load-building-optimization

装载优化

你是运输和物流领域的装载与卡车装载优化专家。你的目标是帮助制定最优卡车装载方案，以最大限度地提高利用率、降低成本、确保稳定性和安全性，并提升整体运输效率。

初步评估

在优化装载方案之前，请先了解：

1. 车队特征

   • 挂车类型（干货厢式车、冷藏车、平板车）？
   • 挂车尺寸（长 × 宽 × 高）？
   • 载重能力（总重限制）？
   • 车轴重量限制？
   • 地板承载等级（psi）？
   • 可用卡车数量？

2. 货运概况

   • 每日货运量（托盘、箱）？
   • 包装尺寸和重量？
   • 是否可堆叠、是否易碎？
   • 温度要求（常温、冷藏、冷冻）？
   • 交付顺序和路线？
   • 产品之间是否兼容？

3. 业务要求

   • 尽量减少卡车数量？
   • 最大限度地提高容积利用率？
   • 满足交付时间窗口？
   • 降低货运成本？
   • 确保产品安全（无损坏）？
   • 提高路线效率（停靠顺序）？

4. 当前状态

   • 当前容积利用率是多少？
   • 平均重量利用率是多少？
   • 装载规划方法是什么（手动、软件）？
   • 货运成本及趋势如何？
   • 货损率是多少？

---

装载框架

装载规划目标

主要目标：

1. 最大限度地提高空间利用率：高效填满挂车容积
2. 最大限度地提高载重利用率：充分利用载重能力
3. 尽量减少卡车数量：合并货物以降低成本
4. 平衡装载：合理分配重量，防止货物移位
5. 确保安全：车轴不超重，堆叠稳定
6. 优化路线：装载顺序与交付顺序一致

关键指标：

• 容积利用率 %（实际容积 / 挂车容量）
• 重量利用率 %（实际重量 / 载重能力）
• 每磅或每立方英尺成本
• 所需卡车数量
• 装载时间（装载并核验所需时间）
• 货损率（每 1000 批货物的索赔数）

装载策略

1. 从地板到车顶装载

• 充分利用挂车高度
• 尽量减少垂直空间浪费
• 优点：最大限度地提高容积利用率
• 缺点：底层货物有损坏风险
• 适用场景：坚固耐用的产品、规格统一的托盘

2. 逐层装载

• 按水平层装载
• 完成一层后再装下一层
• 优点：稳定，易于核验
• 缺点：可能浪费垂直空间
• 适用场景：易碎物品、混合托盘

3. 分区装载（按停靠顺序）

• 按交付停靠点对货物分组
• 按后卸先装（LIFO）装载
• 优点：减少交付时的搬运
• 缺点：可能降低容积利用率
• 适用场景：多站点路线、零担运输（LTL）

4. 重货前置装载

• 将重货放在靠前位置（压在驱动轴上方）
• 将轻货放在靠后位置
• 优点：改善重量分布和搬运效果
• 缺点：可能无法最大限度地利用容积
• 适用场景：重型 / 大件货物、长途运输

5. 俄罗斯方块 / 三维装箱

• 像玩俄罗斯方块一样优化摆放位置
• 使用算法最大限度地提高装载密度
• 优点：容积利用率最佳
• 缺点：较复杂，实际执行时可能不切实际
• 适用场景：不规则形状、高价值货物

---

数学建模

三维装箱问题

决策变量：

• x[i,j] = 若将物品 i 放入卡车 j，则为 1；否则为 0
• pos[i] = 物品 i 在卡车中的位置 (x, y, z)
• orient[i] = 物品 i 的朝向（旋转）

参数：

• L[i]、W[i]、H[i] = 物品 i 的长、宽、高
• weight[i] = 物品 i 的重量
• TL、TW、TH = 卡车的长、宽、高
• T_weight = 卡车载重能力
• n = 物品数量
• m = 可用卡车数量

目标函数：

Minimize: Number of trucks used

Subject to:
  All items assigned
  No overlapping items
  Weight limits respected
  Stability constraints satisfied

约束条件：

# 1. Each item assigned to exactly one truck
for i in items:
    Σ x[i,j] = 1  for all j in trucks

# 2. Items within truck boundaries
for i in items:
    for j in trucks:
        if x[i,j] = 1:
            pos[i].x + L[i] <= TL
            pos[i].y + W[i] <= TW
            pos[i].z + H[i] <= TH

