Google OR-Tools : Solution unable to converge for Assignment with Task Sizes using python

问题

I tried to elaborate on the Assignment with Task Sizes example by adding a multi-dimensional "size"(demand) and "total_size_max" .

The solution seems to decide to allocate everything to 1 worker only despite the fact that others are available. The result when run allocates everything to worker(machine 18).

Sample output :

Machine 18 is assigned to produce Component 0 with minimum Cycle_Time = 10000000
Machine 18 is assigned to produce Component 1 with minimum Cycle_Time = 10000000
Machine 18 is assigned to produce Component 2 with minimum Cycle_Time = 10000000
Machine 18 is assigned to produce Component 3 with minimum Cycle_Time = 10000000
Machine 18 is assigned to produce Component 4 with minimum Cycle_Time = 10000000
Machine 18 is assigned to produce Component 5 with minimum Cycle_Time = 10000000

Code :

# -*- coding: utf-8 -*-

from __future__ import print_function
from ortools.sat.python import cp_model
import time
import numpy as np

def main():
  model = cp_model.CpModel()

  start = time.time()
  # cost = machines on rows and components on columns with least cycle_time
  cost = [[7.995722268,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.995722268,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.995722268,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.995722268,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.764712938,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.64179678,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.764712938,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,26.10110138,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,26.10110138,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,24.79202174,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,27.72432227,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,29.63946277,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,29.4907994,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,24.79202174,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,27.72432227,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,29.63946277,10000000,10000000,10000000],
[10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.271052178,10000000,10000000,10000000,10000000,10000000,10000000],
[8.213437897,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.213437897,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.213437897,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.213437897,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.372568825,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.282863934,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,15.49746661,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,14.36944353,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,14.95278777,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,13.33333333,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,13.33333333,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,6.194286893,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,14.56521739,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,17.57157641,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.194286893,10000000,14.56521739,10000000,10000000,10000000,10000000],
[8.076237035,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.076237035,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.076237035,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.076237035,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.400797794,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[8.019304639,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.019304639,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.019304639,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.019304639,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.496583613,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,3.778990587,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,11.51228733,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,11.06301248,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,4.492667454,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,5.512785364,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358,10000000,10000000,10000000,10000000,10000000,10000000,10000000,1.780837358,10000000,1.780837358],
[10000000,10000000,10000000,10000000,10000000,7.755011055,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.755011055,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.755011055,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,7.755011055,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,25.45422456,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,29.69460764,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,32.00169225,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,25.45422456,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,29.69460764,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,10000000,10000000,10000000,10000000,10000000,28.19319991,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,27.13193117,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,26.59704717,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,28.19319991,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,27.13193117,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,21.5723175,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,8.455696203,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000],
[10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000,6.776314217,10000000,10000000,10000000,10000000,10000000,10000000,10000000,10000000]
]

  #costList = [round(x) for x in cost]
  costlist = np.round(cost).astype(int).tolist()

  # demand for each component
  demand = [28,28,28,28,28,28,28,28,28,56,28,30,30,30,30,30,30,30,30,30,60,176,176,176,176,176,176,176,176,176,352,194,194,194,194,194,194,194,194,194,388,56,56,56,56,56,56,56,56,56,112,56,149,149,149,149,149,149,149,149,149,298,911,911,911,911,911,911,911,911,911,1822]

  # convert to numpy array for division
  arr = np.array(cost)
  # total available hours
  available_hrs = 2592000
  total_size_max =  available_hrs / arr
  total_size_max = total_size_max.astype(int)

  num_workers = len(cost)
  num_tasks = len(cost[1])
  # Variables
  x = []
  for i in range(num_workers):
    t = []
    for j in range(num_tasks):
      t.append(model.NewIntVar(0, 1, "x[%i,%i]" % (i, j)))
    x.append(t)
  x_array = [x[i][j] for i in range(num_workers) for j in range(num_tasks)]

  # Constraints

  # Each component is assigned to at least one machine.
  [model.Add(sum(x[i][j] for i in range(num_workers)) >= 1)
  for j in range(num_tasks)]

  # Total demand of component for each machine is at most total_size_max(available_hrs/cycle_time).
  [model.Add(sum(demand[j] * x[i][j] for j in range(num_tasks)) <= total_size_max[i][j])
  for i in range(num_workers)]
  model.Minimize(sum([np.dot(x_row, cost_row) for (x_row, cost_row) in zip(x, costlist)]))
  solver = cp_model.CpSolver()
  status = solver.Solve(model)

  if status == cp_model.OPTIMAL:
    print('Minimum cost = %i' % solver.ObjectiveValue())
    print()

    for i in range(num_workers):

      for j in range(num_tasks):

        if solver.Value(x[i][j]) == 1:
          print('Machine ', i, ' is assigned to produce Component ', j, ' with minimum Cycle_Time = ', cost[i][j])
    print()
    end = time.time()
    print("Time = ", round(end - start, 4), "seconds")


if __name__ == '__main__':
  main()

I took this from the sample example and tweaked input data according to my need. Can someone help resolve this issue?

