A stochastic programming approach for the scheduling of medical interpreting service under uncertainty

Limited English Proficiency (LEP) patients face higher risks of adverse health outcomes due to communication barriers, making timely medical interpreting services essential for mitigating those risks. This paper addresses the scheduling of medical interpreting services under uncertainty. The problem is formulated as a two-stage stochastic programming model that accounts for uncertainties in emergency patients' arrival and service time. The model handles the hiring decisions of part-time interpreters and the assignment of full-time and hired part-time interpreters. The objective is to minimize the total cost, which encompasses full-time interpreters' overtime cost, the fixed and variable costs of part-time interpreters, and the penalty cost for not serving LEP patients on time. The model is solved using the Sample Average Approximation (SAA) algorithm. To overcome the computational burden of the SAA algorithm, a Tabu Search (TS) algorithm was used to solve the model. A real-life case study is used to validate and evaluate the proposed solution algorithms. The results demonstrate the effectiveness of the proposed stochastic programming-based solutions in concurrently reducing both the total cost and the waiting time. Further, sensitivity analysis reveals how the increase in some key parameters, such as the arrival rate of emergency patients with LEP, impacts scheduling outcomes.