Please see my comment to the question. You are missing the application or command with ZIP capabilities.
So, first approach is to have such application. I would recommend, first of all, open source 7-Zip:
https://en.wikipedia.org/wiki/7-Zip[
^],
http://www.7-zip.org/[
^].
Amazingly, there is no such thing in Windows which you could use directly in a command line or batch file, despite the fact that modern versions of Windows are certainly supplied with the ZIP capabilities hidden inside.
Strictly speaking, batch along is not capable of doing such thing, but the problem can be solved indirectly.
This is one of such solutions (sorry, I did not test it):
http://superuser.com/questions/110991/can-you-zip-a-file-from-the-command-prompt-using-only-windows-built-in-capabili[
^].
Essentially, this approach uses WSH under the hood:
https://en.wikipedia.org/wiki/Windows_Script_Host[
^].
WSH is used through JavaScript or VBScript programming and does not require any installations. So, why not using it directly? One of the ways to do so would be using .WSF file — please see a link below.
Generally, I would recommend to review your whole approach of using batch files, which are pretty much obsolete, hard to debug, and so on. How about using WSH directly, with .WSF file which you can use exactly as batch (also obsolete, but at least you can debug code). Anyway, you can simply click on this file to get it executed, as with a batch file, and don't need to install anything:
https://en.wikipedia.org/wiki/Windows_Script_File[
^].
Or you can use PowerShell, but you need to install it. Or some other application. Do you need archiving? What if this is not what you really need; maybe you need a Revision Control System instead, or something else? Just think about it.
—SA