An objective method for establishing patient prioritization in the context of a radiotherapy waiting list is investigated. This is based on a utilitarian objective, being the greatest probability of local tumour control in the population of patients. A numerical simulation is developed and a clinical patient case-mix is used to determine the influence of the characteristics of the patient population on resulting optimal patient scheduling. With the utilitarian objective, large gains in tumour control probability (TCP) can be achieved for individuals or cohorts by prioritizing patients for that fraction of the patient population with relatively small sacrifices in TCP for a smaller fraction of the population. For a waiting list in steady state with five patients per day commencing treatment and leaving the list (and so with five patients per day entering the list), and a mean wait time of 35 days and a maximum of 90 days, optimized wait times ranged from a mean of one day for patients with tumour types with short effective doubling times to a mean of 66.9 days for prostate cancer patients. It is found that, when seeking the optimal daily order of patients on the waiting list in a constrained simulation, the relative rather than absolute value of TCP is the determinant of the resulting optimal waiting times. An increase in the mean waiting time mostly influences (increases) the optimal waiting times of patients with fast-growing tumours. The proportional representation of groups (separated by tumour type) in the patient population has an influence on the resulting distribution of optimal waiting times for patients in those groups, though has only a minor influence on the optimal mean waiting time for each group.