Applicant Frenzy and No, You Can't "Call Dibs"

Managers cannot "call dibs" on applications received for open positions.

Well, they do and my staff must not play. This is not a game. We have to staff many key positions and the medical center is our focus, not one supervisor or one service line, especially not at the expense of another. And not at the expense of internal HR team function - can you just imagine what that would be like?!  No way. We are neutral and we must work together to remain neutral. To be any other way is a slippery slope down and not somewhere I am willing to go.

Decreased application flow plus increased vacant positions equals applicant frenzy and I absolutely do not want find my department on the front lines of a bidding war. So, a call out to my recruiter and HR readers. How do you manage application flow to ensure that all managers with similar positions open have an equal opportunity to review applications received?  Any and all thoughts greatly appreciated.

Until then, thanks from the front lines!