The appointment scheduling issue has been widely used in a variety of service industries, including healthcare, finance, and legal advice. Uncertainty of processing time and job no-shows make the problem more challenging. Most of the current literature makes unrealistic assumptions about real-world scenarios, such as constant service time, and they use a vast quantity of data to view the service time distribution or failure to account for work no-shows. In this research project, a robust appointment scheduling model is developed to generate appointment dates for a multi-mode system while considering customer no-shows and uncertain service times. The objective is to minimize the total expected cost of the job waiting time and service provider’s idling and overtime for the worst-case scenario under any realization of the processing time of the jobs. The advantage of the suggested methodology is that distributional data about the uncertain service time are not required. Only the extreme boundaries of the uncertain parameters need to be accounted for. Thus, this approach can be employed irrespective of the stochastic nature of the variables being addressed. Mathematical programming is used to solve the model. Test cases are utilized to quantify the impact of the problem parameters on the end of the day, the job waiting time, server idle time, and total overall cost.