Multi-objective Mathematical Programs to Minimize the Makespan, the Patients’ Flow Time, and Doctors’ Workloads Variation Using Dispatching Rules and Genetic Algorithm
Abstract
The World Health Report estimated that 20-40% of health sector resources are wasted globally. Balancing many conflicting objectives such as clinical excellence, cost containment, and patient satisfaction can be challenging. In fact, multiple objective programming is one of the best tools that can be used for logistics optimization in many organizations. The aim of our paper is to propose a multi-objective mixed integer linear program that satisfies the goals of two important actors in the healthcare system: patients and doctors. The problem considers a parallel machine scheduling model that integrates simultaneously the following most known objectives in healthcare systems: minimization of the makespan, the patients' total flow times, and the doctors' workloads variations. The current paper deals with a real case study where the number of doctors exceeds the number of machines. A mathematical model combined with some dispatching rules was developed and solved using the CPLEX software, which shows the practical importance of our approach. For small instances, we use a mathematical programming model and a heuristic method based on the “first come, first served” rule to assign patients to machines and doctors. For larger instances, we use a genetic algorithm to approximately solve our multi-objective model.
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C. Granja, B. Almada-Lobo, F. Janela, J. Seabra and A. Mendes, "An optimization based on simulation approach to the patient admission scheduling problem using a linear programming algorithm," Journal of Biomedical Informatics, vol. 52, pp. 427–437, 2014.
G. Lim, A. Mobasher, and M.J. Côté, "Multi-objective Nurse Scheduling Models with Patient Workload and Nurse Preferences," Management, vol. 2, pp. 149-160, 2012.
Y. Lu, X. Xie, and Z. Jiang, "Dynamic Appointment Scheduling with Wait Dependent Abandonment,", European Journal of Operations Research, 2017.
S. Kanoun, B. Jerbi, H. Kamoun and L.Kallel, "Multi-objective mathematical models to resolve parallel machine scheduling problems with multiple resources," Yugoslav Journal of Operations Research, 2023. DOI: 10.2298/YJOR221215008K.
A. Goli, A. Ala and S. Mirjalili, "A robust possibilistic programming framework for designing an organ transplant supply chain under uncertainty," Annals of Operations Research, vol. 328, pp. 1-38, 2022.
N. Ilyasova, N. Demin and N. Andriyanov, "Development of a Computer System for Automatically Generating a Laser Photocoagulation Plan to Improve the Retinal Coagulation Quality in the Treatment of Diabetic Retinopathy," Symmetry, vol. 15, no. 2, p. 287, 2023. doi: https://doi.org/10.3390/sym15020287.
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A. Goli, A. Ala and M.H. Keshteli, "Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem," Expert Systems with Applications, vol. 213, p. 119077, 2022.
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A. Batamiz, and M. Allahdadi, "Finding efficient solutions in the interval multi-objective linear programming models," Yugoslav journal of operations research, vol. 31, no. 1, pp. 95119, 2021. DOI:https://doi.org/10.2298/yjor190817034b.
A. Goli, and T.E. Babaee, "Designing a portfolio-based closed-loop supply chain network for dairy products with a financial approach: Accelerated Benders decomposition algorithm," Computers & Operations Research, vol. 155, p. 106244, 2023.
J.K. Maurya, and S.K. Mishra, "Strong complementary approximate karush-kuhn-tucker conditions for multi-objective optimization problems," Yugoslav Journal of Operations Research, vol. 32, no. 2, pp. 219-234, 2022. doi: https://doi.org/10.2298/yjor210315024m.
L.R. Mundim, and T.A. Queiroz, "Using a variable neighborhood search to solve a biobjective identical parallel machine scheduling problem," Electronic Notes in Discrete Mathematics, vol. 66, pp. 127-134, 2018.
M.Furlan, B. Almada-Lobo, M. Santos and R. Morabito,"Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines," Computers and Operations Research, vol. 59, pp. 33-50, 2015.
