264 lines
8.3 KiB
Python
264 lines
8.3 KiB
Python
"""
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K_min-有效性分析
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k_min为实数：如2.7表示70%站点最低2次，30%站点最低3次
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"""
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import numpy as np
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import pandas as pd
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try:
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import matplotlib
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# 允许在无GUI环境生成图片
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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_HAS_MPL = True
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except ModuleNotFoundError:
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plt = None
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_HAS_MPL = False
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# 参数
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C_OPT = 250
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N_TOTAL = 722
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ALPHA = 0.4
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BETA = 0.2
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def load_data():
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"""加载数据"""
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df = pd.read_excel('prob/MFP Regular Sites 2019.xlsx')
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df = df.drop(columns=['Unnamed: 10', 'Demand per Visit == the number of clients serviced on that visit'])
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df['TotalDemand'] = df['Average Demand per Visit'] * df['Number of Visits in 2019']
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return df.sort_values('TotalDemand').reset_index(drop=True)
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def allocate_visits(df, k_min_real, n_total, c_opt):
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"""
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根据实数k_min分配访问次数
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k_min=2.7: floor=2, ceil=3, 70%站点得2次, 30%站点得3次
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低需求站点优先获得较低的k_min（已按TotalDemand排序）
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"""
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df = df.copy()
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n = len(df)
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k_floor = int(np.floor(k_min_real))
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k_ceil = int(np.ceil(k_min_real))
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frac = k_min_real - k_floor # 获得ceil的比例
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# 分配最低次数：低需求站点得floor，高需求站点得ceil
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n_ceil = int(round(n * frac))
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n_floor = n - n_ceil
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k_base = np.array([k_floor] * n_floor + [k_ceil] * n_ceil)
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df['K_base'] = k_base
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# 计算剩余运力
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n_reserved = k_base.sum()
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n_free = n_total - n_reserved
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if n_free < 0:
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return None
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# 按需求权重分配剩余运力
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df['Weight'] = df['TotalDemand'] / df['TotalDemand'].sum()
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df['AllocatedVisits'] = (k_base + n_free * df['Weight'].values).round().astype(int)
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df['AllocatedVisits'] = np.maximum(df['AllocatedVisits'], k_base)
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# 调整总数
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diff = n_total - df['AllocatedVisits'].sum()
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if diff != 0:
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sorted_idx = df['Weight'].sort_values(ascending=(diff < 0)).index.tolist()
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for idx in sorted_idx[:abs(diff)]:
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df.loc[idx, 'AllocatedVisits'] += int(np.sign(diff))
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return df
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def calc_effectiveness(df, c_opt=C_OPT, alpha=ALPHA, beta=BETA):
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"""计算有效性指标"""
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d = df['Average Demand per Visit'].values
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k = df['AllocatedVisits'].values
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D = df['TotalDemand'].values
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# 截断：单次有效服务 = min(需求, 容量)
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eff_per_visit = np.minimum(d, c_opt)
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annual_eff = k * eff_per_visit
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# 缺货率、浪费率
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unmet = np.maximum(0, D - annual_eff) / np.maximum(D, 1)
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waste = np.maximum(0, k * c_opt - D) / np.maximum(k * c_opt, 1)
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# 有效性得分
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base = annual_eff / np.maximum(D, 1)
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score = np.clip(base - alpha * unmet - beta * waste, 0, 1)
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n = score.size
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bottom_n = max(1, int(np.ceil(n * 0.10)))
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bottom10_mean = float(np.sort(score)[:bottom_n].mean())
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# 总服务客户数 = Σ min(供给能力, 需求)
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total_served = np.minimum(k * c_opt, D).sum()
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total_demand = D.sum()
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return {
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'mean': score.mean(),
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'min': score.min(),
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'bottom10_mean': bottom10_mean,
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'std': score.std(),
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'total_unmet': (D - annual_eff).clip(min=0).sum(),
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'total_waste': (k * c_opt - D).clip(min=0).sum(),
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'total_served': total_served,
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'total_demand': total_demand,
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'serve_ratio': total_served / total_demand
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}
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def analyze_kmin_range(df, k_range=np.arange(1.0, 10.1, 0.1)):
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"""扫描k_min范围，计算有效性"""
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results = []
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for k_min in k_range:
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df_alloc = allocate_visits(df, k_min, N_TOTAL, C_OPT)
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if df_alloc is None:
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continue
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metrics = calc_effectiveness(df_alloc)
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results.append({
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'k_min': k_min,
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'effectiveness': metrics['mean'],
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'min_eff': metrics['min'],
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'bottom10_eff': metrics['bottom10_mean'],
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'std_eff': metrics['std'],
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'unmet': metrics['total_unmet'],
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'waste': metrics['total_waste'],
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'total_served': metrics['total_served'],
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'total_demand': metrics['total_demand'],
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'serve_ratio': metrics['serve_ratio']
