Does every customer need an order?

Yes. Orders in Fast-Weigh are directly associated with a single customer. If you need the ability to generate an invoice for the customer, then you will need to create an order for that customer.

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What about one-time cash customers?

If you plan on accepting payment at the time of ticketing then you could create a generic Cash Customer and Order. Any one-time customers could be ticketed under this order but keep in mind that you will not be able to break down activity on this Customer in reporting.