<p>This paper focuses on the assignment of attending physicians between the residents they supervise and their own responsibilities. Unlike prior work that assumes patient care can be interrupted at any time, we consider the more realistic and technically challenging situation when patient care is non-preemptive. Under the assumption that a holding cost is incurred when residents and patients wait for a conference with the attending physician and that rewards are earned whenever the attending physician completes a task (on his own or with his residents), we completely characterize the allocation of the attending physician that maximizes the long-run average profit. Furthermore, we show that the optimality conditions are simple thresholds on the holding cost. We also discuss how the optimal allocation of the attending physician differs from those in systems with preemptions. In particular, we show that the main difference occurs when the holding cost is high and there is no resident waiting for a conference. In this case, the attending physician waits for a resident to be ready for consultation in the non-preemptive case, whereas he works on his own responsibilities in the preemptive model. We conclude with a study of various extensions of our attending physician and residents interaction model and show that the structure of the optimal policy remains the same in these more general settings.</p>