I can't think of any archive utilities that automatically delete input files.

And specifying the output file can take any filename path.
...
Since my example was using the unix (linux/OSX) bash shell...
For a batch file, try something like:
Code:
cd C:\User\Docs\
for /d %%d in ("*") do (
7z.exe a C:\path\to\archive\%%d.zip %%d\
)
I am not 100% positive that that is valid batch syntax (I am not a Windows user and I get confused sometimes

), but I *think* that will do it.
You can change the archive name and extension and 7-Zip should do the right thing automatically based on your chosen extension (*.zip, *.7z, *.tar.gz should all work).
%%d is the variable holding the name of the folder and also specifies the filename of the archive.
This uses the
http://7-zip.org command-line 7z.exe so it must be in your PATH or else you must specify the full location of 7z.exe