156 lines
5.2 KiB
Python
156 lines
5.2 KiB
Python
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"""
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Step 03: 频次分配 - Hamilton最大余数法
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输入: 02_demand.xlsx
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输出: 03_allocate.xlsx
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功能:
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1. 按真实需求 μ̃ 比例分配年度访问次数 k_i
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2. 使用 Hamilton 方法保证整数分配且总和 = N
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3. 满足覆盖约束: k_i >= 1
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分配原则:
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- 先给每个站点分配1次 (覆盖约束)
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- 剩余 N-70 次按 μ̃ 比例分配
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"""
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import pandas as pd
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import numpy as np
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from pathlib import Path
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# 路径配置
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INPUT_PATH = Path(__file__).parent / "02_demand.xlsx"
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OUTPUT_PATH = Path(__file__).parent / "03_allocate.xlsx"
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# 分配参数
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N_TOTAL = 730 # 年度总访问次数 (365天 × 2站点/天)
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MIN_VISITS = 1 # 每站点最少访问次数 (覆盖约束)
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def hamilton_allocation(total: int, weights: list) -> list:
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"""
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Hamilton最大余数法整数分配
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Args:
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total: 待分配总数
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weights: 各项权重
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Returns:
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整数分配结果列表
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"""
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n = len(weights)
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w_sum = sum(weights)
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# 连续配额
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quotas = [total * w / w_sum for w in weights]
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# 下取整
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floors = [int(q) for q in quotas]
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remainders = [q - f for q, f in zip(quotas, floors)]
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# 剩余席位按余数从大到小分配
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leftover = total - sum(floors)
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indices = sorted(range(n), key=lambda i: -remainders[i])
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for i in indices[:leftover]:
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floors[i] += 1
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return floors
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def main():
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print("=" * 60)
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print("Step 03: 频次分配 - Hamilton最大余数法")
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print("=" * 60)
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# 1. 读取需求修正后的数据
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print(f"\n[1] 读取输入: {INPUT_PATH}")
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df = pd.read_excel(INPUT_PATH)
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print(f" 读取 {len(df)} 条记录")
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n_sites = len(df)
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# 2. 显示参数
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print(f"\n[2] 分配参数:")
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print(f" 年度总访问次数 N = {N_TOTAL}")
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print(f" 站点数 = {n_sites}")
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print(f" 覆盖约束: 每站点至少 {MIN_VISITS} 次")
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print(f" 剩余可分配次数 = {N_TOTAL} - {n_sites} × {MIN_VISITS} = {N_TOTAL - n_sites * MIN_VISITS}")
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# 3. Hamilton分配
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print(f"\n[3] 执行Hamilton分配...")
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# 权重 = 修正后的真实需求 μ̃
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weights = df['mu_tilde'].tolist()
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# 分配剩余次数
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extra_visits = N_TOTAL - n_sites * MIN_VISITS
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k_extra = hamilton_allocation(extra_visits, weights)
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# 总访问次数 = 基础 + 额外
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df['k'] = [MIN_VISITS + ke for ke in k_extra]
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# 4. 验证分配结果
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print(f"\n[4] 分配结果验证:")
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print(f" 总访问次数: Σk_i = {df['k'].sum()} (应为 {N_TOTAL})")
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print(f" 最小访问次数: min(k_i) = {df['k'].min()} (应 >= {MIN_VISITS})")
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print(f" 最大访问次数: max(k_i) = {df['k'].max()}")
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print(f" 访问次数范围: [{df['k'].min()}, {df['k'].max()}]")
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assert df['k'].sum() == N_TOTAL, f"总访问次数不等于{N_TOTAL}"
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assert df['k'].min() >= MIN_VISITS, f"存在站点访问次数少于{MIN_VISITS}"
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# 5. 计算满足率
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# r_i = k_i * μ_i / μ̃_i (年度服务量 / 真实需求)
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df['annual_service'] = df['k'] * df['mu'] # 年度预期服务量
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df['r'] = df['annual_service'] / df['mu_tilde'] # 满足率代理
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print(f"\n[5] 满足率统计:")
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print(f" 满足率 r = k × μ / μ̃")
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print(f" r 均值: {df['r'].mean():.2f}")
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print(f" r 标准差: {df['r'].std():.2f}")
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print(f" r 范围: [{df['r'].min():.2f}, {df['r'].max():.2f}]")
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print(f" r 变异系数: {df['r'].std() / df['r'].mean():.4f}")
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# 6. 分配结果分布
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print(f"\n[6] 访问次数分布:")
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k_counts = df['k'].value_counts().sort_index()
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for k_val, count in k_counts.items():
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print(f" k = {k_val:2d}: {count:2d} 个站点 {'█' * count}")
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# 7. 与2019年对比
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print(f"\n[7] 与2019年访问次数对比:")
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df['k_2019_scaled'] = df['visits_2019'] * N_TOTAL / df['visits_2019'].sum()
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df['k_diff'] = df['k'] - df['k_2019_scaled']
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print(f" 2019年总访问次数: {df['visits_2019'].sum()}")
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print(f" 2019年缩放后总次数: {df['k_2019_scaled'].sum():.1f}")
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print(f" 新方案 vs 2019缩放:")
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print(f" - 增加访问的站点: {(df['k_diff'] > 0.5).sum()} 个")
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print(f" - 减少访问的站点: {(df['k_diff'] < -0.5).sum()} 个")
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print(f" - 基本不变的站点: {((df['k_diff'] >= -0.5) & (df['k_diff'] <= 0.5)).sum()} 个")
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# 8. 保存输出
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print(f"\n[8] 保存输出: {OUTPUT_PATH}")
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output_cols = ['site_id', 'site_name', 'lat', 'lon', 'visits_2019',
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'mu', 'sigma', 'mu_tilde', 'k', 'annual_service', 'r']
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df[output_cols].to_excel(OUTPUT_PATH, index=False)
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print(f" 已保存 {len(df)} 条记录")
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# 9. 输出预览
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print(f"\n[9] 分配结果预览 (k 最高的10个站点):")
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top10 = df.nlargest(10, 'k')[['site_id', 'site_name', 'mu', 'mu_tilde', 'k', 'annual_service', 'r']]
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print(top10.to_string(index=False))
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print(f"\n 分配结果预览 (k 最低的10个站点):")
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bottom10 = df.nsmallest(10, 'k')[['site_id', 'site_name', 'mu', 'mu_tilde', 'k', 'annual_service', 'r']]
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print(bottom10.to_string(index=False))
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print("\n" + "=" * 60)
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print("Step 03 完成")
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print("=" * 60)
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return df
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if __name__ == "__main__":
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main()
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