[CP-SAT] Modelling a mimimum in a cumulative constraint

[Dan G]

Hello,

We are solving a RCPSP. We are using Cumulative constraints to limit the capacity. Our endusers would like to ensure that the activity is at least above a certain level. For instance, we will not load a given machine if it has not at least a workload of X kg.

From my understanding, we need to switch from Cumulative to Reservoir constraints.

Are we right or we are missing something more efficient in modelling?

Thanks in advance for your answer.

Best Regards,

Dan

[Dan G]

Looking further into the reservoir constraint definition, I think we are wrong .

To clarify my question, we have intervals and associated demands. We would like that the demands d on any given time slot t should respect the following constraints

\forall t;  \sum demands_t = 0 or min_{capacity} <= \sum demands_t <= max_{capacity}

Thanks in advance.

Dan

[Laurent Perron]

This is an extremely hard constraint to propagate, and it is not supported directly.

You will need to iterate over all time points, and add the contributions of all demands that cross that time point.

This is a 'heavy' model.

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00

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[Dan G]

Hello Laurent,

Thank you for your answer. We will try to find another way to model this kind of constraint, maybe by reducing the number of days possible and then post processed the solution.

Best Regards,

Dan

[David Lubinsky]

You might be better off with a big outer loop searching for the right number of machines of each type.  If all machines are the same a simple binary search will work, if you have different machine types you can look at more unconstrained solutions to guess the best machine mix and solve again. 

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[Laurent Perron]

I retract this.

Look at https://github.com/google/or-tools/discussions/4163#discussioncomment-8945141

Laurent Perron | Operations Research | lpe...@google.com | (33) 1 42 68 53 00