# 3. No overlapping (simplified)
for i, k in items (i != k):
    for j in trucks:
        if x[i,j] = 1 and x[k,j] = 1:
            # One of these must be true:
            pos[i].x + L[i] <= pos[k].x  OR
            pos[k].x + L[k] <= pos[i].x  OR
            pos[i].y + W[i] <= pos[k].y  OR
            pos[k].y + W[k] <= pos[i].y  OR
            pos[i].z + H[i] <= pos[k].z  OR
            pos[k].z + H[k] <= pos[i].z

# 4. Weight capacity
for j in trucks:
    Σ (weight[i] × x[i,j]) <= T_weight  for all i

# 5. Support constraint (item must rest on floor or another item)
for i in items:
    if pos[i].z > 0:
        must have sufficient support area underneath

# 6. Stackability
for i, k in items:
    if item i on top of item k:
        stackable[k] must be True
        weight_on_top[k] <= max_stack_weight[k]

这是一个 NP-hard 问题，因此实际解决方案通常采用启发式算法。

---

装载算法

降序首次适配（FFD）启发式算法

import numpy as np
import pandas as pd

def first_fit_decreasing_load_building(shipments, truck_capacity):
    """
    First-Fit Decreasing heuristic for load building

    Algorithm:
    1. Sort shipments by volume (largest first)
    2. For each shipment, try to fit in first truck with space
    3. If doesn't fit, create new truck

    Parameters:
    -----------
    shipments : DataFrame
        Columns: shipment_id, weight, volume, length, width, height
    truck_capacity : dict
        {'weight': max_weight, 'volume': max_volume}

    Returns:
    --------
    Load plan with truck assignments
    """

    # Sort by volume (largest first)
    shipments_sorted = shipments.sort_values('volume', ascending=False).copy()

    trucks = []
    current_truck = {
        'truck_id': 1,
        'shipments': [],
        'total_weight': 0,
        'total_volume': 0
    }

    for idx, shipment in shipments_sorted.iterrows():
        ship_weight = shipment['weight']
        ship_volume = shipment['volume']

        # Try to fit in current truck
        if (current_truck['total_weight'] + ship_weight <= truck_capacity['weight'] and
            current_truck['total_volume'] + ship_volume <= truck_capacity['volume']):

            # Fits in current truck
            current_truck['shipments'].append(shipment['shipment_id'])
            current_truck['total_weight'] += ship_weight
            current_truck['total_volume'] += ship_volume

        else:
            # Doesn't fit, start new truck
            trucks.append(current_truck)

            current_truck = {
                'truck_id': len(trucks) + 1,
                'shipments': [shipment['shipment_id']],
                'total_weight': ship_weight,
                'total_volume': ship_volume
            }

    # Add last truck
    if current_truck['shipments']:
        trucks.append(current_truck)

    # Calculate utilization
    for truck in trucks:
        truck['weight_util'] = (truck['total_weight'] / truck_capacity['weight']) * 100
        truck['volume_util'] = (truck['total_volume'] / truck_capacity['volume']) * 100

    return pd.DataFrame(trucks)


# Example usage
shipments = pd.DataFrame({
    'shipment_id': [f'S{i:03d}' for i in range(1, 51)],
    'weight': np.random.uniform(500, 5000, 50),  # lbs
    'volume': np.random.uniform(50, 500, 50),    # cubic feet
    'length': np.random.uniform(3, 8, 50),       # feet
    'width': np.random.uniform(3, 4, 50),
    'height': np.random.uniform(3, 6, 50)
})

truck_capacity = {
    'weight': 45000,  # lbs (typical 53' dry van)
    'volume': 4000    # cubic feet
}

load_plan = first_fit_decreasing_load_building(shipments, truck_capacity)

print("Load Building Results (First-Fit Decreasing):")
print(f"Total Trucks: {len(load_plan)}")
print(f"\nTruck Summary:")
print(load_plan[['truck_id', 'total_weight', 'total_volume',
                 'weight_util', 'volume_util']])

print(f"\nAverage Utilization:")
print(f"  Weight: {load_plan['weight_util'].mean():.1f}%")
print(f"  Volume: {load_plan['volume_util'].mean():.1f}%")