Expected result is that the machine with lowest time should be assigned according to the demand

回答1:

Here is a full answer:

# -*- coding: utf-8 -*-
"""
Created on Sat Sep 14 00:52:54 2019

@author: 320048504
"""

from __future__ import print_function

from ortools.sat.python import cp_model
import time
import numpy as np


def main():
    model = cp_model.CpModel()

    start = time.time()
    cost = [[
        7.995722268, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7.995722268, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7.995722268, -1, -1, -1, -1,
        -1, -1, -1, -1, -1, -1, 7.995722268, -1, -1, -1, -1, -1, -1, -1, -1,
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
    ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, 6.764712938, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, 6.64179678, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, 6.764712938, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, 26.10110138, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, 26.10110138, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, 24.79202174, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 27.72432227, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 29.63946277, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                29.4907994, -1, -1, -1, -1, -1, -1, -1, -1, -1, 24.79202174,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 27.72432227, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, 29.63946277, -1, -1, -1
            ],
            [
                -1, -1, -1, 6.271052178, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 6.271052178, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                6.271052178, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.271052178,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.271052178, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, 6.271052178, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 6.271052178, -1, -1, -1, -1, -1, -1
            ],
            [
                8.213437897, -1, 4.372568825, -1, -1, -1, -1, -1, -1, -1, -1,
                8.213437897, -1, 4.372568825, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 4.372568825, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                4.372568825, -1, -1, -1, -1, -1, -1, -1, 8.213437897, -1,
                4.372568825, -1, -1, -1, -1, -1, -1, -1, -1, 8.213437897, -1,
                4.372568825, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4.372568825,
                -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, 6.282863934, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 6.282863934, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                6.282863934, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.282863934,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.282863934, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, 6.282863934, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 6.282863934, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 15.49746661, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 14.36944353, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 14.95278777, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 13.33333333, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 13.33333333, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, 6.194286893, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 6.194286893, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                6.194286893, -1, 14.56521739, -1, -1, -1, -1, -1, -1, -1,
                6.194286893, -1, 17.57157641, -1, -1, -1, -1, -1, -1, -1,
                6.194286893, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                6.194286893, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.194286893,
                -1, 14.56521739, -1, -1, -1, -1
            ],
            [
                8.076237035, -1, 4.400797794, -1, -1, -1, -1, -1, -1, -1, -1,
                8.076237035, -1, 4.400797794, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 4.400797794, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                4.400797794, -1, -1, -1, -1, -1, -1, -1, 8.076237035, -1,
                4.400797794, -1, -1, -1, -1, -1, -1, -1, -1, 8.076237035, -1,
                4.400797794, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4.400797794,
                -1, -1, -1, -1, -1, -1, -1
            ],
            [
                8.019304639, -1, 4.496583613, -1, -1, -1, -1, -1, -1, -1, -1,
                8.019304639, -1, 4.496583613, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 4.496583613, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                4.496583613, -1, -1, -1, -1, -1, -1, -1, 8.019304639, -1,
                4.496583613, -1, -1, -1, -1, -1, -1, -1, -1, 8.019304639, -1,
                4.496583613, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4.496583613,
                -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, 3.778990587, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, 3.778990587, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                3.778990587, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3.778990587,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, 3.778990587, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, 3.778990587, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 3.778990587, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                11.51228733, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, 4.492667454, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                4.492667454, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4.492667454,
                -1, -1, -1, -1, -1, -1, -1, 11.06301248, -1, 4.492667454, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, 4.492667454, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 4.492667454, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, 4.492667454, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, -1, 5.512785364, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 5.512785364, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, 5.512785364, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                5.512785364, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5.512785364,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5.512785364, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, 5.512785364, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, -1, 1.780837358, -1, 1.780837358,
                1.780837358, -1, -1, -1, -1, -1, -1, -1, 1.780837358, -1,
                1.780837358, -1, -1, -1, -1, -1, -1, -1, 1.780837358, -1,
                1.780837358, -1, -1, -1, -1, -1, -1, -1, 1.780837358, -1,
                1.780837358, -1, -1, -1, -1, -1, -1, -1, 1.780837358, -1,
                1.780837358, 1.780837358, -1, -1, -1, -1, -1, -1, -1,
                1.780837358, -1, 1.780837358, -1, -1, -1, -1, -1, -1, -1,
                1.780837358, -1, 1.780837358
            ],
            [
                -1, -1, -1, -1, -1, 7.755011055, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, 7.755011055, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 7.755011055, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, 7.755011055, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, 25.45422456, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 29.69460764, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 32.00169225, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, 25.45422456, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 29.69460764, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, -1, -1, -1, -1, -1, 28.19319991, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 27.13193117, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 26.59704717, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, 28.19319991, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 27.13193117, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, 21.5723175, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                21.5723175, -1, -1, -1, -1, -1, -1, -1, -1, -1, 21.5723175, -1,
                -1, -1, -1, -1, -1, -1, -1, -1, 21.5723175, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 21.5723175, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 21.5723175, -1, -1, -1, -1, -1, -1, -1, -1, -1, 21.5723175,
                -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, 8.455696203, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                8.455696203, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8.455696203,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, 8.455696203, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 8.455696203, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 8.455696203, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 8.455696203, -1, -1, -1, -1, -1, -1, -1, -1
            ],
            [
                -1, 6.776314217, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                6.776314217, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.776314217,
                -1, -1, -1, -1, -1, -1, -1, -1, -1, 6.776314217, -1, -1, -1,
                -1, -1, -1, -1, -1, -1, 6.776314217, -1, -1, -1, -1, -1, -1,
                -1, -1, -1, -1, 6.776314217, -1, -1, -1, -1, -1, -1, -1, -1,
                -1, 6.776314217, -1, -1, -1, -1, -1, -1, -1, -1
            ]]

