A Stochastic Mixed Integer Programming Model for Outpatient ‎Appointment Scheduling considering late cancellation and physician ‎lateness

Background Nowadays, the essentiality to provide services to outpatients has been grown in medical centers in developed and particularly developing cities. Outpatients are a kind of patients who register their appointment by requesting a specific website, telephone call or app before entering the medical centers and referring them to be visited within the prescribed time. To achieve optimal outpatient care, health centers must design and implement systems and policies that not only improve outpatient satisfaction but also minimize the costs of medical centers.
This paper develops a model that considers increasing the number of patients admitted, physician lateness and cancelation of outpatient appointments due to extreme delays. It formulates a stochastic mixed-integer programming model that decreases the costs by reducing outpatient waiting time, physician overtime, and physician idle time.  It uses the sample average approximation that defines scenarios based on the model conditions. Moreover, it considers that outpatients may register their appointments but do not go to the medical center.  It also formulates another essential factor, unpunctuality of outpatients (both earliness and lateness conditions).
This paper defines some tests for the sensitivity analysis of the proposed model and then compares it with a model in the literature. These analyses were carried out using GAMS software which shows the results of the proposed model.
Finally, this article shows reviews and evaluations to prove its optimality and utility of the proposed model for using it in the real world.