Balanced Workload Distribution?

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I have N jobs with varied work loads that is to be distributed among n persons so that the work load is as balanced as possible.

e.g-we have to divide 5 jobs with work loads <1,2,3,4,5> between 3 persons. The best way would obviously be to distribute as follows:-

<1,4>,<2,3>,<5>.
Thus the problem is to minimize

z=abs(a-b)+abs(b-c)+abs(c-a)
where a, b, c are the workloads of the three persons.What would be the most efficient way to solve the problem?

Posted 22-Feb-15 7:39am

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Sergey Alexandrovich Kryukov 22-Feb-15 13:47pm

What have you tried so far?
—SA

ZurdoDev 22-Feb-15 22:44pm

Do you have a coding question?

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Peter Leow · Answer 1 · 2015-02-22T17:22:00

This is an optimization problem. If you are asking about the algorithm, then try Genetic Algorithm, you can find relevant articles[^] on CP.
In a nut shell, you can add another effortless job as 0, so there will be a total of 6 jobs. You program will then permutate these 6 jobs among the 3 persons, then use the z=abs(a-b)+abs(b-c)+abs(c-a) as the fitness function to measure the balance-ness of each permutation.

Person            a          b            c
job rotation1   2, 3        0 5         4, 1  => z?
job rotation2   0, 2        3 1         4, 5  => z?
... and so on

Have fun!