As a manager, Have you ever had to fire anyone? How did you feel about that?

I didnt fire directly, but I was invovled indirectly in firing an employee few years ago. It was very unfortunate, he become irresponsble towards the assignments, and couldn't be able to complete tasks on time, and due to him one of the deadline was missed.. We involved HR and put him PIP (Performance improvement program) for3 months, but things didnt change. So, based on the PIP results, HR asked him to resign (few months of compensation was given to him)... I felt very bad about that, and felt unfortunate being in that position. But, it is part of the management job, and as long as I didn't do a mistake I don't have to take the things to heart...

Yes I had to do it atleast three times during my14 years career as a Manager.It has been a very sad moment to lose a colleague and a team member but as a Manager decisions are to be taken in the interest of company and team so that further losses are stopped and the team remains intact:

1.One First line Sales Manager for gross violation of code of conduct entered into an illegal transaction with distributor.

2.One Brand Executive who would sell articles of company in grey market which were  meant for promotion of product and display.

3.One Sales Rep despite providing him lot of support and counselling during field work , was grossly neglecting his duties and  doing false reporting and town visits just to levy expense burden on company  with poor productivity.

The most critical period at any organization that time when new manager has appointed: He has to get enough info about his team and understand the procedures of operations.

In this case he might find some people out of his concept who will be fired instantly, such people I called them the victim of management changes.

This is exactly what I did when I got first managerial position in business life. But I did it fully convenced that they obstruct the operational flow of the project without any regret about my decision.

I did not understand the formula a good question, but I think you mean punishment employee Takia penalty or deduction from salary or incentive monthly and this is happening at work

I usually had people fire themselves.  I am honest with people as to what I expect and tell them when they're not achieving the level desired.  I find that if you do that people will either find a way to get where they need to be, with or without my help, or quit, and leave, telling me that, "It's just not for me."

never happened but i think if an employee has broken the laws & regulations of the company he should be punished according to the company reguilatry  

actuly no 

As a new head of department, how you approach and change the behaviour of a difficult Senior Executive which showing sign of disrespect and poor self discipline?

Any one can have a good solution.So you should not need to be bossy.You should be open to take suggestions.It will not only helpful to find a good good solution to problem but also helpful to encourage the employees