When employees have complaints, should they first go to their immediate superior or should they talk with senior Management?

Some company executives and managers support an "open door policy" allowing employees to approach them with issues.  I support such programs, but I also believe that the immediate supervisor should be given the opportunity to address a works-related problem before the employee goes over the supervisor's head with an issue, regardless of any open door policy.

Professionally suppose to follow the chain of command, unless there is something really fatal.

When we need support from our immediate superior for all our day to day requirements like recommendations for leave, Permission to go out during office hours, recommendations for promotions/increment than for any complaint also he/she should be told at first instant.

for any grievance/complain/problem, employee should go to their immediate supervisor then next step is line manager or shop steward,3rd senior is department manager or union supervisor or last is HOD/GM/Director, if anyone from them recommend to HR then follow the policy for communication. but the preference should be given to hierarchy levels.

I think that you should go to their immediate superior to inquire about the subject well

I would go to my  manager first. In the event he/she does nothing about it then I will see higher management. But its important to give manager the respect of consulting them first.

Hierarchy in the organization should be respected and followed. Escalate issue to immediate superior for an early solution and follow it however, if still left unresolved, raise it to Sr. Management. 

It is always advisable to propose couple of "best possible solutions" to the escalated issue.

It depends on the type of complaint you have. If your complaint includes your immediate superior, then you have to reach the senior management for sure.

And if it's about your counterparts and subordinates, you should first go to your immediate superior and then follow the hierarchy if the matter is not resolved.

The professional approach is to report to the immediate supervisor at the first instance. In some cases, the immediate superior is bias and may not listen to the particular employee, in that case, the employee would be a victim of discrimination, even if he reported to the senior management that won't give proper remedy for his grief. Rather it would affect him adversely.  In such cases, the employee may seek for a good recommendation from another department’s head who can lobby the direct superior and or the senior management to solve the issue with the employee.

Must go to immediate SUPERIOR.

People will always go to their immediate supervisor for any problem, UNLESS the relationship between him and his supervisor is not a "trusting" one. If trust exists between the two, one SHOULD and WILL approach his immediate supervisor, and that's the right thing to do.

Also, people begin to look out for opportunities when their relationship with their immediate supervisor becomes bad, not when the relationship with the HR manager goes bad. The immediate supervisor is the FACE OF THE ORGANIZATION for any employee.