Alright so you're using the Field Service app, that's a good start. I can help you figure out how to invoice your customers but need more info from you first. How do you currently determine who's billed at the first of the month and who's billed at the end of the month? Do you need the process to be fully automated, if so it wouldn't be possible as you can't schedule invoices to be sent out on the first of every month. However, you can automate it through a trigger such as a button being clicked.
With customization you can achieve what you're looking for, the amount of customization required depends on what exactly you need to happen. We can definitely guide you in the right direction but in order to fully scope out what you need and recommend the best solution you should really speak with one of our Consultants.
If this is something you wish to persue let me know and I'll get the ball rolling.
- Ashur