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

Modeling approach using discrete event simulation has been proven to work well in modeling in health care. The aim of our paper is to propose a simulation approach which shows realistic models presenting different possible treatments in different stages of diabetic retinopathy. We have presented three models in order to choose the best treatment for diabetic retinopathy patients. The first model describes the flow of a patient through stages without any medical treatments. It takes 13 years to reach blindness. The second model which includes the laser photocoagulation treatments leads to blindness after 46 years. Then, the third model illustrates the involvement of vitrectomy operation and delays blindness by 23 years. To construct the models, data were taken from experienced doctors and professors of the ophthalmology department in the University hospital Habib Bourguiba and the endocrinology department in the University hospital Hedi Chaker in Sfax, Tunisia. Our objective is to delay reaching the blindness stage as late as possible. Three models were developed, verified and validated through many iterative implementations with ARENA simulation software.