Robust Appointment Scheduling for Random Service Time Using Min-Max Optimization

Appointment Scheduling is an increasingly challenging problem for service-centers, healthcare, production and transportation sector. Challenges include meeting growing demand and high expectation of service level among the customers and ensuring an efficient service system which reduces the expenditure related to idle times and under-utilization of the system. The problem becomes more complicated in the presence of processing time uncertainties. In this study, a Robust Appointment Scheduling model is developed using Min-max Optimization to provide appointment dates for a system with a single processor. The objective is to minimize the cost of the worst-case scenario under any realization of the processing time of the jobs. The proposed methodology requires less information regarding the uncertain parameters and can provide optimal solution while only considering the extreme bounds of the uncertain parameters. Therefore, it is applicable to any probability distribution of the uncertain parameters. The model is well suited for any general case appointment scheduling problem regardless of the application field. Since the problem is NP-hard, an Iterative Solution Procedure and a Dynamic Programming model are developed for solving larger instances of problem in polynomial time. In addition, propositions that support the robust model are provided along with theoretical proofs. Appointment scheduling of two case studies, a Dentist’s clinic and VIA Rail Canada are performed. Both case studies exhibit high performance of the proposed robust model in terms of cost savings and computational efforts. This work will contribute both to the literature related to uncertainty handling in decision making and to the industries, which aim to achieve an efficient service system