What should the CEO have done when he found out that a person with quasi-supervisory authority had a relationship with a subordinate?

Dr. P was a great emergency room (ER) physician. He had worked at Eastern Hospital for about ten years and now was serving as the president of his sixmember ER group. He had the type of personality that put patients and staff members at ease. He was a devoted father and active in his church. Therefore, it came as a shock to the hospital CEO when the ER director pulled him aside to inform him that Dr. P was having an affair with one of the ER staff nurses.
By all accounts it was consensual, but the ER director wanted to know if she should take any action. After discussing the matter for a few minutes, both concluded that because the affair was consensual and Dr. P did not really supervise the nurse, the only thing they could do was try not to have them work the same shift. However, both felt uncomfortable speaking with either Dr. P or the nurse. They felt the relationship was really “none of their business.”
The affair appeared to go on for about six months, until Dr. P’s wife found out and issued an ultimatum. After deep emotional struggles, Dr. P agreed to terminate the relationship. The nurse was upset, as she felt she had been promised marriage as soon as Dr. P divorced his wife. She became even angrier when Dr. P, who primarily worked the day shift, asked that the nurse be scheduled only nights so that he would not work at the same time, as he had promised his wife.