Multi-objective mathematical models to resolve parallel machine scheduling problems with multiple resources

Mathematical programming, and above all, the multi-objective scheduling problems stand as remarkably versatile tools, highly useful for optimizing health care services. In this context, present work is designed to put forward two-fold mixed integer linear programs, simultaneously integrating objectives of minimizing patients? total waiting flow time, while doctors' work-load variations. For purpose, three major health-care system intervening actors are considered, namely, patients, doctors machines. To best our knowledge, such an issue does not seem be actually addressed in relevant literature. end, we opt implementing appropriate lexicographic method, whereby, effective solutions enabling minimize performance two-objective functions could used solve randomly generated small cases. models study have been resolved using CPLEX software. Then, results comparatively assessed terms both CPU times. A real laser-treatment case study, involving a set diabetic retinopathy patients ophthalmology department Habib Bourguiba Hospital Sfax, Tunisia, helps illustrating practicality advanced approach. resolve treated problem, use heuristics which compared first-come first-served rule. We find that program based on second formulation with time-limit provided solution time.