AI and DS Skills

To correctly add an interval variable as the first in a sequence in your model, you need to ensure that the interval variable is appropriately integrated into the sequence constraint. Here's how you can do it:

1. Create the sequence variable for each resource:

   • Collect all interval variables associated with a resource.
   • Create the sequence variable including all these intervals.

2. Create the interval variable that should be first in the sequence:

   • Define the new interval variable for the activity.

3. Add the interval as the first in the sequence:

   • Ensure the new interval variable is included in the sequence variable.
   • Add the constraint to enforce this interval variable to be the first in the sequence.

Here is an example of how you can achieve this:

from docplex.cp.model import CpoModel

# Create the model
model = CpoModel()

# Assuming you have your resources and intervals defined
resources = ['resource1', 'resource2']  # Example resources
intervals = [
    {'resource1': model.interval_var(size=5, name='int1')},
    {'resource1': model.interval_var(size=3, name='int2')},
    {'resource2': model.interval_var(size=4, name='int3')},
    {'resource2': model.interval_var(size=2, name='int4')}
]

# Create sequence variables
for r in resources:
    int_vars = [value for entry in intervals for key, value in entry.items() if r in key]  # list of intvars for this resource
    seq = model.sequence_var(int_vars, name='seq_var_' + r)  # create the sequence_var for each resource & include all int_vars for the resource
    model.add(seq)

    # Create an interval to put first in the sequence
    itv = model.interval_var(size=5, name="Service_Start_" + r, optional=False)  # create interval var for the activity

    # Add the new interval to the sequence variable
    int_vars.append(itv)
    seq = model.sequence_var(int_vars, name='seq_var_' + r)  # recreate the sequence variable with the new interval

    # Enforce the interval to be the first in the sequence
    model.add(model.first(seq, itv))

# Solve the model
solution = model.solve(TimeLimit=20)

if solution:
    print(solution)
else:
    print("No solution found")

Explanation:

1. Creating the Sequence Variable: We gather all interval variables associated with a specific resource and create a sequence variable (seq).
2. Creating the Interval Variable: We define a new interval variable (itv) that we want to place first in the sequence.
3. Adding the Interval to the Sequence: We add the new interval to the list of interval variables and recreate the sequence variable to include this new interval.
4. Adding the Constraint: We add a constraint using model.first(seq, itv) to ensure the new interval variable is the first in the sequence.

Notes:

• Ensure that the interval variable (itv) is included in the sequence variable before enforcing it to be first.
• Recreating the sequence variable after adding the new interval ensures that the constraint model.first(seq, itv) is correctly applied.

By following these steps, you should be able to enforce the interval variable to be the first in the sequence without causing the program to hang.