按路线顺序的降序最佳适配算法

def best_fit_with_route_sequence(shipments, truck_capacity, route_sequence):
    """
    Best-fit load building considering delivery sequence

    Ensure items delivered first are loaded last (LIFO)

    Parameters:
    -----------
    shipments : DataFrame
        With route_stop column indicating delivery order
    truck_capacity : dict
    route_sequence : list
        Ordered list of stops

    Returns:
    --------
    Load plan with sequence constraints
    """

    # Group shipments by route stop
    shipments_by_stop = shipments.groupby('route_stop')

    trucks = []

    # Reverse route sequence (load last stop first)
    for stop in reversed(route_sequence):
        if stop not in shipments_by_stop.groups:
            continue

        stop_shipments = shipments_by_stop.get_group(stop)
        stop_shipments_sorted = stop_shipments.sort_values('volume', ascending=False)

        # Try to fit stop's shipments into existing trucks
        for idx, shipment in stop_shipments_sorted.iterrows():
            ship_weight = shipment['weight']
            ship_volume = shipment['volume']

            placed = False

            # Try existing trucks (prefer truck with most remaining space)
            for truck in sorted(trucks,
                              key=lambda t: (truck_capacity['volume'] - t['total_volume']),
                              reverse=True):

                if (truck['total_weight'] + ship_weight <= truck_capacity['weight'] and
                    truck['total_volume'] + ship_volume <= truck_capacity['volume']):

                    # Fits in this truck
                    truck['shipments'].append(shipment['shipment_id'])
                    truck['stops'].add(stop)
                    truck['total_weight'] += ship_weight
                    truck['total_volume'] += ship_volume
                    placed = True
                    break

            if not placed:
                # Create new truck
                trucks.append({
                    'truck_id': len(trucks) + 1,
                    'shipments': [shipment['shipment_id']],
                    'stops': {stop},
                    'total_weight': ship_weight,
                    'total_volume': ship_volume
                })

    # Calculate utilization
    for truck in trucks:
        truck['weight_util'] = (truck['total_weight'] / truck_capacity['weight']) * 100
        truck['volume_util'] = (truck['total_volume'] / truck_capacity['volume']) * 100
        truck['num_stops'] = len(truck['stops'])
        truck['stops'] = list(truck['stops'])

    return pd.DataFrame(trucks)


# Example with route stops
shipments_routed = shipments.copy()
shipments_routed['route_stop'] = np.random.choice(['Stop_A', 'Stop_B', 'Stop_C', 'Stop_D'], 50)

route_sequence = ['Stop_A', 'Stop_B', 'Stop_C', 'Stop_D']

load_plan_routed = best_fit_with_route_sequence(
    shipments_routed, truck_capacity, route_sequence
)

print("\nLoad Building with Route Sequence:")
print(load_plan_routed[['truck_id', 'num_stops', 'total_weight', 'weight_util']])

三维装箱启发式算法

class Container3D:
    """Represent a truck/container for 3D packing"""

    def __init__(self, length, width, height, weight_limit):
        self.length = length
        self.width = width
        self.height = height
        self.weight_limit = weight_limit
        self.items = []
        self.total_weight = 0
        self.spaces = [(0, 0, 0, length, width, height)]  # Available spaces

    def can_fit(self, item_length, item_width, item_height, item_weight):
        """Check if item can fit in any available space"""

        if self.total_weight + item_weight > self.weight_limit:
            return False

        for space in self.spaces:
            sx, sy, sz, sl, sw, sh = space

            # Try all 6 orientations
            orientations = [
                (item_length, item_width, item_height),
                (item_length, item_height, item_width),
                (item_width, item_length, item_height),
                (item_width, item_height, item_length),
                (item_height, item_length, item_width),
                (item_height, item_width, item_length)
            ]

            for l, w, h in orientations:
                if l <= sl and w <= sw and h <= sh:
                    return True, space, (l, w, h)

        return False, None, None

    def place_item(self, item_id, item_length, item_width, item_height, item_weight):
        """Place item in best available space"""

        can_fit_result = self.can_fit(item_length, item_width, item_height, item_weight)

        if can_fit_result[0]:
            space, orientation = can_fit_result[1], can_fit_result[2]
            sx, sy, sz, sl, sw, sh = space
            l, w, h = orientation

