This paper addresses the problem of appointment scheduling of patients of an oncology outpatient unit. Each patient is first seen by his oncologist, and then the drug is prepared and injected to the patient. Two major resources including oncologists for consultation and beds for injection are considered. Idle times of oncologists are not allowed. The problem consists in scheduling the appointment time of each patient and the starting time of the injection in order to minimize the total weighted cost incurred by patient waiting times and the makespan. A Lagrangian relaxation-based heuristic and a local optimization heuristic are proposed. Numerical results show that the Lagrangian relaxation-based heuristic always outperforms the local optimization heuristic.