Abstract

In this research, we study a stochastic integrated physician and patient scheduling problem with uncertainty in demand, service times, and patients’ pathways in the context of a multidisciplinary clinic. These uncertainties were implemented in order to make our scheduling model more reflective of the real world. We propose a two-stage integer stochastic programming model where physicians’ shifts are set in the first stage while taking into account their preferences and fair distributions of workloads. In the second stage, the demand of patients from different health categories realizes and we admit a portion of them and postpone the rest to the next scheduling horizon. Then, we also allocate appointment times to admitted patients. In this stage, we also may need to reschedule patients due to either the uncertainty in service times of physicians or patients’ pathways caused by the referral of a patient by one physician to another. The second-stage objective function is to minimize the total patients’ waiting, rescheduling, and postponement costs, and physicians’ idle cost. A literature review is presented to study possible approaches toward various definitions of this scheduling problem. We solve the proposed two-stage stochastic programing model in the framework of a sample average approximation algorithm to find statistical upper and lower bounds.
Extensive computational experiments were carried out and a total of 541 instances were solved to evaluate the efficiency of the proposed solution approach and to perform sensitivity analyses. The instances were solved deterministically for the second time, considering only an average scenario for the uncertain parameters. The results show that the solutions obtained from the stochastic approach reduce the objective function value by 25% on average compared to a deterministic approach.