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job assignment problem

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Can someone suggest an algorithm to solve job assignment problem with condition?

With condition means that some jobs cannot be done by some workers. For example table as shown below:


In this table x - means that it is impossible to do. For example, worker 1 cannot do jobs 1,3 and 5.

I encountered such situation and there may be cases as shown above when usual Hungarian algorithm seems cannot solve such task because there is no way to complete all tasks by distributing one task per worker.

However, my main case it is allowed that one worker wil do several tasks (tasks, which worker can do). Main task is to complete all jobs using existing workers, but it is desirable that, all workers do roughly same number of tasks.

So is there some solution of such problem? May be any algorithms do exist?


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Nurlan - welcome.


Not really my scene - but in order to get some of the maths bods more interested you might wish to tidy up and define your parameters a little better.


What are the figures in boxes that do not have an 'x' ? Fraction of a year/day/hour spent on task? Quality of completion? Payment required?


Why does task one have no figures? Are figures for task four correct?


What is actual goal - presume requires all tasks completed - but normally also requires something to be minimized/maximized?

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