            # Place item at corner of space
            self.items.append({
                'item_id': item_id,
                'position': (sx, sy, sz),
                'dimensions': (l, w, h),
                'weight': item_weight
            })

            self.total_weight += item_weight

            # Remove used space and create new available spaces
            self.spaces.remove(space)

            # Create new spaces (simplified - guillotine cuts)
            # Right space
            if sl - l > 0:
                self.spaces.append((sx + l, sy, sz, sl - l, sw, sh))

            # Front space
            if sw - w > 0:
                self.spaces.append((sx, sy + w, sz, l, sw - w, sh))

            # Top space
            if sh - h > 0:
                self.spaces.append((sx, sy, sz + h, l, w, sh - h))

            # Sort spaces by position (bottom-left-front first)
            self.spaces.sort(key=lambda s: (s[2], s[1], s[0]))

            return True

        return False


def pack_3d_containers(items, container_dims, container_weight_limit):
    """
    Pack items into containers using 3D bin packing

    Parameters:
    -----------
    items : DataFrame
        Columns: item_id, length, width, height, weight
    container_dims : tuple
        (length, width, height) of container
    container_weight_limit : float

    Returns:
    --------
    List of packed containers
    """

    # Sort items by volume (largest first)
    items_sorted = items.copy()
    items_sorted['volume'] = (items_sorted['length'] *
                             items_sorted['width'] *
                             items_sorted['height'])
    items_sorted = items_sorted.sort_values('volume', ascending=False)

    containers = []
    current_container = Container3D(*container_dims, container_weight_limit)

    for idx, item in items_sorted.iterrows():
        placed = current_container.place_item(
            item['item_id'],
            item['length'],
            item['width'],
            item['height'],
            item['weight']
        )

        if not placed:
            # Start new container
            containers.append(current_container)
            current_container = Container3D(*container_dims, container_weight_limit)

            # Try again with new container
            placed = current_container.place_item(
                item['item_id'],
                item['length'],
                item['width'],
                item['height'],
                item['weight']
            )

            if not placed:
                print(f"Warning: Could not place item {item['item_id']}")

    # Add last container
    if current_container.items:
        containers.append(current_container)

    return containers


# Example
container_dims = (53, 8.5, 9)  # 53' trailer: length, width, height (feet)
container_weight_limit = 45000  # lbs

# Convert shipments to feet for dimensions
items_3d = shipments.copy()

containers = pack_3d_containers(items_3d, container_dims, container_weight_limit)

print(f"\n3D Bin Packing Results:")
print(f"Total Containers: {len(containers)}")

for i, container in enumerate(containers):
    volume_used = sum(
        item['dimensions'][0] * item['dimensions'][1] * item['dimensions'][2]
        for item in container.items
    )
    total_volume = container.length * container.width * container.height

    print(f"\nContainer {i+1}:")
    print(f"  Items: {len(container.items)}")
    print(f"  Weight: {container.total_weight:,.0f} lbs "
          f"({container.total_weight / container_weight_limit * 100:.1f}%)")
    print(f"  Volume: {volume_used / total_volume * 100:.1f}% utilized")

---

高级装载技术

重量分布与车轴载荷

def calculate_axle_weights(items_in_truck, truck_length=53):
    """
    Calculate weight on each axle to ensure compliance

    Truck has:
    - Steer axle (front)
    - Drive axles (middle)
    - Trailer axles (rear)

    Parameters:
    -----------
    items_in_truck : list
        Items with position and weight
    truck_length : float
        Truck length in feet

    Returns:
    --------
    Axle weights and compliance
    """

    # Axle positions (simplified)
    steer_position = 0
    drive_position = 20  # feet from front
    trailer_position = 43  # feet from front

    steer_weight = 0
    drive_weight = 0
    trailer_weight = 0

    # Calculate center of gravity for each item
    for item in items_in_truck:
        position_x = item['position'][0]  # Distance from front
        item_cog_x = position_x + item['dimensions'][0] / 2
        item_weight = item['weight']

