Staff Utilization Algorithm

Hello - I'm working on a project I can't wrap my brain around this and am hoping to get some help here.

We have a scanning project that involves the 3 tasks of prepping, scanning and reassembling files.

Given the following information:

Total Files = 650
Employees = 5
Number of Hardware Scanners = 3

Prepping – 3 files per hour
Scanning – 5 files per hour
Reassembling – 3 files per hour

What is the formula/algorithm to determine how to best utilize the staff to get all 650 files prepped, scanned and reassembled in the least amount of time? i.e. # of staff performing each task for X period of time/# of files before shifting staff to other tasks.

Any help would be greatly appreciated. I am working on this in excel now.
Thank you!

Forgot to add above that each employee is working 40 hours per week

sounds like a basic priority queue thing... each hour you reallocate personel according to the priorities (i.e. try to make sure your bottlenecks are as close to 100% activity the whole time)

put at most 3 people on scanning in so far as you can give each person the 5 files for that hour
if you still have files to prep, put everyone else on prepping in so far as you can give each one 3 files to prep (except the very last pile of files which won't be complete)
if you still have files to reassemble put whatever personel you have left on reassembling