Let’s imagine you are a team leader (for me it’s really difficult, i’ve never been a manager). Your team consists of 5 different engineers (if you are a good leader, you must see that the engineers are mutually different, otherwise you ought to resign). You just have obtained 10 different tasks to accomplish in a predefined period (say in next quarter).
In how many ways can you assign 10 different tasks to 5 different engineers such that each engineer gets at least one task (an idle engineer is not admissible)?
The answer: 10! * 9! / (5! * 4!) = 457,228,800
General answer for assigning ‘n’ different tasks to ‘r’ different engineers:
n!*(n-1)! /[(n-r)!*(r-1)!]
Because of a natural diversity in your team, each engineer has its own sub-specialization, moreover, the tasks have different time estimations (to be accomplished). Therefore, you need a good algorithm to look through all 457,228,800 various assignments to find the best one, ideally each engineer gets tasks which are appropriate to his/her sub-specialization and his/her wishes, all tasks are finalized in time.
However, for large teams you quickly get to Combinatorics Explosion: For instance, if your team consists of 10 different engineers and you have 25 different tasks to accomplish in a quarter, then brute-force searching for the best assignment is unfeasible. You need a sort of blind search method, e.g. you can use genetics programming methods.
23+ years’ programming and theoretical experience in the computer science fields such as video compression, media streaming and artificial intelligence (co-author of several papers and patents).
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