Scipy 线性规划没有给出正确答案

Question

我正在尝试使用 Scipy 解决以下问题。但是，它不会产生正确的结果。

r是我们拥有的唯一决策变量。 由于等式（2）不符合Scipy要求的格式Ab <= ub我修改为如下形式。

以下是我实现的代码：

# Objective function
def objective():
    return [time[e] for e in edge]

# setting the bounds for the decision variables
def bounds():
    return [(0, V[e[0]]) for e in edge]



# generating the constraints
def constraints():
    
    b = []
    A = []
    const = []
    const_2 = []
    for i in region:
        for e in edge:
            if e[0] != e[1] and (e[0]==i or e[1]==i):
                if (e[0]==i):
                    const.append(1)
                    const_2.append(1)
                else:
                    const.append(-1)
                    const_2.append(0)
         
            else:
                const.append(0)
                const_2.append(0)
        
        # const 1 \sum (r_{ij} - r_{ji}) \leq V_i - D_i
        A.append(const)
        b.append(V[i] - D[i])
        
        # const 2 \sum r_{ij} <= V_i
        A.append(const_2)
        b.append(V[i])
        
        const = []
        const_2 = []
                            
    return A, b

obj_fn = objective()
a_up, b_up = constraints()
res = linprog(obj_fn, A_ub=a_up, b_ub=b_up, bounds=bounds())