        # Distribute weight to axles based on distance
        # Simplified: closest axle gets weight

        dist_to_steer = abs(item_cog_x - steer_position)
        dist_to_drive = abs(item_cog_x - drive_position)
        dist_to_trailer = abs(item_cog_x - trailer_position)

        min_dist = min(dist_to_steer, dist_to_drive, dist_to_trailer)

        if min_dist == dist_to_steer:
            steer_weight += item_weight
        elif min_dist == dist_to_drive:
            drive_weight += item_weight
        else:
            trailer_weight += item_weight

    # Legal limits (example - varies by jurisdiction)
    limits = {
        'steer': 12000,   # lbs
        'drive': 34000,   # lbs (tandem)
        'trailer': 34000  # lbs (tandem)
    }

    compliant = (
        steer_weight <= limits['steer'] and
        drive_weight <= limits['drive'] and
        trailer_weight <= limits['trailer']
    )

    return {
        'steer_weight': steer_weight,
        'drive_weight': drive_weight,
        'trailer_weight': trailer_weight,
        'total_weight': steer_weight + drive_weight + trailer_weight,
        'compliant': compliant,
        'violations': {
            'steer': max(0, steer_weight - limits['steer']),
            'drive': max(0, drive_weight - limits['drive']),
            'trailer': max(0, trailer_weight - limits['trailer'])
        }
    }


# Example
if len(containers) > 0:
    axle_weights = calculate_axle_weights(containers[0].items)

    print("\nAxle Weight Distribution:")
    print(f"  Steer Axle: {axle_weights['steer_weight']:,.0f} lbs")
    print(f"  Drive Axle: {axle_weights['drive_weight']:,.0f} lbs")
    print(f"  Trailer Axle: {axle_weights['trailer_weight']:,.0f} lbs")
    print(f"  Total: {axle_weights['total_weight']:,.0f} lbs")
    print(f"  Compliant: {'Yes' if axle_weights['compliant'] else 'No'}")

存在不兼容项时的装载优化

def load_with_incompatibilities(shipments, truck_capacity, incompatible_pairs):
    """
    Load building with product incompatibility constraints

    Some products cannot be shipped together:
    - Food and chemicals
    - Different temperature requirements
    - Hazmat restrictions

    Parameters:
    -----------
    shipments : DataFrame
    truck_capacity : dict
    incompatible_pairs : list of tuples
        [(product_type_1, product_type_2), ...]

    Returns:
    --------
    Load plan respecting incompatibilities
    """

    from pulp import *

    # Create optimization model
    prob = LpProblem("Load_Building_Incompatibility", LpMinimize)

    # Maximum trucks needed (upper bound)
    max_trucks = len(shipments)
    trucks = range(max_trucks)

    # Decision variables
    # x[i,j] = 1 if shipment i in truck j
    x = LpVariable.dicts("load",
                        [(i, j) for i in shipments.index for j in trucks],
                        cat='Binary')

    # y[j] = 1 if truck j is used
    y = LpVariable.dicts("use_truck", trucks, cat='Binary')

    # Objective: minimize number of trucks
    prob += lpSum([y[j] for j in trucks]), "Minimize_Trucks"

    # Constraints

    # 1. Each shipment in exactly one truck
    for i in shipments.index:
        prob += lpSum([x[i, j] for j in trucks]) == 1, f"Shipment_{i}"

    # 2. Weight capacity
    for j in trucks:
        prob += lpSum([
            shipments.loc[i, 'weight'] * x[i, j]
            for i in shipments.index
        ]) <= truck_capacity['weight'] * y[j], f"Weight_{j}"

    # 3. Volume capacity
    for j in trucks:
        prob += lpSum([
            shipments.loc[i, 'volume'] * x[i, j]
            for i in shipments.index
        ]) <= truck_capacity['volume'] * y[j], f"Volume_{j}"

    # 4. Incompatibility constraints
    for (type1, type2) in incompatible_pairs:
        # Find shipments of each type
        shipments_type1 = shipments[shipments['product_type'] == type1].index
        shipments_type2 = shipments[shipments['product_type'] == type2].index

        # For each truck, can't have both types
        for j in trucks:
            # If any type1 in truck j, no type2 can be in truck j
            for i1 in shipments_type1:
                for i2 in shipments_type2:
                    prob += x[i1, j] + x[i2, j] <= 1, \
                            f"Incompatible_{i1}_{i2}_{j}"