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})
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return pd.DataFrame(results)
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def plot_results(results):
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"""绘制k_min-有效性曲线"""
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if not _HAS_MPL:
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raise RuntimeError("缺少依赖: matplotlib（无法绘图）。请先安装 matplotlib 再运行绘图部分。")
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fig, axes = plt.subplots(3, 2, figsize=(12, 10))
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# 找最优点
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best_idx = results['effectiveness'].idxmax()
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best_k = results.loc[best_idx, 'k_min']
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best_eff = results.loc[best_idx, 'effectiveness']
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# 1. 有效性均值
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ax = axes[0, 0]
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ax.plot(results['k_min'], results['effectiveness'], 'b-', lw=2)
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ax.axvline(best_k, color='r', ls='--', label=f'Best k_min={best_k:.1f}')
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ax.scatter([best_k], [best_eff], c='r', s=100, zorder=5)
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ax.set_xlabel('k_min')
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ax.set_ylabel('Mean Effectiveness')
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ax.set_title('Mean Effectiveness vs k_min')
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ax.legend()
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ax.grid(True, alpha=0.3)
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# 2. 最低10%有效性均值
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ax = axes[0, 1]
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ax.plot(results['k_min'], results['bottom10_eff'], 'm-', lw=2)
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ax.axvline(best_k, color='r', ls='--')
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ax.set_xlabel('k_min')
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ax.set_ylabel('Bottom 10% Mean Effectiveness')
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ax.set_title('Bottom 10% Mean Effectiveness vs k_min')
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ax.grid(True, alpha=0.3)
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# 3. 总服务客户数
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ax = axes[1, 0]
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ax.plot(results['k_min'], results['total_served'] / 1000, 'c-', lw=2)
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ax.axhline(results['total_demand'].iloc[0] / 1000, color='gray', ls=':', label='Total Demand')
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ax.axvline(best_k, color='r', ls='--')
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ax.set_xlabel('k_min')
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ax.set_ylabel('Served Families (×1000)')
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ax.set_title('Total Served vs k_min')
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ax.legend()
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ax.grid(True, alpha=0.3)
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# 4. 最小有效性
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ax = axes[1, 1]
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ax.plot(results['k_min'], results['min_eff'], 'g-', lw=2)
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ax.axvline(best_k, color='r', ls='--')
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ax.set_xlabel('k_min')
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ax.set_ylabel('Min Effectiveness')
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ax.set_title('Worst Site Effectiveness vs k_min')
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ax.grid(True, alpha=0.3)
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# 5. 未满足需求 vs 浪费
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ax = axes[2, 0]
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ax.plot(results['k_min'], results['unmet'] / 1000, 'r-', lw=2, label='Unmet')
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ax.plot(results['k_min'], results['waste'] / 1000, 'b-', lw=2, label='Waste')
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ax.axvline(best_k, color='gray', ls='--')
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ax.set_xlabel('k_min')
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ax.set_ylabel('Families (×1000)')
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ax.set_title('Unmet Demand vs Wasted Capacity')
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ax.legend()
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ax.grid(True, alpha=0.3)
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# 6. 有效性标准差
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ax = axes[2, 1]
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ax.plot(results['k_min'], results['std_eff'], color='tab:orange', lw=2)
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ax.axvline(best_k, color='gray', ls='--')
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ax.set_xlabel('k_min')
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ax.set_ylabel('Std Effectiveness')
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ax.set_title('Effectiveness Std vs k_min')
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('kmin_effectiveness.png', dpi=150)
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plt.close(fig)
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return best_k, best_eff
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def main():
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# 1. 加载数据
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df = load_data()
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print(f"站点数: {len(df)}, 总运力: {N_TOTAL}")
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print(f"总需求: {df['TotalDemand'].sum():,.0f} 家庭次")
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# 2. 扫描k_min
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print("\n扫描 k_min ∈ [1.0, 10.0]...")
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results = analyze_kmin_range(df)
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# 3. 绘图
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best_idx = results['effectiveness'].idxmax()
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best_k = results.loc[best_idx, 'k_min']
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best_eff = results.loc[best_idx, 'effectiveness']
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if _HAS_MPL:
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plot_results(results)
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else:
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print("\n未检测到 matplotlib，跳过绘图（仍会保存CSV结果）。")
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# 4. 输出最优结果
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print(f"\n最优 k_min = {best_k:.1f}")
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print(f"最优有效性 = {best_eff:.4f}")
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# 5. 生成最优方案
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df_opt = allocate_visits(df, best_k, N_TOTAL, C_OPT)
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metrics = calc_effectiveness(df_opt)
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print(f"\n最优方案统计:")
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print(f" 有效性: {metrics['mean']:.4f} (min={metrics['min']:.4f})")
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print(f" 总服务: {metrics['total_served']:,.0f} / {metrics['total_demand']:,.0f} ({metrics['serve_ratio']:.1%})")
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print(f" 未满足: {metrics['total_unmet']:,.0f} 家庭次")
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print(f" 浪费: {metrics['total_waste']:,.0f} 家庭次")
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print(f" 访问次数: [{df_opt['AllocatedVisits'].min()}, {df_opt['AllocatedVisits'].max()}]")
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# 6. 保存
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results.to_csv('kmin_effectiveness_data.csv', index=False)
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print("\n已保存: kmin_effectiveness.png, kmin_effectiveness_data.csv")
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if __name__ == '__main__':
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main()
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