当我运行代码时，它会为每个边缘生成以下结果，即r_e ：

{(0, 1): 0, (0, 2): 0, (0, 3): 0, (0, 4): 0, (0, 5): 0, (0, 6): 0, (0, 7): 0, (0, 8): 0, (0, 9): 0, (0, 10): 0, (0, 11): 0, (0, 12): 0, (0, 13): 0, (0, 14): 0, (0, 15): 0, (1, 0): 55, (1, 2): 0, (1, 3): 0, (1, 4): 0, (1, 5): 0, (1, 6): 0, (1, 7): 0, (1, 8): 0, (1, 9): 0, (1, 10): 0, (1, 11): 0, (1, 12): 0, (1, 13): 0, (1, 14): 0, (1, 15): 0, (2, 0): 0, (2, 1): 0, (2, 3): 0, (2, 4): 0, (2, 5): 0, (2, 6): 0, (2, 7): 0, (2, 8): 0, (2, 9): 0, (2, 10): 0, (2, 11): 0, (2, 12): 0, (2, 13): 0, (2, 14): 0, (2, 15): 0, (3, 0): 0, (3, 1): 0, (3, 2): 0, (3, 4): 0, (3, 5): 0, (3, 6): 0, (3, 7): 0, (3, 8): 0, (3, 9): 0, (3, 10): 0, (3, 11): 0, (3, 12): 0, (3, 13): 0, (3, 14): 0, (3, 15): 0, (4, 0): 0, (4, 1): 0, (4, 2): 0, (4, 3): 0, (4, 5): 0, (4, 6): 0, (4, 7): 0, (4, 8): 0, (4, 9): 0, (4, 10): 0, (4, 11): 0, (4, 12): 0, (4, 13): 0, (4, 14): 0, (4, 15): 0, (5, 0): 0, (5, 1): 0, (5, 2): 0, (5, 3): 0, (5, 4): 29, (5, 6): 0, (5, 7): 0, (5, 8): 0, (5, 9): 0, (5, 10): 0, (5, 11): 0, (5, 12): 0, (5, 13): 0, (5, 14): 0, (5, 15): 0, (6, 0): 0, (6, 1): 0, (6, 2): 0, (6, 3): 0, (6, 4): 0, (6, 5): 0, (6, 7): 0, (6, 8): 0, (6, 9): 0, (6, 10): 0, (6, 11): 0, (6, 12): 0, (6, 13): 0, (6, 14): 0, (6, 15): 0, (7, 0): 0, (7, 1): 0, (7, 2): 32, (7, 3): 0, (7, 4): 0, (7, 5): 0, (7, 6): 21, (7, 8): 0, (7, 9): 0, (7, 10): 0, (7, 11): 0, (7, 12): 0, (7, 13): 0, (7, 14): 0, (7, 15): 0, (8, 0): 0, (8, 1): 0, (8, 2): 0, (8, 3): 0, (8, 4): 0, (8, 5): 0, (8, 6): 0, (8, 7): 0, (8, 9): 0, (8, 10): 0, (8, 11): 0, (8, 12): 0, (8, 13): 0, (8, 14): 0, (8, 15): 0, (9, 0): 0, (9, 1): 0, (9, 2): 0, (9, 3): 0, (9, 4): 0, (9, 5): 0, (9, 6): 0, (9, 7): 0, (9, 8): 0, (9, 10): 0, (9, 11): 0, (9, 12): 0, (9, 13): 0, (9, 14): 0, (9, 15): 0, (10, 0): 0, (10, 1): 0, (10, 2): 0, (10, 3): 0, (10, 4): 0, (10, 5): 0, (10, 6): 25, (10, 7): 0, (10, 8): 0, (10, 9): 0, (10, 11): 0, (10, 12): 0, (10, 13): 0, (10, 14): 15, (10, 15): 0, (11, 0): 0, (11, 1): 0, (11, 2): 0, (11, 3): 6, (11, 4): 0, (11, 5): 0, (11, 6): 0, (11, 7): 0, (11, 8): 0, (11, 9): 0, (11, 10): 0, (11, 12): 0, (11, 13): 0, (11, 14): 10, (11, 15): 10, (12, 0): 38, (12, 1): 0, (12, 2): 0, (12, 3): 0, (12, 4): 3, (12, 5): 0, (12, 6): 0, (12, 7): 0, (12, 8): 46, (12, 9): 6, (12, 10): 0, (12, 11): 0, (12, 13): 5, (12, 14): 0, (12, 15): 0, (13, 0): 0, (13, 1): 0, (13, 2): 0, (13, 3): 0, (13, 4): 0, (13, 5): 0, (13, 6): 0, (13, 7): 0, (13, 8): 0, (13, 9): 0, (13, 10): 0, (13, 11): 0, (13, 12): 0, (13, 14): 15, (13, 15): 0, (14, 0): 0, (14, 1): 0, (14, 2): 0, (14, 3): 0, (14, 4): 0, (14, 5): 0, (14, 6): 0, (14, 7): 0, (14, 8): 0, (14, 9): 0, (14, 10): 0, (14, 11): 0, (14, 12): 0, (14, 13): 0, (14, 15): 0, (15, 0): 0, (15, 1): 0, (15, 2): 0, (15, 3): 0, (15, 4): 0, (15, 5): 0, (15, 6): 0, (15, 7): 0, (15, 8): 0, (15, 9): 0, (15, 10): 0, (15, 11): 0, (15, 12): 0, (15, 13): 0, (15, 14): 0}