    scaling = 100
    int_cost = [[int(round(x * scaling)) for x in line] for line in cost]

    # demand for each component
    demand = [
        28, 28, 28, 28, 28, 28, 28, 28, 28, 56, 28, 30, 30, 30, 30, 30, 30, 30,
        30, 30, 60, 176, 176, 176, 176, 176, 176, 176, 176, 176, 352, 194, 194,
        194, 194, 194, 194, 194, 194, 194, 388, 56, 56, 56, 56, 56, 56, 56, 56,
        56, 112, 56, 149, 149, 149, 149, 149, 149, 149, 149, 149, 298, 911,
        911, 911, 911, 911, 911, 911, 911, 911, 1822
    ]

    # total available hours
    available_hrs = 2592000

    num_workers = len(int_cost)
    num_tasks = len(int_cost[1])
    print('num_workers =', num_workers, ', num_tasks =', num_tasks)

    # Variables
    x = [[
        0 if int_cost[i][j] < 0 else model.NewBoolVar('x[%i,%i]' % (i, j))
        for j in range(num_tasks)
    ] for i in range(num_workers)]

    # Constraints

    # For each component, demand is met.
    for j in range(num_tasks):
        model.Add(
            sum(x[i][j] for i in range(num_workers)
                if int_cost[i][j] >= 0) == 1)

    # Total worked hours for each machine is at most available_hrs.
    for i in range(num_workers):
        model.Add(
            sum(x[i][j] * int_cost[i][j] * demand[j] for j in range(num_tasks)
                if int_cost[i][j] >= 0) <= available_hrs * scaling)

    # Objective: minimize worked hours.
    model.Minimize(
        sum(x[i][j] * int_cost[i][j] * demand[j] for i in range(num_workers)
            for j in range(num_tasks) if int_cost[i][j] >= 0))
    model.Proto().objective.scaling_factor = 1.0 / scaling

    # Solve.
    solver = cp_model.CpSolver()
    solver.parameters.log_search_progress = True
    solver.parameters.num_search_workers = 8
    status = solver.Solve(model)

    # Print solution.
    if status == cp_model.OPTIMAL:
        print('Minimum cost = %f' % solver.ObjectiveValue())
        print()

        for i in range(num_workers):

            for j in range(num_tasks):
                qty = 0 if cost[i][j] == -1 else solver.Value(x[i][j])
                if qty > 0:
                    print('Machine ', i, ' is assigned to produce Component ',
                          j, ' with minimum Cycle_Time = ', cost[i][j])
        print()
        end = time.time()
        print("Time = ", round(end - start, 4), "seconds")


if __name__ == '__main__':
    main()

I have added cost scaling to improve precision

Here is the output:

Minimum cost = 123887.560000

Machine  0  is assigned to produce Component  0  with minimum Cycle_Time =  7.995722268
Machine  0  is assigned to produce Component  11  with minimum Cycle_Time =  7.995722268
...
Machine  24  is assigned to produce Component  53  with minimum Cycle_Time =  6.776314217
Machine  24  is assigned to produce Component  63  with minimum Cycle_Time =  6.776314217

Time =  0.0834 seconds

回答2:

This is discussed in https://github.com/google/or-tools/issues/1578

If you cross-post, please indicate it.

Thanks

来源：https://stackoverflow.com/questions/57929840/google-or-tools-solution-unable-to-converge-for-assignment-with-task-sizes-usi