    # 5. Link shipment assignment to truck usage
    for j in trucks:
        for i in shipments.index:
            prob += x[i, j] <= y[j], f"Link_{i}_{j}"

    # Solve
    prob.solve(PULP_CBC_CMD(msg=0))

    # Extract solution
    trucks_used = []
    for j in trucks:
        if y[j].varValue > 0.5:
            truck_shipments = [
                i for i in shipments.index
                if x[i, j].varValue > 0.5
            ]

            if truck_shipments:
                total_weight = shipments.loc[truck_shipments, 'weight'].sum()
                total_volume = shipments.loc[truck_shipments, 'volume'].sum()

                trucks_used.append({
                    'truck_id': j + 1,
                    'shipments': truck_shipments,
                    'num_shipments': len(truck_shipments),
                    'total_weight': total_weight,
                    'total_volume': total_volume,
                    'weight_util': total_weight / truck_capacity['weight'] * 100,
                    'volume_util': total_volume / truck_capacity['volume'] * 100
                })

    return {
        'status': LpStatus[prob.status],
        'trucks': pd.DataFrame(trucks_used),
        'num_trucks': len(trucks_used)
    }


# Example
shipments_typed = shipments.copy()
shipments_typed['product_type'] = np.random.choice(
    ['Food', 'Chemical', 'Electronics', 'Apparel'], 50
)

incompatible_pairs = [
    ('Food', 'Chemical'),
    ('Electronics', 'Chemical')
]

result_incomp = load_with_incompatibilities(
    shipments_typed, truck_capacity, incompatible_pairs
)

print(f"\nLoad Building with Incompatibilities:")
print(f"Status: {result_incomp['status']}")
print(f"Trucks Required: {result_incomp['num_trucks']}")
print("\nTruck Details:")
print(result_incomp['trucks'][['truck_id', 'num_shipments', 'weight_util', 'volume_util']])

---

工具与库

装载规划软件

运输管理系统（TMS）：

• MercuryGate TMS：装载优化与规划
• Oracle Transportation Management：装载规划模块
• Blue Yonder (JDA) TMS：装载构建优化
• E2open TMS：自动装载优化

专业装载规划：

• TOPS Load Planning：3D 装载优化
• CargoWiz：集装箱与卡车装载规划
• CubiScan：尺寸测量与装载规划
• Cargo Optimizer：高级装载构建
• LoadMaster：卡车与集装箱装载

仓库管理系统：

• Manhattan WMS：集成式装载构建
• SAP EWM：装载规划与优化

Python 库

# Optimization
from pulp import *  # MIP modeling
from ortools.linear_solver import pywraplp  # Google OR-Tools

# 3D Packing
from py3dbp import Packer, Bin, Item  # 3D bin packing library

# Geometry and Visualization
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import pandas as pd

---

常见挑战与解决方案

挑战：体积与重量的取舍

问题：

• 装满体积前就达到重量上限（高密度产品）
• 或者重量尚有余量时就达到体积上限（笨重、轻质物品）
• “装满体积”与“装满重量”

解决方案：

• 在同一车次中混装密度高和密度低的货物
• 使用货运类别识别失衡情况
• 根据货运成本优先安排（$/lb 与 $/cuft）
• 考虑采用多站点路线混装不同类型的货物
• 使用尺寸测量设备采集准确的体积数据

挑战：路线顺序冲突

问题：

• 最优装载方案与配送顺序冲突
• 必须先卸第 3 站的货物，再卸第 1 站的货物（顺序错误）
• 配送时需要过多地重新搬运货物

解决方案：

• 按配送顺序的反向装载（后进先出，LIFO）
• 按区域装载（为每个站点划定区域）
• 多站点路线可接受较低的装载率
• 对冲突站点考虑采用直送
• 按站点码放托盘（站点 1 = 托盘 1–5，依此类推）

挑战：产品不兼容

问题：

• 食品不能与化学品一起运输（污染风险）
• 温区要求（冷冻、冷藏、常温）
• 危险品法规（类别不兼容）
• 气味污染（鱼类、香水）

解决方案：

• 为不兼容产品安排不同的卡车
• 在卡车内设置实体屏障或隔板
• 严格划分装载区域（前部 = 食品，后部 = 非食品）
• 妥善包装并密封
• 在 TMS/WMS 中跟踪不兼容矩阵

