How should administration punish sexual abuse/trade for grade?
Initially, like xLeitix, my response to this question was "Say what?"

Then I did some reading. For those who are interested, here are some articles on the subject:


Sex, grades and power in higher education in Ghana and Tanzania
Kenyan tutor on 'sex for grades'
Teachers Demanding Sex for Grades
Liberian women battle against 'sex for grades' at universities
Sex for grades in Africa's academy 


Given this context: if sex-for-grades is sufficiently "popular" in your department that it can "strongly weaken the quality of education," then you have a bigger problem then how and whom to punish the next time it happens.


  What should a head/dean do in this regard to preserve the education quality?


In a department where sex-for-grades is common, you can't stop it by punishing it in an ad-hoc manner. You have to create a comprehensive policy; educate students, faculty, and administration about this policy; and then enforce it. 

If you don't have a university policy (or your university policy is not sufficient), you can create a school-wide or departmental policy, depending on the scope of your position.

Your sexual harassment policy should clearly describe:


Exactly what constitutes sexual harassment,
What the consequences will be for those involved,
and (the most important of all), How to safely report harassment.


In addition, you should then take steps to educate 


Faculty, on how to protect themselves against sexual advances from students (steps such as: keep a strictly professional tone in emails and other communication with students, have meetings with students with office door open, etc.)
Administration, on how to respond to allegations against students/faculty with sensitivity and discretion
Students, on how they can report harassment without fear of retaliation



  Who to be punished? Student or professor? Or both ?


As for who to punish: any faculty or administrative staff member who


solicits sex from a student in return for grades, or threatens to fail a student who won't have sex with them, or
responds to an offer of sex for grades with anything other than a firm "NO"


should be punished.  Of course, it must say so in your policy and you must make sure to educate faculty about this policy.

Students are usually the disadvantaged group in this scenario, and punishing students could deter them from reporting sexual harassment. Therefore, I would advise against punishing students in most cases. I can think of a few exceptions, where it is appropriate to punish students: e.g., students who make repeated sexual advances, despite being warned more than once in an official capacity not to do so.


  How to punish?


depends entirely on what kind of punishment you can enforce, as a department head/dean. I have no idea what kind of power you have as a department head/dean in your educational system.

Typically in the U.S. it would be handled at a higher level, as   Nate Eldredge pointed out, because department heads in the U.S. don't usually handle disciplinary matters.