, it demonstrated the potential to more than double the production with the same resources. The results underscore the existing capacity to take on new products and clients, highlighting the potential for increased efficiency. Spatial optimization allows for processing more parts per cycle, thus reducing time, costs, and environmental impact. This study adds value to optimization literature, offering a novel approach to a real and multifaceted problem in the surface treatment industry, with applications extending to other industrial contexts where spatial optimization and efficient scheduling are key.
References
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P. E. D. Love, J. Matthews, and H. Mahamivanan, “Non-conformances in infrastructure engineerto-order production systems,” International Journal of Production Research, Early Access, 2025, doi: 10.1080/00207543.2025.2505156.
C. S. Tang, J. D. Zimmerman, and J. I. Nelson, “Managing new-product development and supplychain risks: The Boeing 787 case,” Supply Chain Forum: An International Journal, vol. 10, no. 2, pp. 74–86, Jan. 2009, doi: 10.1080/16258312.2009.11517219.
M. Rohaninejad, M. Janota, and Z. Hanzálek, “Integrated lot-sizing and scheduling: Mitigation of uncertainty in demand and processing time by machine learning,” Engineering Applications of Artificial Intelligence, vol. 118, Art. no. 105676, 2023, doi: 10.1016/j.engappai.2022.105676.
J. Mula, M. Díaz-Madroñero, B. Andres, R. Poler, and R. Sanchis, “A capacitated lot-sizing model with sequence-dependent setups, parallel machines and bi-part injection moulding,” Applied Mathematical Modelling, vol. 100, pp. 805–820, 2021, doi: 10.1016/j.apm.2021.07.028.
N. Acevedo, C. Rey, C. Contreras-Bolton, and V. Parada, “Automatic design of specialized algorithms for the binary knapsack problem,” Expert Systems with Applications, vol. 141, Art. no. 112908, 2020, doi: 10.1016/j.eswa.2019.112908.
S. Goebbels, F. Gurski, and D. Komander, “The knapsack problem with special neighbor constraints,” Mathematical Methods of Operations Research, vol. 95, no. 1, pp. 1–34, 2022, doi: 10.1007/s00186-021-00767-5.
P. Georgiadis and C. Michaloudis, “Real-time production planning and control system for jobshop manufacturing: A system-dynamics analysis,” European Journal of Operational Research, vol. 216, no. 1, pp. 94–104, 2012, doi: 10.1016/j.ejor.2011.07.022.
H. Missbauer and R. Uzsoy, “Order release in production planning and control systems: Challenges and opportunities,” International Journal of Production Research, vol. 60, no. 1, pp. 256–276, 2022, doi: 10.1080/00207543.2021.1994165.
N. Absi and S. Kedad-Sidhoum, “The multi-item capacitated lot-sizing problem with setup times and shortage costs,” European Journal of Operational Research, vol. 185, no. 3, pp. 1351–1374, 2008, doi: 10.1016/j.ejor.2006.01.053.
N. Sereshti and M. Bijari, “Profit maximization in simultaneous lot-sizing and scheduling problem,” Applied Mathematical Modelling, vol. 37, no. 23, pp. 9516–9523, 2013, doi: 10.1016/j.apm.2013.05.004.
S. A. De Araujo, B. De Reyck, Z. Degraeve, I. Fragkos, and R. Jans, “Period decompositions for the capacitated lot-sizing problem with setup times,” INFORMS Journal on Computing, vol. 27, no. 3, pp. 431–448, 2015, doi: 10.1287/ijoc.2014.0636.
H. W. Lee and K. Ho, “Regional constellation reconfiguration problem: Integer linear programming formulation and Lagrangian heuristic method,” Journal of Spacecraft and Rockets, Early Access, 2023, doi: 10.2514/1.A35685.
C. Hicks and P. M. Braiden, “Computer-aided production-management issues in the engineerto-order production of complex capital goods explored using a simulation approach,” International Journal of Production Research, vol. 38, no. 18, pp. 4783–4810, 2000, doi: 10.1080/00207540010001019.
P. Pongcharoen, C. Hicks, and P. M. Braiden, “Development of genetic algorithms for finitecapacity scheduling of complex products with multiple levels of product structure,” European Journal of Operational Research, vol. 152, no. 1, pp. 215–225, 2004, doi: 10.1016/S03772217(02)00645-8.
W. Xie, C. Hicks, and P. Pongcharoen, “A multiple-criteria genetic-algorithm scheduling tool for production scheduling in the capital-goods industry,” International Journal of Engineering and Technology Innovation, vol. 4, no. 1, pp. 18–31, 2014.
L. Jin, Q. Tang, C. Zhang, X. Shao, and G. Tian, “More MILP models for integrated process planning and scheduling,” International Journal of Production Research, vol. 54, no. 4, pp. 1076–1093, 2016, doi: 10.1080/00207543.2016.1140917.
