Python Cplex Ceil() Function

Question

ceil() in the constraint

Hello, I am studying a published paper. One of the constraints from this paper(which can be shown in the link) requires the ceil() function. We can use the ceil() function at the OPL but I couldn't find the Python equality.

Notice: I tried the math.ceil() and cp.moduler ceil(), but I did not get any solution.

Edit: I still haven't found its Python equivalent, but there is an alternative way:

slack_var = model.continuous_var(name="slack")

ceiled_var = model.integer_var(name='ceiled')

Notice: The slack variable has to be less than "1". ( 0 <= slack < 1)

ceiled_var - slack_var = "your calculations"

Answer 1

For ceil, you can use both math or numpy, however, numpy can be overkill.

import math
ceiled_variable = math.ceil(your_variable)

or

import numpy as np
ceiled_variable = np.ceil(your_variable)

Answer 2

ceil is not a linear function so you should linearize. See example here.

from docplex.mp.model import Model

mdl = Model(name='ceil')

r=range(0,4)
x=[1.5,4.0,2.0001,5.9999]

y = mdl.integer_var_list(4,0,1000,name="y")
f = mdl.continuous_var_list(4,0,0.9999999,name="f")

for i in r:
    mdl.add(y[i]==x[i]+f[i])

mdl.solve()

for i in r:
    print(x[i]," ==> ",y[i].solution_value)

"""
which gives
1.5  ==>  2.0
4.0  ==>  4.0
2.0001  ==>  3.0
5.9999  ==>  6.0
"""