From the stacktrace I infer you're using DynamicData in your website, and you said you're using the Web Site template in Visual Studio.
There are a couple of issues with that, but you can try a couple of things:
1: Don't use the Web Site template, but the Web Application template
or
2: Precompile the Website before deploying
or
3: Move the edmx file from the App_Code directory to a seperate library, compile it and add the resulting .dll to the websites bin folder.