Integer Linear Programming Models for Preventive Maintenance of Medical Devices: A Case Study

Todsapol  Huana; Apichai Ritvirool

doi:10.55003/ETH.430308

Authors

Todsapol Huana Faculty of Engineering, Naresuan University, Thailand
Apichai Ritvirool Faculty of Engineering, Naresuan University, Thailand

DOI:

https://doi.org/10.55003/ETH.430308

Keywords:

Workforce allocation, Operational planning, Spreadsheet-based optimization, Binary integer linear programming

Abstract

This study aims to develop a mathematical decision-support framework for optimizing workforce allocation and operational planning in medical device preventive maintenance (PM). An investigation a case study at a public hospital revealed that the PM plan for medical devices at the operational level often lacks decision-support tools for effective work planning. Due to the large number and diverse range of medical devices in hospitals, the head of the medical device department often encounters difficulties in allocating technicians efficiently across different device categories according to their skill levels and time constraints. This limitation frequently results in disproportionate workloads and an inequitable distribution of tasks among personnel. To address these inefficiencies, this study employs a sequential optimization framework consisting of a Binary Integer Linear Programming (BILP) model followed by an Integer Linear Programming (ILP) model. First, the BILP model assigns maintenance tasks based on technician skills and time constraints with the simultaneous optimization of workload balance and equitable distribution of maintenance tasks among technicians within a single model. The optimized BILP output is then used as input for the ILP model to determine optimal daily task allocation. This sequential approach effectively reduces computational complexity. The proposed models are implemented within Microsoft Excel and integrated with OpenSolver, a free and open-source optimization solver, to provide a flexible and cost-effective alternative to manual planning. The results indicate that the proposed BILP and ILP models reduced labor costs by 12.64% and 12.60%, respectively, compared with the current maintenance planning. The proposed model effectively balances workloads among technicians within the same skill group, resulting in workload deviations of 0.70% and 0.84% for the skilled and general groups, respectively. Furthermore, equitable task distribution is achieved, as the difference in the number of assigned devices of each type among technicians within the same skill group does not exceed one device.

References

Y. Wu, M. Dong, and Z. Zheng, “Patient scheduling with periodic deteriorating maintenance on single medical device,” Computers & Operations Research, vol. 49, pp. 107–116, 2014, doi: 10.1016/j.cor.2014.04.005.

Division of Medical Engineering and RFS Co., Ltd., “Medical Equipment Maintenance Management Procedural Guidelines,” Department of Health Service Support, Ministry of Public Health, Nonthaburi, Thailand, Rep. MEP 01-21, 2019.

R. Manzini, R. Accorsi, T. Cennerazzo, E. Ferrari, and F. Maranesi, “The scheduling of maintenance. A resource-constraints mixed integer linear programming model,” Computers & Industrial Engineering, vol. 87, pp. 561–568, 2015, doi: 10.1016/j.cie.2015.06.006.

H. M. Wagner, R. J. Giglio, and R. G. Glaser, “Preventive Maintenance Scheduling by Mathematical Programming,” Management Science, vol. 10, no. 2, pp. 316–334, 1964.

M. I. H. Tusar and B. R. Sarker, “Technician assignment in multi-shift maintenance schedules in an offshore wind farm,” Renewable Energy Focus, vol. 51, 2024, Art. no. 100616, doi: 10.1016/j.ref.2024.100616.

T. Zhang, W. Liang, H. Ji, and C. Zhang, “A linear programming joint optimization model of overnight train timetabling and maintenance planning on high-speed railway,” Scientific Reports, vol. 15, 2025, Art. no. 42073, doi: 10.1038/s41598-025-26026-9.

M. S. L. Delgadillo, V. J. Garcia, S. D. Rodrigues, G. R. Moreira, L. F. Braghirolli, and L. G. F. Castro, “Allocation of Field Service Technicians Considering Backlog Management Using a Mixed Integer Linear Programming Approach in an Electric Power Utility,” in 2025 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT LA), Panama, Panama, Sep. 16–19, 2025, pp. 1–6, doi: 10.1109/ISGTLA64895.2025.11371043.

C. C. Micheal and E. E. Ikechi, “Application of Integer Linear Programming in Workforce Scheduling: Evidence from ABInBev (International Breweries Port Harcourt) Logistics Facility,” International Journal of Scientific Research and Modern Technology, vol. 5, no. 1, pp. 146–154, 2026, doi: 10.38124/ijsrmt.v5i1.1213.

K. B. Artana and K. Ishida, “Spreadsheet modeling of optimal maintenance schedule for components in wear-out phase,” Reliability Engineering & System Safety, vol. 77, no. 1, pp. 81–91, 2002, doi: 10.1016/S0951-8320(02)00033-9.

