Filemaker can handle all these tasks. You can download a 30day trail of Filemaker12. http://info.filemaker.com/US-en-FMP-Trial-Form.html
There is a starter Inventory app that you can look at to give you an idea or use / modify. I'm sure you will have to modify the app to work with your batch numbers. There is a lot of help on this forum, so if you get stuck you can all ways ask questions.
There are webpages that may help your quest. The first 5 in this list especially.
Starting Point would be useful for ideas on fields and tables required. It was created by the company that made the Starter Solutions in FMP.