234 lines
8.0 KiB
Python
234 lines
8.0 KiB
Python
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"""
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Step 04: 评估指标计算
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输入: 03_allocate.xlsx
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输出: 04_metrics.xlsx
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功能:
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1. 计算有效性指标 (E1, E2)
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2. 计算公平性指标 (F1, F2, F3)
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3. 与基线方案对比
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4. 输出综合评估报告
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指标定义:
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- E1: 原始总服务量 = Σ k_i × μ_i
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- E2: 质量加权服务量 = Σ k_i × μ_i × q(μ_i), q(μ) = min(1, 250/μ)
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- F1: 满足率基尼系数 Gini(r)
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- F2: 最差站点满足率 min(r)
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- F3: 满足率变异系数 CV(r)
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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 / "03_allocate.xlsx"
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OUTPUT_PATH = Path(__file__).parent / "04_metrics.xlsx"
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# 评估参数
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C_BAR = 250 # 典型服务量 (质量折扣阈值)
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def quality_discount(mu: float, c_bar: float = C_BAR) -> float:
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"""
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质量折扣因子: 当 μ > c_bar 时，服务质量打折
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q(μ) = min(1, c_bar / μ)
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"""
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return min(1.0, c_bar / mu) if mu > 0 else 1.0
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def gini_coefficient(values: list) -> float:
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"""
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计算基尼系数
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Gini = Σ_i Σ_j |x_i - x_j| / (2n Σ_i x_i)
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"""
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values = np.array(values)
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n = len(values)
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if n == 0 or values.sum() == 0:
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return 0.0
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# 排序后计算
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sorted_values = np.sort(values)
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cumsum = np.cumsum(sorted_values)
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return (2 * np.sum((np.arange(1, n + 1) * sorted_values)) - (n + 1) * cumsum[-1]) / (n * cumsum[-1])
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def compute_metrics(df: pd.DataFrame, method_name: str) -> dict:
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"""计算单个方案的所有指标"""
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# 有效性指标
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E1 = (df['k'] * df['mu']).sum()
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E2 = (df['k'] * df['mu'] * df['mu'].apply(quality_discount)).sum()
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# 满足率
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r = df['k'] * df['mu'] / df['mu_tilde']
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# 公平性指标
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F1 = gini_coefficient(r.tolist())
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F2 = r.min()
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F3 = r.std() / r.mean()
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return {
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'method': method_name,
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'E1_total_service': E1,
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'E2_quality_weighted': E2,
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'F1_gini': F1,
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'F2_min_satisfaction': F2,
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'F3_cv_satisfaction': F3
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}
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def compute_baseline_uniform(df: pd.DataFrame, n_total: int = 730) -> pd.DataFrame:
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"""基线1: 均匀分配"""
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df_baseline = df.copy()
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k_uniform = n_total // len(df)
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remainder = n_total - k_uniform * len(df)
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df_baseline['k'] = k_uniform
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# 将余数分配给前 remainder 个站点
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df_baseline.iloc[:remainder, df_baseline.columns.get_loc('k')] += 1
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return df_baseline
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def compute_baseline_2019_scaled(df: pd.DataFrame, n_total: int = 730) -> pd.DataFrame:
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"""基线2: 2019年访问次数等比例缩放"""
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df_baseline = df.copy()
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total_2019 = df['visits_2019'].sum()
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# 按比例缩放
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k_float = df['visits_2019'] * n_total / total_2019
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k_floor = k_float.astype(int)
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remainder = n_total - k_floor.sum()
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# 按余数分配
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remainders = k_float - k_floor
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indices = remainders.nlargest(remainder).index
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k_floor.loc[indices] += 1
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df_baseline['k'] = k_floor
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return df_baseline
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def compute_baseline_mu_raw(df: pd.DataFrame, n_total: int = 730) -> pd.DataFrame:
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"""基线3: 按原始μ比例分配 (无截断修正)"""
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df_baseline = df.copy()
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# 覆盖约束
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k_base = 1
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extra = n_total - len(df) * k_base
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# 按μ比例分配额外次数
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weights = df['mu'].tolist()
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w_sum = sum(weights)
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quotas = [extra * w / w_sum for w in weights]
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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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leftover = extra - sum(floors)
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indices = sorted(range(len(weights)), 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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df_baseline['k'] = [k_base + f for f in floors]
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return df_baseline
