無法使用 ILOG CPLEX Optimizer 解決分配問題

Question

分配問題來自Google OR-Tools

其他框架可以解決這個問題，即使使用 Excel Solver。 但是 ILOG CPLEX 不能解決這個問題。

這是我在 jupyter notebook 中的代碼：

import cplex
import docplex.mp
from docplex.mp.model import Model
import numpy as np
assignment_model = Model(name='Assignemnt_Problem', log_output=True)
costs = np.array([[90,80,75,70],
  [35,85,55,65],
  [125,95,90,95],
  [45,110,95,115],
  [50,100,90,100]])
x = assignment_model.binary_var_matrix(costs.shape[0], costs.shape[1], name="a")
assignment_model.add_constraints((sum(x[i,j] for i in range (costs.shape[0])) <=1 
                              for j in range (costs.shape[1])), names ="workers")
assignment_model.add_constraints((sum(x[i,j] for j in range (costs.shape[1])) ==1 
                              for i in range (costs.shape[0])), names ="tasks")
obj_fn = sum(x[i,j]*costs[i,j] for i in range (costs.shape[0]) for j in range(costs.shape[1]))
assignment_model.set_objective('min', obj_fn)
assignment_model.print_information()
assignment_model.solve()
print('Optimization is done. Objective Function Value: %.2f' % assignment_model.objective_value)

錯誤“DOcplexException: Model<Assignemnt_Problem> 沒有成功解決”

謝謝

Answer 1

的確。 如果您添加該行

print("status = ",assignment_model.solve_details.status)

解決后你會看到

status =  integer infeasible

這就是為什么打印解決方案不起作用

現在如果你改變

costs = np.array([[90,80,75,70],
  [35,85,55,65],
  [125,95,90,95],
  [45,110,95,115],
  [50,100,90,100]])

進入

costs = np.array([[90,80,75,70],
  [35,85,55,65],
  [125,95,90,95],
  [45,110,95,115],
  [50,100,90,100]])
costs=costs.transpose()

然后你會得到一個解決方案。

（狄利克雷抽屜原理）

import cplex
import docplex.mp
from docplex.mp.model import Model
import numpy as np
assignment_model = Model(name='Assignemnt_Problem', log_output=True)
costs = np.array([[90,80,75,70],
  [35,85,55,65],
  [125,95,90,95],
  [45,110,95,115],
  [50,100,90,100]])
costs=costs.transpose()
x = assignment_model.binary_var_matrix(costs.shape[0], costs.shape[1], name="a")
assignment_model.add_constraints((sum(x[i,j] for i in range (costs.shape[0])) <=1 
                              for j in range (costs.shape[1])), names ="workers")
assignment_model.add_constraints((sum(x[i,j] for j in range (costs.shape[1])) ==1 
                              for i in range (costs.shape[0])), names ="tasks")
obj_fn = sum(x[i,j]*costs[i,j] for i in range (costs.shape[0]) for j in range(costs.shape[1]))
assignment_model.set_objective('min', obj_fn)
assignment_model.print_information()
assignment_model.solve()
print('Optimization is done. Objective Function Value: %.2f' % assignment_model.objective_value)

for i in range(costs.shape[0]):
            for j in range(costs.shape[1]):
                if (x[i,j].solution_value>=0.9):
                    print('Worker ',i,' assigned to task ',j)

給

Optimization is done. Objective Function Value: 265.00
Worker  0  assigned to task  3
Worker  1  assigned to task  2
Worker  2  assigned to task  1
Worker  3  assigned to task  0