但是，它不等于 CPLEX 产生的结果（cplex 结果是我用来比较我的结果的正确结果）：

{(0, 1): 0, (0, 2): 0, (0, 3): 0, (0, 4): 0, (0, 5): 0, (0, 6): 0, (0, 7): 0, (0, 8): 0, (0, 9): 0, (0, 10): 0, (0, 11): 0, (0, 12): 0, (0, 13): 0, (0, 14): 0, (0, 15): 0, (1, 0): 55, (1, 2): 0, (1, 3): 0, (1, 4): 0, (1, 5): 0, (1, 6): 0, (1, 7): 0, (1, 8): 0, (1, 9): 0, (1, 10): 0, (1, 11): 0, (1, 12): 0, (1, 13): 0, (1, 14): 0, (1, 15): 0, (2, 0): 0, (2, 1): 0, (2, 3): 0, (2, 4): 0, (2, 5): 0, (2, 6): 0, (2, 7): 0, (2, 8): 0, (2, 9): 0, (2, 10): 0, (2, 11): 0, (2, 12): 0, (2, 13): 0, (2, 14): 0, (2, 15): 0, (3, 0): 0, (3, 1): 0, (3, 2): 0, (3, 4): 0, (3, 5): 0, (3, 6): 0, (3, 7): 0, (3, 8): 0, (3, 9): 0, (3, 10): 0, (3, 11): 0, (3, 12): 0, (3, 13): 0, (3, 14): 0, (3, 15): 0, (4, 0): 0, (4, 1): 0, (4, 2): 0, (4, 3): 0, (4, 5): 0, (4, 6): 0, (4, 7): 0, (4, 8): 0, (4, 9): 0, (4, 10): 0, (4, 11): 0, (4, 12): 0, (4, 13): 0, (4, 14): 0, (4, 15): 0, (5, 0): 0, (5, 1): 0, (5, 2): 0, (5, 3): 0, (5, 4): 29, (5, 6): 0, (5, 7): 0, (5, 8): 0, (5, 9): 0, (5, 10): 0, (5, 11): 0, (5, 12): 0, (5, 13): 0, (5, 14): 0, (5, 15): 0, (6, 0): 0, (6, 1): 0, (6, 2): 0, (6, 3): 0, (6, 4): 0, (6, 5): 0, (6, 7): 0, (6, 8): 0, (6, 9): 0, (6, 10): 0, (6, 11): 0, (6, 12): 0, (6, 13): 0, (6, 14): 0, (6, 15): 0, (7, 0): 12, (7, 1): 0, (7, 2): 32, (7, 3): 6, (7, 4): 3, (7, 5): 0, (7, 6): 0, (7, 8): 0, (7, 9): 0, (7, 10): 0, (7, 11): 0, (7, 12): 0, (7, 13): 0, (7, 14): 0, (7, 15): 0, (8, 0): 0, (8, 1): 0, (8, 2): 0, (8, 3): 0, (8, 4): 0, (8, 5): 0, (8, 6): 0, (8, 7): 0, (8, 9): 0, (8, 10): 0, (8, 11): 0, (8, 12): 0, (8, 13): 0, (8, 14): 0, (8, 15): 0, (9, 0): 0, (9, 1): 0, (9, 2): 0, (9, 3): 0, (9, 4): 0, (9, 5): 0, (9, 6): 0, (9, 7): 0, (9, 8): 0, (9, 10): 0, (9, 11): 0, (9, 12): 0, (9, 13): 0, (9, 14): 0, (9, 15): 0, (10, 0): 0, (10, 1): 0, (10, 2): 0, (10, 3): 0, (10, 4): 0, (10, 5): 0, (10, 6): 40, (10, 7): 0, (10, 8): 0, (10, 9): 0, (10, 11): 0, (10, 12): 0, (10, 13): 0, (10, 14): 0, (10, 15): 0, (11, 0): 0, (11, 1): 0, (11, 2): 0, (11, 3): 0, (11, 4): 0, (11, 5): 0, (11, 6): 6, (11, 7): 0, (11, 8): 0, (11, 9): 0, (11, 10): 0, (11, 12): 0, (11, 13): 0, (11, 14): 4, (11, 15): 10, (12, 0): 26, (12, 1): 0, (12, 2): 0, (12, 3): 0, (12, 4): 0, (12, 5): 0, (12, 6): 0, (12, 7): 0, (12, 8): 46, (12, 9): 6, (12, 10): 0, (12, 11): 0, (12, 13): 26, (12, 14): 0, (12, 15): 0, (13, 0): 0, (13, 1): 0, (13, 2): 0, (13, 3): 0, (13, 4): 0, (13, 5): 0, (13, 6): 0, (13, 7): 0, (13, 8): 0, (13, 9): 0, (13, 10): 0, (13, 11): 0, (13, 12): 0, (13, 14): 36, (13, 15): 0, (14, 0): 0, (14, 1): 0, (14, 2): 0, (14, 3): 0, (14, 4): 0, (14, 5): 0, (14, 6): 0, (14, 7): 0, (14, 8): 0, (14, 9): 0, (14, 10): 0, (14, 11): 0, (14, 12): 0, (14, 13): 0, (14, 15): 0, (15, 0): 0, (15, 1): 0, (15, 2): 0, (15, 3): 0, (15, 4): 0, (15, 5): 0, (15, 6): 0, (15, 7): 0, (15, 8): 0, (15, 9): 0, (15, 10): 0, (15, 11): 0, (15, 12): 0, (15, 13): 0, (15, 14): 0}

