Modified formulation for the appointment scheduling problem of outpatient chemotherapy departments

The problem of appointment scheduling in outpatient chemotherapy departments is a hard problem due to the fact of a large number of variables, and thus unrealistic computation times are required. In this paper, we propose a new approach inspired by the cellular manufacturing concept to reduce the number of variables and constraints in a current approach retrieved from the literature. The developed model assigns every nurse to a cluster of patients and chairs on the optimum time slot to achieve the minimum completion time of all the treatments. The modified formulation has the advantage of reducing the number of variables and constraints, and thus increases the ability to give optimal solutions for real problems in reasonable computation times. Another advantage, it dedicates a nurse for each group of patients in their whole treatment time other than assigning a nurse just to start up the treatment. Moreover, this model balances the nurse workload along the working time as much as possible. We conduct numerical experiments to highlight the computation times of the current model and the modified one and also give a benchmark analysis for a small instance. The results show that the computation times of the developed model are less than the current model. Finally, we propose a solution framework for the modified model based on clustering and mathematical programming.