O. Shahvari, and R. Logendran, "An Enhanced tabu search algorithm to minimize a bicriteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes," Computers and Operations Research, vol. 77, pp. 154176, 2017.
J. Luo, D. Fujimura El Baz, and B. Plazolles, "GPU based parallel genetic algorithm for solving an energy efficient dynamic flexible flow shop scheduling problem," Journal of Parallel and Distributed Computing, vol.133, pp. 244-257, 2019.
B. Rolf, T. Reggelin, A. Nahhas, S. Lang and M. Müller, "Assigning dispatching rules using a genetic algorithm to solve a hybrid flow shop scheduling problem," Procedia Manufacturing, vol. 42, pp. 442-449, 2020.
L. Sheremetov, J. Martínez-Muñozand M. Chi-Chim, "Two stage genetic algorithm for parallel machines scheduling problem: Cyclic steam stimulation of high viscosity oil reservoirs," Applied Soft Computing, vol. 64, pp. 317-330, 2018.
L. Soares and M.Carvalho, "Biased random-key genetic algorithm for scheduling identical parallel machines with tooling constraints," European Journal of Operational Research, vol. 285, pp. 955-964, 2020.
Y. Woo, S. Jung and B.S. Kim, "A rule-based genetic algorithm with an improvement heuristic for unrelated parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities," Computers & Industrial Engineering, vol. 109, pp.179-190, 2017.
P.R. Harper, M.G. Sayyad, V. de Senna, A.K. Shahani, C.S. Yajnik and K.M. Shelgikar, "A systems modeling approach for the prevention and treatment of diabetic retinopathy," European Journal of Operational Research, vol. 150, no. 1, pp. 81–91, 2002.
A. Boutayeb, and E.H. Twizell, "An age structured model for complications of diabetes mellitus in Morocco," Simulation Modeling Practice and Theory, vol. 12, pp. 77–87, 2004.
A. Imai, E. Nishimura and S. Papadimitriou, "The dynamic berth allocation problem for a container port," Transportation Research Part B, vol. 35, pp. 401-417, 2001.
S. Kanoun, B. Jerbi, and H. Kamoun, "Discrete Event Simulation to Evaluate Different Treatments of Diabetic Retinopathy Disease," American Journal of Operations Research, vol. 12, pp. 250-260, 2022. doi: https://doi.org/10.4236/ajor.2022.126014.
M. Garey and D. Johnson, "Computers and intractability a guide to the theory of NP completeness," Freeman, San Francisco, 1979.
J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker, "Complexity of machine scheduling problems," Annals of Discrete Mathematics, vol. 1, pp. 343-36, 1977.
O. Kettani, B. Aouni, and J.M. Martel, "The double role of the weight factor in the goal programming model,", Computers & Operations Research, vol. 31, pp. 1833 – 1845, 2004.
J.H. Holland, "Adaptation in natural and artificial systems," The university of Michigan Press, 1975.Thl Journal of Advanced Manufacturing Technology
I.A. Chaudhry, "Minimizing flow time for the worker assignment problem in identical parallel machine models using GA," The International Journal of Advanced Manufacturing Technology, vol. 48, pp. 747–760, 2010.
A. Andreica, and C. Chira, "Best-order crossover for permutation-based evolutionary algorithms," Applied Intelligence, 42: 751–776, 2014.
Published
2025-01-14
How to Cite
JERBI, Badreddine; KANOUN, Salma; KAMOUN, Hichem.
Multi-objective Mathematical Programs to Minimize the Makespan, the Patients’ Flow Time, and Doctors’ Workloads Variation Using Dispatching Rules and Genetic Algorithm.
Yugoslav Journal of Operations Research, [S.l.], jan. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1315>. Date accessed: 18 jan. 2025.
doi: https://doi.org/10.2298/YJOR240115032J.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
