With Charlie Sheen, the star of the hit CBS comedy “Two and a Half Men,” now in rehabilitation for his persistent problems with addiction, the initial reaction at the network  and at the show’s production company, Warner Brothers  has been relief.

Executives seem less concerned that the show is on hiatus than thankful that the circus that has surrounded Mr. Sheen’s life in recent years may be over, at least for now.

CBS executives, who had for at least a year quietly expressed worry about Mr. Sheen’s problems, would not comment on the record about his decision to enter rehab because they said it was a personal matter. This week, the executives privately acknowledged that securing a healthier future for Mr. Sheen in the long term was more important than how to resolve the production issues his absence may cause.

The network’s overall intention, executives have indicated, is to try to ride out the situation, see how the ratings come in and get a better idea as the weeks go by how long Mr. Sheen will be unavailable.