我不确定，但我认为问题出在约束上。 有人可以帮我找出我的错误吗？

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运行代码所需的最少数据：

V = {0: 1, 1: 71, 2: 6, 3: 0, 4: 34, 5: 51, 6: 88, 7: 61, 8: 0, 9: 0, 10: 43, 11: 62, 12: 144, 13: 36, 14: 0, 15: 12}

D = {0: 94, 1: 16, 2: 38, 3: 6, 4: 66, 5: 22, 6: 134, 7: 8, 8: 46, 9: 6, 10: 3, 11: 36, 12: 39, 13: 26, 14: 40, 15: 22}

edge = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (1, 0), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (1, 12), (1, 13), (1, 14), (1, 15), (2, 0), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (3, 0), (3, 1), (3, 2), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (4, 0), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (10, 0), (10, 1), (10, 2), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (11, 0), (11, 1), (11, 2), (11, 3), (11, 4), (11, 5), (11, 6), (11, 7), (11, 8), (11, 9), (11, 10), (11, 12), (11, 13), (11, 14), (11, 15), (12, 0), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), (12, 6), (12, 7), (12, 8), (12, 9), (12, 10), (12, 11), (12, 13), (12, 14), (12, 15), (13, 0), (13, 1), (13, 2), (13, 3), (13, 4), (13, 5), (13, 6), (13, 7), (13, 8), (13, 9), (13, 10), (13, 11), (13, 12), (13, 14), (13, 15), (14, 0), (14, 1), (14, 2), (14, 3), (14, 4), (14, 5), (14, 6), (14, 7), (14, 8), (14, 9), (14, 10), (14, 11), (14, 12), (14, 13), (14, 15), (15, 0), (15, 1), (15, 2), (15, 3), (15, 4), (15, 5), (15, 6), (15, 7), (15, 8), (15, 9), (15, 10), (15, 11), (15, 12), (15, 13), (15, 14)]

region = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

time = {(0, 1): 1, (0, 2): 1, (0, 3): 2, (0, 4): 2, (0, 5): 2, (0, 6): 2, (0, 7): 3, (0, 8): 3, (0, 9): 3, (0, 10): 3, (0, 11): 4, (0, 12): 4, (0, 13): 3, (0, 14): 4, (0, 15): 5, (1, 0): 1, (1, 2): 1, (1, 3): 1, (1, 4): 2, (1, 5): 2, (1, 6): 2, (1, 7): 3, (1, 8): 3, (1, 9): 3, (1, 10): 3, (1, 11): 4, (1, 12): 4, (1, 13): 3, (1, 14): 4, (1, 15): 4, (2, 0): 2, (2, 1): 1, (2, 3): 1, (2, 4): 3, (2, 5): 2, (2, 6): 2, (2, 7): 2, (2, 8): 4, (2, 9): 3, (2, 10): 3, (2, 11): 3, (2, 12): 5, (2, 13): 4, (2, 14): 4, (2, 15): 4, (3, 0): 2, (3, 1): 2, (3, 2): 1, (3, 4): 3, (3, 5): 3, (3, 6): 2, (3, 7): 2, (3, 8): 4, (3, 9): 4, (3, 10): 3, (3, 11): 3, (3, 12): 5, (3, 13): 5, (3, 14): 5, (3, 15): 4, (4, 0): 2, (4, 1): 2, (4, 2): 2, (4, 3): 3, (4, 5): 1, (4, 6): 2, (4, 7): 2, (4, 8): 2, (4, 9): 2, (4, 10): 2, (4, 11): 3, (4, 12): 2, (4, 13): 3, (4, 14): 3, (4, 15): 4, (5, 0): 2, (5, 1): 2, (5, 2): 2, (5, 3): 2, (5, 4): 1, (5, 6): 2, (5, 7): 2, (5, 8): 2, (5, 9): 2, (5, 10): 2, (5, 11): 3, (5, 12): 3, (5, 13): 2, (5, 14): 3, (5, 15): 3, (6, 0): 2, (6, 1): 2, (6, 2): 2, (6, 3): 2, (6, 4): 2, (6, 5): 1, (6, 7): 1, (6, 8): 3, (6, 9): 2, (6, 10): 2, (6, 11): 2, (6, 12): 3, (6, 13): 3, (6, 14): 3, (6, 15): 3, (7, 0): 3, (7, 1): 3, (7, 2): 2, (7, 3): 2, (7, 4): 2, (7, 5): 2, (7, 6): 2, (7, 8): 3, (7, 9): 3, (7, 10): 2, (7, 11): 2, (7, 12): 4, (7, 13): 4, (7, 14): 3, (7, 15): 3, (8, 0): 3, (8, 1): 3, (8, 2): 3, (8, 3): 3, (8, 4): 1, (8, 5): 2, (8, 6): 3, (8, 7): 3, (8, 9): 2, (8, 10): 2, (8, 11): 2, (8, 12): 1, (8, 13): 2, (8, 14): 2, (8, 15): 3, (9, 0): 3, (9, 1): 3, (9, 2): 3, (9, 3): 4, (9, 4): 2, (9, 5): 2, (9, 6): 2, (9, 7): 3, (9, 8): 2, (9, 10): 2, (9, 11): 2, (9, 12): 2, (9, 13): 1, (9, 14): 2, (9, 15): 2, (10, 0): 4, (10, 1): 3, (10, 2): 3, (10, 3): 3, (10, 4): 3, (10, 5): 2, (10, 6): 2, (10, 7): 2, (10, 8): 2, (10, 9): 2, (10, 11): 2, (10, 12): 2, (10, 13): 2, (10, 14): 2, (10, 15): 2, (11, 0): 4, (11, 1): 4, (11, 2): 3, (11, 3): 2, (11, 4): 3, (11, 5): 3, (11, 6): 2, (11, 7): 2, (11, 8): 2, (11, 9): 2, (11, 10): 2, (11, 12): 2, (11, 13): 3, (11, 14): 2, (11, 15): 1, (12, 0): 3, (12, 1): 4, (12, 2): 4, (12, 3): 4, (12, 4): 2, (12, 5): 3, (12, 6): 3, (12, 7): 4, (12, 8): 1, (12, 9): 2, (12, 10): 2, (12, 11): 3, (12, 13): 1, (12, 14): 2, (12, 15): 2, (13, 0): 5, (13, 1): 3, (13, 2): 4, (13, 3): 5, (13, 4): 3, (13, 5): 3, (13, 6): 3, (13, 7): 3, (13, 8): 2, (13, 9): 2, (13, 10): 2, (13, 11): 2, (13, 12): 2, (13, 14): 1, (13, 15): 2, (14, 0): 5, (14, 1): 4, (14, 2): 4, (14, 3): 4, (14, 4): 3, (14, 5): 3, (14, 6): 3, (14, 7): 3, (14, 8): 2, (14, 9): 2, (14, 10): 2, (14, 11): 2, (14, 12): 2, (14, 13): 1, (14, 15): 1, (15, 0): 5, (15, 1): 5, (15, 2): 4, (15, 3): 4, (15, 4): 4, (15, 5): 3, (15, 6): 3, (15, 7): 3, (15, 8): 3, (15, 9): 2, (15, 10): 2, (15, 11): 2, (15, 12): 2, (15, 13): 2, (15, 14): 2}

