Teleconsultation Appointment Scheduling Under Uncertain Service Duration and Doctor Availability

This study explores the appointment scheduling problem for telemedicine consultation services within the context of telemedicine. With the objective of cost minimization, it considers uncertainties in stochastic service times and the availability of doctors. The problem is modeled using a distributionally robust optimization framework, where scenarios are depicted based on relevant uncertain events, and partial distribution information of random variables is extracted from these scenarios to construct scenario-wise ambiguity set. The model is reformulated as a mixed-integer linear programming problem, which can be directly solved using existing solvers. Numerical experiments using real data reveal that the solutions provided by this model are not overly conservative, offering reasonable scheduling solutions for different numbers of patients over a period., and with shorter solution times compared to stochastic programming models. Additionally, sensitivity analyses are conducted on model parameters, investigating the impact of fixed doctor costs and ambiguity set parameters on the results.