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Staff Utilization Algorithm

Posted on 2013-06-18
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Last Modified: 2013-06-19
Hello - I'm working on a project I can't wrap my brain around 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 - each working 40 hours per week
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!
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Question by:tempadmin
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by:d-glitch
d-glitch earned 100 total points
ID: 39257335
Prepping takes    650/3 =  217 hours
Scanning takes    650/5 =  130 hours
Reassembly takes  650/3 =  217 hours

Total = 464 hours  or 10+ man-weeks

With five people it will take more than two weeks.

You can't start scanning until you have prepped a bunch of files ahead.

You can scan 3*8*3 = 72 files a day.

So spend the first day day prepping ==>  5*8*3 =120 files ready to scan.
On the second day, whoever isn't scanning should be prepping or reassembling.
The highest priority is to make sure you have files ready to scan for the
next day.

The two non-scanning employees can only prep 2*8*3 so they can't quite
really keep up.

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mccarl earned 400 total points
ID: 39258208
The answer is quite simple. With NO other constraints then what you have communicated above, then to get all files done in the least total time (ie. this is our only optimization goal), then this is simply achieved when the staff are maximally utilized, ie. you minimize the time that any employee is sitting idle.

In this case, there are solutions that exist where you have 100% utilization, ie. no employee is ever sitting idle. The simplest of these, I would say, is this...

Have all 5 employee prep the 650 files until they are finished
Once the prep has finished, set 3 people to scan the 650 files until they are all finished. At the same time, set the 2 other people to start assembling. Scanning will occur at 5 files per hour * 3 people = 15 files per hour, and assembling will occur at 3 files per hour * 2 people = 6 files per hour. So the scanners will always keep the assemblers in work
Once the scanning has finished, set the 3 scanning people on to the assembling task, then all 5 people are assembling until all the files are done

Timings...

Prepping will take 650 / 3 = 217 manhours / 5 people = 43.4 elapsed hours
Scanning will take 650 / 5 = 130 manhours / 3 people = 43.3 elapsed hours
   (In that time wihile scanning...
    Assemblers will assemble 43.3hours * 3 files/hour * 2 people = 260 files)
Final part of assembly will take (650 - 260) / 3 = 130 manhours / 5 people = 26 elapsed hours

Total elapsed time = 112.7 hours (ie. two weeks and 4 days)
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