Dynamic worker constraint in CPLEX python

Question

I've been working at a rcpsp problem using docplex in python. I consider 10 tasks with indicative costs and a worker that has to complete these tasks in 10 timeframes (can be weeks, days etc.).

One of my constraints is that the worker can perform a specific set of tasks per timeframe (worker_availability list). If I consider the example on the link below, one can restrict a worker's availability to not exceed a specific point i.e. mdl.sum(resources) <= capacity, where capacity is a fixed number.

I want to use a dynamic constraint that obeys worker_availability, i.e. at point 0 my worker can process 2 tasks, at 1 0 tasks etc.

Does anyone know how to that with docplex in python?

link: http://ibmdecisionoptimization.github.io/docplex-doc/cp/visu.rcpsp.py.html?highlight=rcpsp

import numpy as np
import pandas as pd
import sys
import time
from docplex.cp.model import *

# Tasks to be planned
Tasks= ["task1",
             "task2",
             "task3",
             "task4",
             "task5",
             "task6",
             "task7",
             "task8",
             "task9",
             "task10"]

# Duration of Tasks
Task_Duration =  [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

# Cost of tasks
Cost= {"task1": 700,
         "task2": 1200,
         "task3": 189,
         "task4": 296,
         "task5": 562,
         "task6": 584,
         "task7": -100,
         "task8": -200,
         "task9": - 189,
         "task10": -296
}

# Define time interval, worker availability
time_interval = number_of_week - ReleaseDate
worker_availability = [2,0,2,0,2,0,2,1,1,1]
timespan = 10

# Create  model
model = CpoModel()

# Create interval variables
itvs = {}
for i,t in enumerate(Tasks):
    _name = '_'+str(t)
    itvs[t] = model.interval_var(start=(0, INTERVAL_MAX), end = (INTERVAL_MIN,10), size = Duration[i], name = _name)

# case of static constraints - this is where we need to get it to dynamic
tasks = [model.pulse(itvs[t], 1) for t in Tasks]
model.add(model.sum(tasks) <= 2)

# Solve the model
tmp = 0
time_interval = number_of_week - ReleaseDate
for task in Tasks:
    tmp += Cost[task] + Cost[task] * model.max([time_interval - model.start_of(itvs[task]),0])
model.add(model.minimize(tmp))
msol = model.solve(FailLimit=300000)

# Print output
for t in Tasks:
    wt = msol.get_var_solution(itvs[t])
    print(t,'start at:',wt.get_start())
print('Cost: ', msol.get_objective_values()[0])
print('worker availability: ',worker_availability)

score 0 · Accepted Answer · answered Mar 02 '21 at 16:25

you could rely on always_in

Let me give you an example with OPL.

 using CP;
 
 range r=1..2;
 
 dvar interval itvs[r] size 3;
 cumulFunction simultaneousJobs=sum(i in r) pulse(itvs[i],1);
 
 minimize max(i in r) endOf(itvs[i]);
 
 subject to
 {
   simultaneousJobs<=2;
   
   //alwaysIn(simultaneousJobs,0,1,0,1);
 }

gives 3 as best objective and for simultaneousJob we see

If we uncomment the alwaysIn, we get 4 as the objective and for the cumul we then see

Dynamic worker constraint in CPLEX python

1 Answers1