如何解决这个整数编程？

Question

您好我正在进行整数编程。

我的作品现在直到：

 Decision Variable: 
Yi = 1 if the ambulances located in region i, 
Yi = 0 otherwises




Objective: maximize the no. of resident that can be reached within 5
mins, Z =

Y1(43+45)+Y2(52+58)+Y3(45+58)+.......+Y8(52+45+58+58)

43 + 45是，没有。如果救护车位于Y1，则可在5分钟内到达Y1和Y5的居民。

 Constraints: Y1+Y2+Y3+...+Y8 = 2  (only two locations)

然后，我不知道应该在约束中添加什么，目标似乎是错误的......

有人能帮帮我吗？谢谢你！

Answer 1

如果你对普通编程没问题，这里有一个Python实现。

Y = [{}]*100
Y[1]={1:43, 5:45}
Y[2]={2:52, 8:58}
Y[3]={3:45, 6:58}
Y[4]={4:40, 5:45}
Y[5]={1:43, 5:45, 4:40, 8:58}
Y[6]={3:45, 6:58, 7:44, 8:58}
Y[7]={6:58, 7:44}
Y[8]={2:52, 5:45, 6:58, 8:58}

result = {'loc1':0, 'loc2': 0, 'total':0}
for i in range(1, 9):
    for j in range (i + 1, 9):
        Y[i * 10 + j] = Y[i].copy()
        Y[i * 10 + j].update(Y[j])
        total = 0
        for key in Y[i * 10 + j]:
            total += Y[i * 10 + j][key]
        if total > result['total']:
            result['loc1'] = i
            result['loc2'] = j
            result['total'] = total
        print i, " ", j, " ", total

print result