Answer 1

您的问题没有唯一的解决方案。 Scipy 和 CPLEX 解是等价的，因为它们具有相同的 OF 值。 这是一个验证：

S_scipy = {(0, 1): 0, (0, 2): 0, (0, 3): 0, (0, 4): 0, (0, 5): 0, (0, 6): 0, (0, 7): 0, (0, 8): 0, (0, 9): 0, (0, 10): 0, (0, 11): 0, (0, 12): 0, (0, 13): 0, (0, 14): 0, (0, 15): 0, (1, 0): 55, (1, 2): 0, (1, 3): 0, (1, 4): 0, (1, 5): 0, (1, 6): 0, (1, 7): 0, (1, 8): 0, (1, 9): 0, (1, 10): 0, (1, 11): 0, (1, 12): 0, (1, 13): 0, (1, 14): 0, (1, 15): 0, (2, 0): 0, (2, 1): 0, (2, 3): 0, (2, 4): 0, (2, 5): 0, (2, 6): 0, (2, 7): 0, (2, 8): 0, (2, 9): 0, (2, 10): 0, (2, 11): 0, (2, 12): 0, (2, 13): 0, (2, 14): 0, (2, 15): 0, (3, 0): 0, (3, 1): 0, (3, 2): 0, (3, 4): 0, (3, 5): 0, (3, 6): 0, (3, 7): 0, (3, 8): 0, (3, 9): 0, (3, 10): 0, (3, 11): 0, (3, 12): 0, (3, 13): 0, (3, 14): 0, (3, 15): 0, (4, 0): 0, (4, 1): 0, (4, 2): 0, (4, 3): 0, (4, 5): 0, (4, 6): 0, (4, 7): 0, (4, 8): 0, (4, 9): 0, (4, 10): 0, (4, 11): 0, (4, 12): 0, (4, 13): 0, (4, 14): 0, (4, 15): 0, (5, 0): 0, (5, 1): 0, (5, 2): 0, (5, 3): 0, (5, 4): 29, (5, 6): 0, (5, 7): 0, (5, 8): 0, (5, 9): 0, (5, 10): 0, (5, 11): 0, (5, 12): 0, (5, 13): 0, (5, 14): 0, (5, 15): 0, (6, 0): 0, (6, 1): 0, (6, 2): 0, (6, 3): 0, (6, 4): 0, (6, 5): 0, (6, 7): 0, (6, 8): 0, (6, 9): 0, (6, 10): 0, (6, 11): 0, (6, 12): 0, (6, 13): 0, (6, 14): 0, (6, 15): 0, (7, 0): 0, (7, 1): 0, (7, 2): 32, (7, 3): 0, (7, 4): 0, (7, 5): 0, (7, 6): 21, (7, 8): 0, (7, 9): 0, (7, 10): 0, (7, 11): 0, (7, 12): 0, (7, 13): 0, (7, 14): 0, (7, 15): 0, (8, 0): 0, (8, 1): 0, (8, 2): 0, (8, 3): 0, (8, 4): 0, (8, 5): 0, (8, 6): 0, (8, 7): 0, (8, 9): 0, (8, 10): 0, (8, 11): 0, (8, 12): 0, (8, 13): 0, (8, 14): 0, (8, 15): 0, (9, 0): 0, (9, 1): 0, (9, 2): 0, (9, 3): 0, (9, 4): 0, (9, 5): 0, (9, 6): 0, (9, 7): 0, (9, 8): 0, (9, 10): 0, (9, 11): 0, (9, 12): 0, (9, 13): 0, (9, 14): 0, (9, 15): 0, (10, 0): 0, (10, 1): 0, (10, 2): 0, (10, 3): 0, (10, 4): 0, (10, 5): 0, (10, 6): 25, (10, 7): 0, (10, 8): 0, (10, 9): 0, (10, 11): 0, (10, 12): 0, (10, 13): 0, (10, 14): 15, (10, 15): 0, (11, 0): 0, (11, 1): 0, (11, 2): 0, (11, 3): 6, (11, 4): 0, (11, 5): 0, (11, 6): 0, (11, 7): 0, (11, 8): 0, (11, 9): 0, (11, 10): 0, (11, 12): 0, (11, 13): 0, (11, 14): 10, (11, 15): 10, (12, 0): 38, (12, 1): 0, (12, 2): 0, (12, 3): 0, (12, 4): 3, (12, 5): 0, (12, 6): 0, (12, 7): 0, (12, 8): 46, (12, 9): 6, (12, 10): 0, (12, 11): 0, (12, 13): 5, (12, 14): 0, (12, 15): 0, (13, 0): 0, (13, 1): 0, (13, 2): 0, (13, 3): 0, (13, 4): 0, (13, 5): 0, (13, 6): 0, (13, 7): 0, (13, 8): 0, (13, 9): 0, (13, 10): 0, (13, 11): 0, (13, 12): 0, (13, 14): 15, (13, 15): 0, (14, 0): 0, (14, 1): 0, (14, 2): 0, (14, 3): 0, (14, 4): 0, (14, 5): 0, (14, 6): 0, (14, 7): 0, (14, 8): 0, (14, 9): 0, (14, 10): 0, (14, 11): 0, (14, 12): 0, (14, 13): 0, (14, 15): 0, (15, 0): 0, (15, 1): 0, (15, 2): 0, (15, 3): 0, (15, 4): 0, (15, 5): 0, (15, 6): 0, (15, 7): 0, (15, 8): 0, (15, 9): 0, (15, 10): 0, (15, 11): 0, (15, 12): 0, (15, 13): 0, (15, 14): 0}

