CP-SAT to balance task assignment

Question

Dears,
I'm wondering if CP-SAT as any built-in function that allow me to balance the number of tasks assigned to the users.
Now I'm calculating the variance and I'm minimizing it in the objective function, so it would be great to have the possibility to calculate the variance with a built-in function, but I'm wondering if I have alternatives.

Thanks

score 1 · Answer 1 · answered Jan 29 '21 at 11:34

1

There are no alternative.

If the number of tasks and of workers is fixed. You can compute the average, and using an epsilon, add the following constraints:

for all workers:
  model.Add(sum(assigned_tasks) <= average + epsilon)
  model.Add(sum(assigned_tasks) >= average - epsilon)

model.Minimize(epsilon)

This is less precise, but much faster.

answered Jan 29 '21 at 11:34

Laurent Perron

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to minimize epslon I need to find epsolon as a function of the operator per task decisions, Am I right? – stefano guerrieri Jan 29 '21 at 12:20
could be a global epsilon, could be one per operator, and minimize the sum of epsilons – Laurent Perron Jan 29 '21 at 12:27
Not sure I understood. If I have 3 workers and 9 tasks for example how epsilon function should be?. Thanks – stefano guerrieri Jan 30 '21 at 13:42
Constraint each worker to have between 3-epsilon and 3+epsilon tasks assigned to him, and minimize epsilon. – Laurent Perron Feb 01 '21 at 11:35

CP-SAT to balance task assignment

1 Answers1