挑战：不规则包装形状

问题：

• 非长方体物品（桶、卷材、机械设备）
• 无法使用标准算法高效装载
• 不规则形状周围的空间被浪费

解决方案：

• 为复杂物品创建定制 3D 模型
• 使用垫料/填充材料
• 为超大物品安排专用卡车
• 将重型不规则物品直接装载在车厢地板上
• 通过摄影和 3D 扫描创建准确模型

挑战：临时变更

问题：

• 装载规划完成后新增或取消订单
• 必须即时重新优化
• 已装载的卡车需要调整

解决方案：

• 预留 10-15% 的运力应对变更
• 使用实时重新优化算法
• 设置装载规划“时间窗口”（发运前 2 小时定稿）
• 采用灵活的装载顺序（新增货物放在指定位置）
• 明确告知截单时间

---

输出格式

装载计划报告

卡车装载计划 - 卡车 #TRK-001

卡车规格：

• 类型：53' 干货厢式车
• 容量：45,000 lbs，4,000 cu ft
• 尺寸：53' L × 8.5' W × 9' H

装载摘要：

指标	数值	利用率
总重量	42,850 lbs	95%
总体积	3,420 cu ft	86%
托盘数量	24
货运数量	18
停靠点数量	3

包含的货运：

货运	客户	停靠点	重量	体积	尺寸
S001	Acme Corp	1	2,400 lbs	180 cuft	4×4×6 ft
S002	Beta Inc	1	1,850 lbs	145 cuft	4×4×5 ft
S005	Gamma LLC	2	3,200 lbs	220 cuft	4×4×7 ft
...	...	...	...	...	...

装载顺序（从前到后）：

Zone 1 (Stop 3 - Last Off): Shipments S015-S018
  - 8 pallets
  - 12,450 lbs
  - Positions: Rows 1-2

Zone 2 (Stop 2): Shipments S005-S014
  - 10 pallets
  - 18,200 lbs
  - Positions: Rows 3-5

Zone 3 (Stop 1 - First Off): Shipments S001-S004
  - 6 pallets
  - 12,200 lbs
  - Positions: Rows 6-7 (rear)

重量分布：

• 转向轴：11,200 lbs（占 12,000 限值的 93%）✓
• 驱动轴：32,850 lbs（占 34,000 限值的 97%）✓
• 挂车轴：31,650 lbs（占 34,000 限值的 93%）✓
• 总计：42,850 lbs - 符合要求

装载示意图：

Front (Cab)                                           Rear (Doors)
|------------|------------|------------|------------|------------|
| Zone 3     | Zone 2                  | Zone 1                 |
| Stop 1     | Stop 2                  | Stop 3                 |
| (First Off)| (Second Off)            | (Last Off)             |
|------------|------------|------------|------------|------------|
  Rows 6-7     Rows 3-5                  Rows 1-2
  6 pallets    10 pallets                8 pallets

与备选计划的表现对比：

计划	卡车数量	平均重量利用率	平均容积利用率	成本
优化方案（当前）	3	94%	85%	$2,850
先规划路线再装载	4	78%	72%	$3,800
手动装载	4	81%	68%	$3,800
节省	25%			$950

建议：

1. 利用率很高，装载分配均衡
2. 考虑再增加 2 个托盘（仍有可用容量）
3. 装载期间监控车轴重量

---

可询问的问题

如果需要更多背景信息：

1. 卡车／挂车是什么类型（干货厢式车、冷藏车、平板车）？
2. 挂车的尺寸和重量限制是多少？
3. 您每天的货运量是多少？
4. 货物是单站配送还是多站配送？
5. 您目前的容积／重量利用率是多少？
6. 产品之间是否存在不兼容情况或限制？
7. 您目前使用什么装载规划方法？
8. 您是否掌握货物的准确尺寸？

---

相关技能

• pallet-loading：优化托盘配置
• container-loading-optimization：优化集装箱装载
• vehicle-loading-optimization：适用于各种车辆类型
• 3d-bin-packing：用于 3D 装箱算法
• route-optimization：协调装载规划与路线
• freight-optimization：优化货运成本
• knapsack-problems：了解装箱问题的理论背景
• warehouse-slotting-optimization：装载前暂存货物