A. Ovchinnikov and J. Milner, “Spreadsheet model helps to assign medical residents at the University of Vermont's College of Medicine,” Interfaces, vol. 38, no. 4, pp. 311–323, 2008, doi: 10.1287/inte.1070.0337.

Z. Zheng and X. Gong, “Solving Real Life Nurse Rostering Problem in a Local Hospital Based on Spreadsheet,” in Proc. 2020 4th International Conference on Electronic Information Technology and Computer Engineering, Xiamen China, Nov. 6–8, 2020, pp. 959–964, doi: 10.1145/3443467.3443887.

H. K. Smalley and P. Keskinocak, “Automated medical resident rotation and shift scheduling to ensure quality resident education and patient care,” Health Care Management Science, vol. 19, no. 1, pp. 66–88, 2016, doi: 10.1007/s10729-014-9289-8.

M. Anderson, M. Bodur, S. Rathwell, and V. Sarhangian, “Optimization helps scheduling nursing staff at the long-term care homes of the city of Toronto,” INFORMS Journal on Applied Analytics, vol. 53, no. 2, pp. 133–154, 2022, doi: 10.1287/inte.2022.1132.

S. Alkhatib, R. Katmah, D. Kosaji, S. Afzal, M. H. Tariq, M. C. E. Simsekler, and S. Ellahham, “AI-Driven Decision Support Framework for Preventing Medical Equipment Failure and Enhancing Patient Safety: A New Perspective,” Journal of Multidisciplinary Healthcare, vol. 18, pp. 6299–6313, 2025, doi: 10.2147/JMDH.S528612.

K. Li, L. Su, J. Cheng, Y. Sun, and X. Ma, “Improving maintenance efficiency and controlling costs in healthcare institutions through advanced analytical method,” Scientific Reports, vol. 15, 2025, Art. no. 18377, doi: 10.1038/s41598-025-02176-8.

Z. B. Houria, M. Masmoudi, A. A. Hanbali, I. Khatrouch, and F. Masmoudi, “Quantitative techniques for medical equipment maintenance management,” European Journal of Industrial Engineering, vol. 10, no. 6, pp. 703–723, 2016, doi: 10.1504/EJIE.2016.081017.

A. H. Nobil, S. M. E. Sharifnia, and L. E. Cárdenas-Barrón, “Mixed integer linear programming problem for personnel multi-day shift scheduling: A case study in an Iran hospital,” Alexandria Engineering Journal, vol. 61, no. 1, pp. 419–426, 2022, doi: 10.1016/j.aej.2021.06.030.

K. Khalafa, K. Djouani, Y. Hamam, and Y. Alayli, “Mixed-integer linear programming (MILP) for optimisation of medical equipment maintenance schedules,” in 2015 22nd Iranian Conference on Biomedical Engineering (ICBME), Tehran, Iran, Nov. 25–27, 2015, pp. 205–209, doi: 10.1109/ICBME.2015.7404143.

E. A. Ramadan, A. A. Abu-Ghaleb, and M. A. El-Brawany, “Medical equipment maintenance management and optimization in healthcare facilities: Literature review,” in 2023 3rd International Conference on Electronic Engineering (ICEEM), Menouf, Egypt, Oct. 7–8, 2023, pp. 1–11, doi: 10.1109/ICEEM58740.2023.10319481.

A. J. Mason, “OpenSolver – An open source add-in to solve linear and integer programmes in Excel,” in Operations Research Proceedings 2011, D. Klatte, H.-J. Lüthi, and K. Schmedders, Eds. Zurich, Switzerland, 2011, pp. 401–406, doi: 10.1007/978-3-642-29210-1_64.

J. Forrest and R. Lougee-Heimer, “CBC User Guide,” in INFORMS Annual Meeting. in Emerging Theory, Methods, and Applications, in INFORMS TutORials in Operations Research, 2005, pp. 257–277, doi: 10.1287/educ.1053.0020.

L. Scavuzzo, K. Aardal, A. Lodi, and N. Yorke-Smith, “Machine learning augmented branch and bound for mixed-integer linear programming,” Mathematical Programming, vol. 217, pp. 123–166, 2024, doi: 10.1007/s10107-024-02130-y.

M. S. Song, A. Kulp, Y. Lu, and F. J. Vasko, “Determining when Gurobi generates optimal solutions for the partial coverage weighted set covering problem,” Computation, vol. 14, no. 3, 2026, Art. no. 68, doi: 10.3390/computation14030068.

E. I. Ásgeirsson and G. L. Sigurðardóttir, “Near-optimal MIP solutions for preference based self-scheduling,” Annals of Operations Research, vol. 239, no. 1, pp. 273–293, 2014, doi: 10.1007/s10479-014-1597-3.