### 题目重述 我们需要根据提供的订单需求和原材料缺陷信息，设计一个简单的Python代码，重新制定最优切割方案，并计算调整后切割方案的整体切割损失率及利用率。 ### 给出答案（答案为带注释的代码块） ```python import numpy as np # 读取订单需求数据 orders_data = [ {"order_id": 1, "quantity": 10, "width_target": 1.6, "height_target": 2.2, "price_per_set": 480}, {"order_id": 2, "quantity": 20, "width_target": 1.8, "height_target": 2.4, "price_per_set": 680}, {"order_id": 3, "quantity": 20, "width_target": 1.7, "height_target": 2.3, "price_per_set": 550}, {"order_id": 4, "quantity": 15, "width_target": 1.5, "height_target": 2.0, "price_per_set": 420} ] # 读取原材料数据及缺陷信息 materials_data = [ {"material_id": 1, "length": 5.5, "defects": [(1.0, 0.03), (2.5, 0.04)], "cost_per_meter": 18}, {"material_id": 2, "length": 6.2, "defects": [(0.5, 0.02), (1.8, 0.05)], "cost_per_meter": 22}, {"material_id": 3, "length": 7.8, "defects": [(3.0, 0.03)], "cost_per_meter": 28} ] # 锯口宽度 kerf_width = 0.005 # 定义计算单个窗框所需长度的函数 def calculate_frame_length(width, height, kerf_width): return (width + kerf_width) * 2 + (height + kerf_width) * 2 # 计算每个订单所需的总长度 orders_length_requirements = [ {"order_id": order["order_id"], "total_length_needed": calculate_frame_length(order["width_target"], order["height_target"], kerf_width) * order["quantity"]} for order in orders_data ] # 函数：计算去除缺陷后的有效长度区间 def get_valid_intervals(material_length, defects): valid_intervals = [] last_end = 0 for start, length in defects: if start > last_end: valid_intervals.append((last_end, start)) last_end = start + length if last_end < material_length: valid_intervals.append((last_end, material_length)) return valid_intervals # 计算总的原材料长度和有效的可用长度 total_material_length = sum(material['length'] for material in materials_data) valid_material_length = 0 for material in materials_data: valid_intervals = get_valid_intervals(material['length'], material['defects']) valid_material_length += sum(end - start for start, end in valid_intervals) # 分配订单至原材料 allocation = {} for material in materials_data: allocation[material['material_id']] = {'used_length': 0, 'cut_sets': []} for order in orders_data: remaining_quantity = order['quantity'] for material in materials_data: valid_intervals = get_valid_intervals(material['length'], material['defects']) for start, end in valid_intervals: available_length = end - start while remaining_quantity > 0 and available_length >= calculate_frame_length(order['width_target'], order['height_target'], kerf_width): available_length -= calculate_frame_length(order['width_target'], order['height_target'], kerf_width) allocation[material['material_id']]['cut_sets'].append({ "order_id": order['order_id'], "quantity": 1, "width_target": order['width_target'], "height_target": order['height_target'] }) remaining_quantity -= 1 allocation[material['material_id']]['used_length'] += calculate_frame_length(order['width_target'], order['height_target'], kerf_width) if remaining_quantity == 0: break # 计算切割损失率和利用率 total_used_length = sum(allocation[material['material_id']]['used_length'] for material in materials_data) total_waste_length = total_material_length - total_used_length utilization_rate = (total_used_length / total_material_length) * 100 if total_material_length != 0 else 0 waste_rate = (total_waste_length / total_material_length) * 100 if total_material_length != 0 else 0 # 打印结果 for material_id, details in allocation.items(): print(f'Material {material_id}:') for set_info in details['cut_sets']: print(f' Cut 1 set for Order {set_info["order_id"]}') print(f' Used Length: {details["used_length"]:.2f} meters') print() print(f'Total Utilization Rate: {utilization_rate:.2f}%') print(f'Total Waste Rate: {waste_rate:.2f}%') ``` ### 代码解析 1. **读取订单需求和原材料数据**：定义了订单需求和原材料的缺陷信息。 2. **定义辅助函数**： - `calculate_frame_length`：计算单个窗框所需的长度。 - `get_valid_intervals`：计算去除缺陷后的有效长度区间。 3. **计算订单所需总长度**：根据每个订单的需求计算所需的总长度。 4. **分配订单至原材料**：根据每个订单的需求，在去除缺陷后的有效长度内进行切割分配。 5. **计算切割损失率和利用率**：基于求解结果，计算总的利用率和损失率。 6. **打印结果**：输出每种原材料的切割方案及其利用率和损失率。 ### 知识点 1. **有效长度计算**：去除缺陷后计算原材料的有效长度区间。 2. **循环分配逻辑**：通过循环分配订单至原材料，确保每种原材料的有效利用。 3. **损失率和利用率计算**：根据切割结果计算总的利用率和损失率。