Multiserver time window allowance schedules for virtual visits with uncertain time-dependent no-shows and service times

Abstract

Virtual care serves as a new mode that can divert non-urgent visits from traditional office visits. Whether virtual service can improve the access to medical treatment and reduce the burden of traditional office services, the key issue is to generate efficient appointment schedules with the lowest operation cost. In this paper, considering the uncertainty of time-dependent no-shows and service times, we investigate a multiserver time window allowance appointment scheduling problem, where time window constraints that restricts virtual visits to be served during the particular period are explicitly modeled. We formulate the problem as a stochastic mixed-integer program to optimize decisions of physician allocation and appointment time simultaneously. Based on the sample average approximation, a stabilized Benders decomposition algorithm is developed by incorporating acceleration techniques, such as cut aggregation and feasibility cuts. Numerical results based on real data indicate the effectiveness of the proposed multiserver time window allowance schedules (MTWAS) and algorithm. Comparing with the off-the-shelf solver Gurobi, the developed algorithm demonstrates high performance in terms of computation speed and solution quality. Under different time-dependent no-show patterns of virtual and office visits, the obtained MTWAS perform better than previous solutions in almost all test cases. In addition, we offer useful managerial insights to aid the virtual service provider in making better scheduling decisions.