distribution/work load assignments - who gets next?

zhitz18

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Jul 15, 2011
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Hi!

Essentially, I would love if someone could help point me to an article, some key words I could search in google or the 'realm' of math under which the following problem would fall:

-I have 'x' workers.
-X is a positive integer, not equal to zero.
-These 'x' workers make up a 'pool' of workers.
-Each worker within the pool has a number of work-items they currently have on their plate, and their capacity.
-Work-items are essentially that, work that is assigned to them.. if I was given 10 'widgets' or 'work-items', my work-items would be at 10.
-Capacity is a percentage representing how much work one worker would get relative to others in their pool. For example, we have a pool of workers that consists of myself and one other worker, if I'm at 70% capacity, and the other worker is at 100% capacity, he would have the better chance of getting the next work item.

The problem/question: With the given information about a worker (current work items and their capacity), how can you figure out what worker would be best to serve the next work item? By best, I mean has the most bandwidth to take on the work-item.

Example- we have 4 workers in the pool with 5, 6, 7, and 8 work-items each, respectively. Their respective capacities are 50%, 90%, 70% and 60%. Who would be the best worker to take on the next work item?

I was handed this problem to solve at work - but I need some leads on how one could go about solving it - what type of math does this fall under? Articles you could point me to? Keywords to google? I don't know if I have enough information to make this decision either.I googled distribution methods (I have a computer science degree, not math :) ) but got a lot of hits that don't appear to apply in this type of problem.

Thank you for any direction you can provide!!!!
 
I may or may not have solved it... can anyone check my method?

Dataset:
Worker A, 8 work items, 70% capacity
Worker B, 5 work items, 80% capacity
Worker C, 11 work items, 90% capacity

For each worker - I take their work-items divided by their capacity, to find what they would be working at IF they were at 100% (I think that's what I'm uncovering here??).
Worker A -> 8 / .7 = 11.5.
Worker B -> 5 / .8 = 6.25.
Worker C -> 11 / .9 = 12.2.

I then take the average of these numbers (11.5+6.25+12.2 = 29.95, then do 29.95/3 = 9.9) which is 9.9.

Whoever is less than the average would get the next work item. In this case worker B would get the next work item because 6.25 is less than 9.9. If there are more than 1 who are less than the average, I would just be taking the lowest one..

make any sense?
 
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