S_cplex = {(0, 1): 0, (0, 2): 0, (0, 3): 0, (0, 4): 0, (0, 5): 0, (0, 6): 0, (0, 7): 0, (0, 8): 0, (0, 9): 0, (0, 10): 0, (0, 11): 0, (0, 12): 0, (0, 13): 0, (0, 14): 0, (0, 15): 0, (1, 0): 55, (1, 2): 0, (1, 3): 0, (1, 4): 0, (1, 5): 0, (1, 6): 0, (1, 7): 0, (1, 8): 0, (1, 9): 0, (1, 10): 0, (1, 11): 0, (1, 12): 0, (1, 13): 0, (1, 14): 0, (1, 15): 0, (2, 0): 0, (2, 1): 0, (2, 3): 0, (2, 4): 0, (2, 5): 0, (2, 6): 0, (2, 7): 0, (2, 8): 0, (2, 9): 0, (2, 10): 0, (2, 11): 0, (2, 12): 0, (2, 13): 0, (2, 14): 0, (2, 15): 0, (3, 0): 0, (3, 1): 0, (3, 2): 0, (3, 4): 0, (3, 5): 0, (3, 6): 0, (3, 7): 0, (3, 8): 0, (3, 9): 0, (3, 10): 0, (3, 11): 0, (3, 12): 0, (3, 13): 0, (3, 14): 0, (3, 15): 0, (4, 0): 0, (4, 1): 0, (4, 2): 0, (4, 3): 0, (4, 5): 0, (4, 6): 0, (4, 7): 0, (4, 8): 0, (4, 9): 0, (4, 10): 0, (4, 11): 0, (4, 12): 0, (4, 13): 0, (4, 14): 0, (4, 15): 0, (5, 0): 0, (5, 1): 0, (5, 2): 0, (5, 3): 0, (5, 4): 29, (5, 6): 0, (5, 7): 0, (5, 8): 0, (5, 9): 0, (5, 10): 0, (5, 11): 0, (5, 12): 0, (5, 13): 0, (5, 14): 0, (5, 15): 0, (6, 0): 0, (6, 1): 0, (6, 2): 0, (6, 3): 0, (6, 4): 0, (6, 5): 0, (6, 7): 0, (6, 8): 0, (6, 9): 0, (6, 10): 0, (6, 11): 0, (6, 12): 0, (6, 13): 0, (6, 14): 0, (6, 15): 0, (7, 0): 12, (7, 1): 0, (7, 2): 32, (7, 3): 6, (7, 4): 3, (7, 5): 0, (7, 6): 0, (7, 8): 0, (7, 9): 0, (7, 10): 0, (7, 11): 0, (7, 12): 0, (7, 13): 0, (7, 14): 0, (7, 15): 0, (8, 0): 0, (8, 1): 0, (8, 2): 0, (8, 3): 0, (8, 4): 0, (8, 5): 0, (8, 6): 0, (8, 7): 0, (8, 9): 0, (8, 10): 0, (8, 11): 0, (8, 12): 