The patient appointment scheduling problem in outpatient chemotherapy clinics is one of the most important and challenging problems due to large numbers of binary variables and thus unrealistic computation times. In this paper, we propose a new approach inspired from cellular manufacturing to reduce the number of binary variables and constraints. The proposed approach consists of two stages: the clustering stage and the mathematical programming stage. In the clustering stage, current clustering algorithms are used to find the optimum cluster members for a given patient mix. The resulted clusters are used in the second stage, namely the mathematical programming stage to optimally assign every nurse to a cluster of patients and a group of chairs at the optimum time slot. The objective function of the mathematical programming model is to achieve the minimum total completion time of all treatments. Compared to the previous models, the proposed approach has the advantage of giving the optimum solution for real problems in much fewer computation time. Another advantage is that a nurse is assigned to each cluster of patients along their treatment durations instead of assigning a nurse just to start up the treatment.