Coordinated appointment scheduling with multiple providers and patient-and-physician matching cost in specialty care

To achieve effective care, it is critical to match patients with capable physicians in specialty care. Motivated by the rising popularity of patient-and-physician matching applications in specialty care, this study optimizes the matching and appointment scheduling problems simultaneously in a stochastic environment, in which a decision-maker determines the patient-and-physician pair assignment and the starting times of services. We develop a stochastic optimization model to minimize the matching and operational costs (i.e., patients’ waiting time costs, service providers’ idle time and overtime costs). This paper is the first study that incorporates matching and appointment scheduling problems together. The benefits of combining these two problems are enormous. The experimental results show that the operational costs gap is as large as 51% between the ill-matched and the well-matched patient-and-physician scenarios. We first reformulate this problem as a two-stage optimization problem. With the analysis for the optimal solution of the second stage problem, a Benders decomposition algorithm is developed. To improve the efficiency of the proposed algorithm, we also prove a low bound of our problem and use it to construct a set of feasibility cuts. Then, we extend our method to incorporate no-shows. Our algorithm can solve problems efficiently, and it can obtain optimal solutions for medium-size problems within 2 or 3 min. In contrast, traditional optimal methods require nearly 2 h. For large-size problems, our algorithm can obtain optimal solutions within 5 or 6 min, whereas traditional optimal methods cannot generate a result within 5 h. Finally, numerical experiments are conducted to evaluate the performance of our proposed algorithm and to investigate the variation of the optimal solutions in different scenarios. To provide quality care as well as minimize the total cost of appointment scheduling in specialty care, we suggest that physicians should develop or train their specialties based on the local patients’ disease pattern. We also disclose that the no-show has less influence on the service system when the weight of the matching cost is substantial.