opposite of no_overlap constraint in docplex for CP

Question

I am using python for CP solving. I would like to know if there is constraint that does the opposite of no_overlap. This will be like overlap(interval, arr, n)

interval - single interval variable

arr - array of interval variables

n - positive integer less than length of arr

this will mean that atleast n interval variables from arr overlap in the interval of interval

This is for a situation in job scheduling when a job is not possible to be scheduled on a machine because there are already n higher priority jobs.

Answer 1

You can use overlap_length

docplex.cp.modeler.overlap_length(interval, interval2, absentValue=None)

    Returns the length of the overlap of two interval variables.

and count true constraints

from docplex.mp.model import Model

# Data

Buses=[
    (40,500),
    (30,400),
    (35,450),
    (20,300)
    ]

nbKids=300

# Indexes

busSize=0;
busCost=1;

for b in Buses:
    print("buses with ",b[busSize]," seats cost ",b[busCost])

print()    

mdl = Model(name='buses')

#decision variables
mdl.nbBus=mdl.integer_var_dict(Buses,name="nbBus")

# Constraint
mdl.add_constraint(mdl.sum(mdl.nbBus[b]*b[busSize] for b in Buses) >= nbKids, 'kids')

# Objective
mdl.minimize(sum(mdl.nbBus[b]*b[busCost] for b in Buses))

mdl.solve()

# Display solution
for b in Buses:
    print(mdl.nbBus[b].solution_value," buses with ",b[busSize]," seats");

#Add a constraint
# Number of sizes where we have 1 or 2 buses should be at least 3

mdl.add(mdl.sum(mdl.logical_and(1<=mdl.nbBus[b],mdl.nbBus[b]<=2) for b in Buses) >=3)

mdl.solve()

print()
print("Number of sizes where we have 1 or 2 buses should be at least 3")
print()

# Display solution
for b in Buses:
    print(mdl.nbBus[b].solution_value," buses with ",b[busSize]," seats");

in OPL I would write

using CP;

int N=4;
int n=2;
dvar interval itvs;
dvar interval arr[1..N];

subject to
{
  (sum(i in 1..N) (1<=overlapLength(itvs,arr[i])))>=n;
}

and the same can be done with all APIs