用python代码实现以上问题
时间: 2023-08-10 21:31:03 浏览: 41
由于该问题的复杂度较高,需要进行大量的数学建模和算法设计。在这里,我提供一个简单的 Python 代码,展示如何使用贪心算法解决该问题。这里我们假设所有快递的派送地址在第一象限内。
```python
import math
# 计算两个点之间的距离
def distance(x1, y1, x2, y2):
return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
# 贪心算法确定业务员的派送顺序
def find_delivery_order(delivery_list, start_x, start_y):
delivery_order = []
while delivery_list:
min_distance = float('inf')
min_index = -1
for i in range(len(delivery_list)):
x, y, weight = delivery_list[i]
d = distance(start_x, start_y, x, y)
if d < min_distance:
min_distance = d
min_index = i
delivery_order.append(delivery_list[min_index])
start_x, start_y, _ = delivery_list.pop(min_index)
return delivery_order
# 计算每个业务员的路程
def calculate_distance(delivery_order):
total_distance = 0
for i in range(len(delivery_order) - 1):
x1, y1, _ = delivery_order[i]
x2, y2, _ = delivery_order[i+1]
total_distance += distance(x1, y1, x2, y2)
return total_distance
# 将所有快递按照派送地址分组
def group_deliveries(delivery_list, max_weight=25):
groups = []
group = []
total_weight = 0
for delivery in delivery_list:
x, y, weight = delivery
if total_weight + weight > max_weight:
groups.append(group)
group = []
total_weight = 0
group.append(delivery)
total_weight += weight
if group:
groups.append(group)
return groups
# 计算需要的业务员数量
def calculate_num_deliverymen(delivery_list, max_weight=25, max_working_hours=6):
num_deliveries = len(delivery_list)
max_num_deliveries = max_weight * (max_working_hours * 60 / 10)
return math.ceil(num_deliveries / max_num_deliveries)
# 模拟运行
def run(delivery_list):
# 公司总部位于坐标原点
start_x = 0
start_y = 0
# 将所有快递按照派送地址分组
groups = group_deliveries(delivery_list)
# 计算需要的业务员数量
num_deliverymen = calculate_num_deliverymen(delivery_list)
# 分配快递给每个业务员
deliverymen = [[] for _ in range(num_deliverymen)]
for i in range(len(groups)):
deliveryman_index = i % num_deliverymen
deliveryman = deliverymen[deliveryman_index]
deliveryman.extend(groups[i])
# 计算每个业务员的派送顺序
for i in range(num_deliverymen):
deliveryman = deliverymen[i]
delivery_order = find_delivery_order(deliveryman, start_x, start_y)
deliverymen[i] = delivery_order
# 计算每个业务员的路程
total_distance = 0
for i in range(num_deliverymen):
delivery_order = deliverymen[i]
distance = calculate_distance(delivery_order)
total_distance += distance
return deliverymen, total_distance
if __name__ == '__main__':
delivery_list = [
(10, 20, 15),
(30, 40, 10),
(50, 60, 20),
(70, 80, 30),
(90, 100, 40),
(110, 120, 25),
(130, 140, 35),
(150, 160, 5),
(170, 180, 10),
]
deliverymen, total_distance = run(delivery_list)
print(f"需要 {len(deliverymen)} 个业务员")
print(f"总路程为 {total_distance:.2f} km")
for i in range(len(deliverymen)):
print(f"业务员 {i+1} 的派送顺序为:")
for delivery in deliverymen[i]:
print(f"({delivery[0]}, {delivery[1]}),重量为 {delivery[2]} 千克")
```