具有惩罚成本的VRPT用gurobi求解代码

下面是一个具有惩罚成本的VRPT用Gurobi求解的Python代码示例：

import gurobipy as gp
from gurobipy import GRB

# 输入数据
n_customers = 10 # 客户数量
n_vehicles = 3 # 车辆数量
capacity = 50 # 车辆容量
demand = [0, 10, 20, 5, 15, 10, 30, 5, 10, 20] # 客户需求量
service_time = [0, 10, 15, 5, 10, 5, 20, 5, 10, 15] # 客户服务时间
travel_time = [[0, 10, 20, 15, 35, 25, 50, 30, 15, 10],
               [10, 0, 25, 20, 30, 15, 40, 25, 5, 20],
               [20, 25, 0, 30, 40, 30, 10, 40, 25, 35],
               [15, 20, 30, 0, 25, 20, 45, 25, 10, 20],
               [35, 30, 40, 25, 0, 30, 25, 50, 35, 40],
               [25, 15, 30, 20, 30, 0, 35, 20, 10, 25],
               [50, 40, 10, 45, 25, 35, 0, 45, 30, 50],
               [30, 25, 40, 25, 50, 20, 45, 0, 25, 35],
               [15, 5, 25, 10, 35, 10, 30, 25, 0, 15],
               [10, 20, 35, 20, 40, 25, 50, 35, 15, 0]] # 客户之间的行驶时间

# 创建模型
m = gp.Model('VRPTW')

# 创建变量
x = m.addVars(n_customers + 1, n_customers + 1, n_vehicles, vtype=GRB.BINARY, name='x')
y = m.addVars(n_customers + 1, n_vehicles, vtype=GRB.CONTINUOUS, name='y')
t = m.addVars(n_customers + 1, n_vehicles, vtype=GRB.CONTINUOUS, name='t')

# 添加约束
for i in range(1, n_customers + 1):
    m.addConstr(sum(x[i, j, k] for j in range(n_customers + 1) for k in range(n_vehicles)) == 1, f'c1_{i}')

for k in range(n_vehicles):
    m.addConstr(sum(x[0, j, k] for j in range(1, n_customers + 1)) == 1, f'c2_{k}')
    m.addConstr(sum(x[i, 0, k] for i in range(1, n_customers + 1)) == 1, f'c3_{k}')
    m.addConstr(y[0, k] == capacity, f'c4_{k}')
    for i in range(1, n_customers + 1):
        m.addConstr(y[i, k] >= demand[i])
        m.addConstr(y[i, k] <= capacity)
        m.addConstr(t[i, k] >= service_time[i] + t[j, k] + travel_time[j][i] - (1 - x[j, i, k]) * 1e6 for j in range(n_customers + 1))
        m.addConstr(t[i, k] >= service_time[i])
        m.addConstr(t[i, k] <= 480)
    for j in range(n_customers + 1):
        m.addConstr(sum(x[i, j, k] for i in range(n_customers + 1)) == sum(x[j, i, k] for i in range(n_customers + 1)))
        m.addConstr(sum(x[i, j, k] for i in range(n_customers + 1)) <= 1)

# 添加目标函数
obj = sum(travel_time[i][j] * x[i, j, k] for i in range(n_customers + 1) for j in range(n_customers + 1) for k in range(n_vehicles))
obj += sum(1000 * (t[i, k] - demand[i]) * (t[i, k] > demand[i]) for i in range(1, n_customers + 1) for k in range(n_vehicles))
m.setObjective(obj, GRB.MINIMIZE)

# 求解模型
m.optimize()

# 输出结果
print('Total Cost:', m.objVal)
for k in range(n_vehicles):
    print(f'Vehicle {k}:')
    route = []
    for i in range(n_customers + 1):
        for j in range(n_customers + 1):
            if x[i, j, k].x > 0.5:
                route.append(i)
    print(route)

在上面的代码中，我们添加了一个惩罚成本，用于惩罚超出客户需求量的量。具体来说，我们将惩罚成本设置为1000，然后将每个客户的服务时间与需求量进行比较，如果服务时间超过了需求量，则会产生惩罚成本。最终目标函数将行驶时间和惩罚成本相加，以得出总成本。