0, (8, 13): 0, (8, 14): 0, (8, 15): 0, (9, 0): 0, (9, 1): 0, (9, 2): 0, (9, 3): 0, (9, 4): 0, (9, 5): 0, (9, 6): 0, (9, 7): 0, (9, 8): 0, (9, 10): 0, (9, 11): 0, (9, 12): 0, (9, 13): 0, (9, 14): 0, (9, 15): 0, (10, 0): 0, (10, 1): 0, (10, 2): 0, (10, 3): 0, (10, 4): 0, (10, 5): 0, (10, 6): 40, (10, 7): 0, (10, 8): 0, (10, 9): 0, (10, 11): 0, (10, 12): 0, (10, 13): 0, (10, 14): 0, (10, 15): 0, (11, 0): 0, (11, 1): 0, (11, 2): 0, (11, 3): 0, (11, 4): 0, (11, 5): 0, (11, 6): 6, (11, 7): 0, (11, 8): 0, (11, 9): 0, (11, 10): 0, (11, 12): 0, (11, 13): 0, (11, 14): 4, (11, 15): 10, (12, 0): 26, (12, 1): 0, (12, 2): 0, (12, 3): 0, (12, 4): 0, (12, 5): 0, (12, 6): 0, (12, 7): 0, (12, 8): 46, (12, 9): 6, (12, 10): 0, (12, 11): 0, (12, 13): 26, (12, 14): 0, (12, 15): 0, (13, 0): 0, (13, 1): 0, (13, 2): 0, (13, 3): 0, (13, 4): 0, (13, 5): 0, (13, 6): 0, (13, 7): 0, (13, 8): 0, (13, 9): 0, (13, 10): 0, (13, 11): 0, (13, 12): 0, (13, 14): 36, (13, 15): 0, (14, 0): 0, (14, 1): 0, (14, 2): 0, (14, 3): 0, (14, 4): 0, (14, 5): 0, (14, 6): 0, (14, 7): 0, (14, 8): 0, (14, 9): 0, (14, 10): 0, (14, 11): 0, (14, 12): 0, (14, 13): 0, (14, 15): 0, (15, 0): 0, (15, 1): 0, (15, 2): 0, (15, 3): 0, (15, 4): 0, (15, 5): 0, (15, 6): 0, (15, 7): 0, (15, 8): 0, (15, 9): 0, (15, 10): 0, (15, 11): 0, (15, 12): 0, (15, 13): 0, (15, 14): 0}

sum([S_scipy[s]*time[s] for s in S_scipy]) == sum([S_cplex[s]*time[s] for s in S_cplex])

> True

Answer 2

res = linprog(obj_fn, A_ub=a_up, b_ub=b_up, bounds=bounds())

你打电话obj_fn还是Objetc() ？