有一个CVRP问题有300个客户的坐标和配送需求目标函数是最小成本包括固定成本与车辆数成正比和行驶成本行驶距离成正比配送中心的车辆数目足够每辆车有最长工作时间约束和载重约束车辆同构工作时间包括两客户之间的行驶时间和客户服务时间服务时间与配送量成正比运用python的gurobipy库求解怎么写程序

首先，需要定义变量和模型：

from gurobipy import *

# 定义CVRP模型
m = Model("CVRP")

# 定义变量
x = {}
for i in range(num_customers + 1):
    for j in range(num_customers + 1):
        if i != j:
            x[i, j] = m.addVar(vtype=GRB.BINARY, name="x(%s,%s)" % (i, j))

其中，num_customers表示客户数量，x[i,j]表示从i到j是否有路径。

接下来，需要添加约束条件：

# 每个客户只能被访问一次
for i in range(1, num_customers + 1):
    m.addConstr(quicksum(x[i, j] for j in range(num_customers + 1) if i != j) == 1)

# 每辆车的起点和终点分别为配送中心
for k in range(num_vehicles):
    m.addConstr(quicksum(x[0, j] for j in range(1, num_customers + 1)) <= num_customers)

for k in range(num_vehicles):
    m.addConstr(quicksum(x[i, 0] for i in range(1, num_customers + 1)) <= num_customers)

# 车辆载重约束
for k in range(num_vehicles):
    m.addConstr(quicksum(d[i] * x[i, j] for i in range(num_customers + 1)
                         for j in range(num_customers + 1) if i != j and j != 0) <= Q)

# 每辆车的行驶距离不超过最大距离
for k in range(num_vehicles):
    m.addConstr(quicksum(c[i, j] * x[i, j] for i in range(num_customers + 1)
                         for j in range(num_customers + 1) if i != j) <= max_distance)

其中，d[i]表示客户i的配送需求，Q表示每辆车的载重限制，c[i,j]表示从i到j的距离，max_distance表示每辆车的最大行驶距离。

然后，需要定义目标函数：

# 定义目标函数
m.setObjective(quicksum(c[i, j] * x[i, j] for i in range(num_customers + 1) for j in range(num_customers + 1) if i != j),
               GRB.MINIMIZE)

最后，调用solve()方法求解：

# 求解模型
m.optimize()

完整代码如下：

from gurobipy import *

# 数据准备
num_customers = 300
num_vehicles = 10
Q = 100
max_distance = 500

# 坐标和配送需求
locations = {}
demands = {}
for i in range(num_customers):
    locations[i + 1] = (random.randint(0, 100), random.randint(0, 100))
    demands[i + 1] = random.randint(1, 10)

# 计算距离
c = {}
for i in range(num_customers + 1):
    for j in range(num_customers + 1):
        if i == j:
            c[i, j] = 0
        else:
            c[i, j] = math.sqrt((locations[i][0] - locations[j][0]) ** 2 + (locations[i][1] - locations[j][1]) ** 2)

# 需求量
d = {}
for i in range(num_customers + 1):
    if i == 0:
        d[i] = 0
    else:
        d[i] = demands[i]

# 定义CVRP模型
m = Model("CVRP")

# 定义变量
x = {}
for i in range(num_customers + 1):
    for j in range(num_customers + 1):
        if i != j:
            x[i, j] = m.addVar(vtype=GRB.BINARY, name="x(%s,%s)" % (i, j))

# 每个客户只能被访问一次
for i in range(1, num_customers + 1):
    m.addConstr(quicksum(x[i, j] for j in range(num_customers + 1) if i != j) == 1)

# 每辆车的起点和终点分别为配送中心
for k in range(num_vehicles):
    m.addConstr(quicksum(x[0, j] for j in range(1, num_customers + 1)) <= num_customers)

for k in range(num_vehicles):
    m.addConstr(quicksum(x[i, 0] for i in range(1, num_customers + 1)) <= num_customers)

# 车辆载重约束
for k in range(num_vehicles):
    m.addConstr(quicksum(d[i] * x[i, j] for i in range(num_customers + 1)
                         for j in range(num_customers + 1) if i != j and j != 0) <= Q)

# 每辆车的行驶距离不超过最大距离
for k in range(num_vehicles):
    m.addConstr(quicksum(c[i, j] * x[i, j] for i in range(num_customers + 1)
                         for j in range(num_customers + 1) if i != j) <= max_distance)

# 定义目标函数
m.setObjective(quicksum(c[i, j] * x[i, j] for i in range(num_customers + 1) for j in range(num_customers + 1) if i != j),
               GRB.MINIMIZE)

# 求解模型
m.optimize()
``