CPLEX python中的动态工作人员约束

Question

我一直在使用python中的docplex解决rcpsp问题。我考虑了10个具有指示性成本的任务和一个必须在10个时间框架内完成这些任务的工人（可以是周、天等）。

我的限制之一是工作人员可以在每个时间帧（worker_availability列表）中执行一组特定的任务。如果我考虑下面链接上的示例，可以将辅助角色的可用性限制为不超过特定点，即mdl.sum（资源）

我希望使用符合worker_可用性的动态约束，即在0点，我的worker可以处理2个任务，在10个任务等。

有人知道如何使用python中的docplex实现这一点吗？

链接：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)

Answer 1

你可以信赖always_in

让我给你举一个OPL的例子。

 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);
 }

给出3作为最佳目标，同时我们看到

如果我们取消注释alwaysIn，我们得到4作为目标，对于cumul，我们将看到