Help!! Is it possible to use a Motor and encoder for my machine?

I am new to all this forum chat etc so please bare with me.
can I ask a simple question.
I need to stop and start a motor that is feeding in a product I manufacture.
I need it to feed in a set distance (1078mm) and stop. I’m thinking I need an encoder to measure how much product has been fed before it tells the motor to stop.
It is a continuous feed of material that needs to be cut every 1078mm.
Bare in mind I know nothing about plc’s and encoders.
I would usually do this myself simply with a magic eye sensor but I always have product in the way of the sensor after the cut. So I’m thinking encoder?
I have had a guy price it up for me but it seems like he has really over sold the job.
I thought it should be a pretty straight forward thing to ask a motor and encoder to do. Is it possible to just start the motor going with a signal in. Then encoder reads the material and stops at set distance. Then repeat.
is this possible
Your cost and complexity will go up with the needed precision and repeatability of your 1078mm cut. The cost will also go up with the power requirements of the motor.

Some questions you would need to consider:
Will the material be stopped while it's being cut or is it a type of flying shear?
How fast does it feed?
What's your required cycle rate?
Does the feed mechanism have a lot of mechanical slop?
Is it possible to apply an encoder mechanism to the material itself (like a wheel that rides on the material) without slip?

The slower it feeds, the easier it'll be to accurately stop at 1078mm. If the feed mechanism is tight with little slop, it'll be easier/simpler to put the encoder on the motor rather than deal with slip on the material.