Geodesic
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, Tome 35 (2025) no. 2, p. 365

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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.
Keywords: Makespan, flow time, scheduling, doctors' workload variation, multiobjective mixed integer linear programming, genetic algorithm 
Badreddine Jerbi; Salma Kanoun; Hichem Kamoun. 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, Tome 35 (2025) no. 2, p. 365 . http://geodesic.mathdoc.fr/item/YJOR_2025_35_2_a5/
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