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Problem for very strong brains

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I have a problem that seems so common yet so tricky to manage. I wonder if there are any process tools or other methodologies to approach it. I would also like to generally discuss it and brainstorm.

I have 1000 files. I have a waterfall process of five steps that each file needs to go through one after the other.
Each of the five stages has its own speed (eg 5h per file, 10h per file etc), based on the average time of processing per file and the number of people available to process files in that stage.
You have a number of files to be processed (through all the stages) by a specific deadline.

How can you allocate the resources (people) to complete the files in the shortest time?
The tricky bit is that a specific number of people can do stage 1 and 3 only, and the rest can do stages 2, 4, 5 only.

To add to the complexity, you have additional bunches for files with different deadlines, let's say 2000 files to be completed three months after the first deadline and 5000 five months after the first deadline.

Any opinions?
I have some ideas but would like some input first.


You can imagine it as if each file is a piece of string of specific length with five different regions (let's say coloured differently).

How can you determine the start and the end of each string in a timeline, placed one below the other, so that the thickness (total concurrent strings) are within the limits (people capacity) and the total length of the distribution of the strings is within specific length.

Hope I did not confuse you with that geometric analogue :)

Is it only me, or does anyone else at DC think that we are asked to do the homework for the Excel course he is taking (only he didn't mention Excel in this specific request)...  :P

If it is project management homework, you most likely have to calculate the critical path.

If it is a real business problem I would suggest going to the workplace and following the process, understanding what happens in each hour. Is it really 10 hours of processing time, or is it 5 minutes of processing time and 9 hours and 55 minutes of waiting time? After identifying all the blockers and impediments I'd suggest working with the employees on reducing that times. In addition, identifying the pacemaker operation and then load balancing following it. Keep repeating the process until the end of time.

Main problem stays the same, unable to open and read a book.


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