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def main():
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print("=" * 60)
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print("Step 04: 评估指标计算")
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print("=" * 60)
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# 1. 读取分配结果
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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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# 2. 计算推荐方案指标
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print(f"\n[2] 计算推荐方案指标 (按μ̃比例分配)")
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metrics_recommended = compute_metrics(df, 'Recommended (μ̃ proportional)')
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for key, value in metrics_recommended.items():
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if key != 'method':
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print(f" {key}: {value:.4f}")
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# 3. 计算基线方案指标
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print(f"\n[3] 计算基线方案指标")
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# 基线1: 均匀分配
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df_b1 = compute_baseline_uniform(df)
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metrics_b1 = compute_metrics(df_b1, 'Baseline 1: Uniform')
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print(f"\n 基线1 (均匀分配, k={df_b1['k'].iloc[0]}~{df_b1['k'].max()}):")
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for key, value in metrics_b1.items():
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if key != 'method':
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print(f" {key}: {value:.4f}")
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# 基线2: 2019年缩放
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df_b2 = compute_baseline_2019_scaled(df)
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metrics_b2 = compute_metrics(df_b2, 'Baseline 2: 2019 Scaled')
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print(f"\n 基线2 (2019年缩放):")
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for key, value in metrics_b2.items():
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if key != 'method':
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print(f" {key}: {value:.4f}")
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# 基线3: 按原始μ比例
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df_b3 = compute_baseline_mu_raw(df)
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metrics_b3 = compute_metrics(df_b3, 'Baseline 3: μ proportional (no correction)')
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print(f"\n 基线3 (按原始μ比例, 无截断修正):")
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for key, value in metrics_b3.items():
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if key != 'method':
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print(f" {key}: {value:.4f}")
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# 4. 汇总对比
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print(f"\n[4] 方案对比汇总")
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all_metrics = [metrics_recommended, metrics_b1, metrics_b2, metrics_b3]
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df_metrics = pd.DataFrame(all_metrics)
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# 计算相对于推荐方案的变化
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for col in ['E1_total_service', 'E2_quality_weighted']:
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base_val = metrics_recommended[col]
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df_metrics[f'{col}_pct'] = (df_metrics[col] / base_val - 1) * 100
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print("\n " + "-" * 90)
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print(f" {'方案':<45} {'E1':>12} {'E2':>12} {'F1(Gini)':>10} {'F2(min r)':>10} {'F3(CV)':>10}")
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print(" " + "-" * 90)
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for _, row in df_metrics.iterrows():
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print(f" {row['method']:<45} {row['E1_total_service']:>12.1f} {row['E2_quality_weighted']:>12.1f} {row['F1_gini']:>10.4f} {row['F2_min_satisfaction']:>10.2f} {row['F3_cv_satisfaction']:>10.4f}")
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print(" " + "-" * 90)
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# 5. 推荐方案优势分析
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print(f"\n[5] 推荐方案优势分析")
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print(f" 相对于均匀分配 (基线1):")
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print(f" - E1 提升: {(metrics_recommended['E1_total_service']/metrics_b1['E1_total_service']-1)*100:+.2f}%")
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print(f" - E2 提升: {(metrics_recommended['E2_quality_weighted']/metrics_b1['E2_quality_weighted']-1)*100:+.2f}%")
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print(f"\n 相对于2019缩放 (基线2):")
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print(f" - E1 变化: {(metrics_recommended['E1_total_service']/metrics_b2['E1_total_service']-1)*100:+.2f}%")
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print(f" - E2 变化: {(metrics_recommended['E2_quality_weighted']/metrics_b2['E2_quality_weighted']-1)*100:+.2f}%")
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print(f" - F1(Gini)变化: {(metrics_recommended['F1_gini']-metrics_b2['F1_gini']):+.4f}")
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# 6. 保存输出
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print(f"\n[6] 保存输出: {OUTPUT_PATH}")
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with pd.ExcelWriter(OUTPUT_PATH, engine='openpyxl') as writer:
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# Sheet 1: 指标汇总
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df_metrics.to_excel(writer, sheet_name='metrics_summary', index=False)
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# Sheet 2: 站点级详情 (推荐方案)
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df_detail = df[['site_id', 'site_name', 'mu', 'mu_tilde', 'k', 'annual_service', 'r']].copy()
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df_detail['quality_factor'] = df['mu'].apply(quality_discount)
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df_detail['service_quality_weighted'] = df_detail['k'] * df_detail['mu'] * df_detail['quality_factor']
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df_detail.to_excel(writer, sheet_name='site_details', index=False)
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# Sheet 3: 参数记录
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params = pd.DataFrame([
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{'parameter': 'C_BAR (quality threshold)', 'value': C_BAR},
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{'parameter': 'N_TOTAL', 'value': 730},
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{'parameter': 'n_sites', 'value': len(df)},
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])
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params.to_excel(writer, sheet_name='parameters', index=False)
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print(f" 已保存3个工作表: metrics_summary, site_details, parameters")
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print("\n" + "=" * 60)
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print("Step 04 完成")
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print("=" * 60)
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return df_metrics
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if __name__ == "__main__":
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main()
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