Q. Liu, X. Li, L. Gao, & J. Fan, “Two novel MILP models with different flexibilities for solving integrated process planning and scheduling problems,” Journal of the Operational Research Society, vol. 74, no. 9, pp. 1955–1967, 2023. doi: 10.1080/01605682.2022.2122738.
S. P. Oliveira, J. R. D. Luche, F. A. S. Marins, A. F. Silva, and A. F. B. Costa, “Design of a bike–bus network for a city of half a million citizens,” Journal of Urban Planning and Development, vol. 147, no. 3, Art. no. 04021029, 2021, doi: 10.1061/(ASCE)UP.19435444.0000709.
S. d. L. Pinto, J. Muniz Jr., C. R. Freitas, and J. R. D. Luche, “A framework for the innovationmanagement capacity: Empirical evidence from the Porto Digital cluster in Brazil,” Administrative Sciences, vol. 15, no. 5, Art. no. 191, 2025, doi: 10.3390/admsci15050191.
A. Ala, M. Yazdani, M. Ahmadi, A. Poorianasab, and M. Y. N. Attari, “An efficient healthcarechain design for resolving the patient-scheduling problem: Queuing theory and MILP-ASA optimisation approach,” Annals of Operations Research, Early Access, 2023, doi: 10.1007/s10479-023-05287-5.
Y. Yuhua, S. Marcella, P. Dario, and N. Shaoquan, “Train timetabling with passenger data and heterogeneous rolling-stock circulation on an urban rail-transit line,” Soft Computing, vol. 27, no. 18, pp. 12959–12977, 2023, doi: 10.1007/s00500-022-07057-0.
K. Copil, M. Wörbelauer, H. Meyr, and H. Tempelmeier, “Simultaneous lot-sizing and scheduling problems: A classification and review of models,” OR Spectrum, vol. 39, pp. 1–64, 2017, doi: 10.1007/s00291-015-0429-4.
F. W. Harris, “How many parts to make at once,” Factory, The Magazine of Management, vol. 10, no. 2, pp. 135–136, 1913.
R. H. Wilson, “A scientific routine for stock control,” Harvard Business Review, vol. 13, no. 1, pp. 116–128, 1934.
J. Rogers, “A computational approach to the economic lot-scheduling problem,” Management Science, vol. 4, no. 3, pp. 264–291, 1958, doi: 10.1287/mnsc.4.3.264.
N. Brahimi, S. Dauzere-Peres, N. M. Najid, and A. Nordli, “Single-item lot-sizing problems,” European Journal of Operational Research, vol. 168, no. 1, pp. 1–16, 2006, doi: 10.1016/j.ejor.2004.01.054.
H. M. Wagner and T. M. Whitin, “Dynamic version of the economic lot-size model,” Management Science, vol. 5, no. 1, pp. 89–96, 1958, doi: 10.1287/mnsc.5.1.89.
R. Jans and Z. Degraeve, “Modeling industrial lot-sizing problems: A review,” International Journal of Production Research, vol. 46, no. 6, pp. 1619–1643, 2008, doi: 10.1080/00207540600902262.
G. R. Bitran and H. H. Yanasse, “Computational complexity of the capacitated lot-size problem,” Management Science, vol. 28, no. 10, pp. 1174–1186, 1982, doi: 10.1287/mnsc.28.10.1174.
W. W. Trigeiro, L. J. Thomas, and J. O. McClain, “Capacitated lot-sizing with setup times,” Management Science, vol. 35, no. 3, pp. 353–366, 1989, doi: 10.1287/mnsc.35.3.353.
J. R. D. Luche, R. Morabito, and V. Pureza, “Combining process-selection and lot-sizing models for production scheduling of electrofused grains,” Asia-Pacific Journal of Operational Research, vol. 26, no. 3, pp. 421–443, 2009, doi: 10.1142/S0217595909002286.
H. Na and J. Park, “Multi-level job scheduling in a flexible job-shop environment,” International Journal of Production Research, vol. 52, no. 13, pp. 3877–3887, 2014, doi: 10.1080/00207543.2013.848487.
H. Y. Fuchigami and S. Rangel, “A survey of case studies in production scheduling: Analysis and perspectives,” Journal of Computational Science, vol. 25, pp. 425–436, 2018, doi: 10.1016/j.jocs.2017.06.004.
K. Zhou, M. R. Kılınç, X. Chen, and N. V. Sahinidis, “An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver,” Journal of Global Optimization, vol. 70, pp. 497–516, 2018, doi: 10.1007/s10898-017-0559-0.
Published
2025-10-20
How to Cite
LUCHE, José Roberto Dale et al.
A Mixed Integer Linear Programming Approach to Production Optimization in a Surface Treatment Area of the Aerospace Industry.
Yugoslav Journal of Operations Research, [S.l.], oct. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1368>. Date accessed: 25 oct. 2025.
doi: https://doi.org/10.2298/YJOR250524033L.
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Section
Research Articles
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