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Let's say nurses normally do 1 shift

for d in all_days:
    for s in all_shifts:
        model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 1)

But I want to make nurses either do 1 shift or 3 shifts (but no 2 shifts). How do I combine between

        model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 1)

and

        model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 3)

?

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2 Answers 2

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You can also do:

model.AddLinearExpressionInDomain(sum(variables), cp_model.Domain.FromValues([1, 3]))

Or even:

for d in all_days:
    for s in all_shifts:
        b = model.NewBoolVar("")
        model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 1).OnlyEnforceIf(b)
        model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 3).OnlyEnforceIf(b.Not())

PS:

Let's say nurses normally do 1 shift

Wouldn't that be:

for n in all_nurses:
    model.Add(sum(shifts[(n, d, s)] for d in all_days for s in all_shifts) == 1)
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Introduce a binary variable $x_{d,s}$ and change the right hand side to $1+2x_{d,s}$.

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  • $\begingroup$ Good library-agnostic solution! $\endgroup$
    – Rizky Luthfianto
    Jun 9, 2020 at 5:57

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