P1: fix kmin.py

.gitignore

@@ -1,3 +1,4 @@
+__pycache__/
 latex-template/
 .DS_Store
 ~$*.*

kmin_effectiveness.py

@@ -1,10 +1,13 @@
 """
 K_min-有效性分析
 k_min为实数：如2.7表示70%站点最低2次，30%站点最低3次
+
+有效性计算支持引入需求标准差（正态分布），并通过 Monte Carlo 多次模拟求均值。
 """
 
 import numpy as np
 import pandas as pd
+import math
 
 try:
     import matplotlib
@@ -21,8 +24,82 @@ except ModuleNotFoundError:
 # 参数
 C_OPT = 250
 N_TOTAL = 722
-ALPHA = 0.4
+ALPHA = 0.5
 BETA = 0.2
+N_SIMS = 2000
+RANDOM_SEED = 42
+
+
+def gini_coefficient(values):
+    """
+    计算基尼系数（0=完全均等，1=完全不均等）
+    约定：values 非负；若总和为0，则返回0。
+    """
+    x = np.asarray(values, dtype=float)
+    x = x[np.isfinite(x)]
+    if x.size == 0:
+        return 0.0
+    x = np.clip(x, 0, None)
+    total = x.sum()
+    if total <= 0:
+        return 0.0
+
+    x_sorted = np.sort(x)
+    n = x_sorted.size
+    idx = np.arange(1, n + 1, dtype=float)
+    return float((2.0 * (idx * x_sorted).sum()) / (n * total) - (n + 1.0) / n)
+
+
+def _norm_pdf(z):
+    return np.exp(-0.5 * z * z) / np.sqrt(2.0 * np.pi)
+
+
+def _norm_cdf(z):
+    z = np.asarray(z, dtype=float)
+    erf_vec = np.vectorize(math.erf, otypes=[float])
+    return 0.5 * (1.0 + erf_vec(z / np.sqrt(2.0)))
+
+
+def expected_clipped_normal(mu, sigma, lower=0.0, upper=1.0):
+    """
+    X ~ Normal(mu, sigma^2). 返回 E[clip(X, lower, upper)].
+    - 支持 lower=0 用于避免负需求
+    - sigma<=0 时退化为 clip(mu, lower, upper)
+    """
+    mu = np.asarray(mu, dtype=float)
+    sigma = np.asarray(sigma, dtype=float)
+    lower = float(lower)
+    upper = float(upper)
+
+    if lower > upper:
+        raise ValueError("lower must be <= upper")
+
+    out = np.empty_like(mu, dtype=float)
+    mask = sigma > 0
+    out[~mask] = np.clip(mu[~mask], lower, upper)
+
+    if np.any(mask):
+        m = mu[mask]
+        s = sigma[mask]
+
+        z_u = (upper - m) / s
+        z_l = (lower - m) / s
+
+        Phi_u = _norm_cdf(z_u)
+        Phi_l = _norm_cdf(z_l)
+        phi_u = _norm_pdf(z_u)
+        phi_l = _norm_pdf(z_l)
+
+        # E[X 1_{X<=a}] = mu*Phi(z) - sigma*phi(z), z=(a-mu)/sigma
+        ex_le_u = m * Phi_u - s * phi_u
+        ex_le_l = m * Phi_l - s * phi_l
+
+        p_le_l = Phi_l
+        p_gt_u = 1.0 - Phi_u
+
+        out[mask] = lower * p_le_l + (ex_le_u - ex_le_l) + upper * p_gt_u
+
+    return out
 
 
 def load_data():
@@ -76,67 +153,148 @@ def allocate_visits(df, k_min_real, n_total, c_opt):
     return df
 
 
-def calc_effectiveness(df, c_opt=C_OPT, alpha=ALPHA, beta=BETA):
-    """计算有效性指标"""
+def calc_effectiveness(
+    df,
+    c_opt=C_OPT,
+    alpha=ALPHA,
+    beta=BETA,
+    method="mc",
+    n_sims=N_SIMS,
+    seed=RANDOM_SEED,
+):
+    """计算有效性指标（method='mc' 多次模拟取均值；method='analytic' 用闭式期望）"""
     d = df['Average Demand per Visit'].values
+    d_std = df.get('StDev(Demand per Visit)', pd.Series(0.0, index=df.index)).values
+    d_std = np.clip(d_std, 0, None)
     k = df['AllocatedVisits'].values
     D = df['TotalDemand'].values
 
-    # 截断：单次有效服务 = min(需求, 容量)
-    eff_per_visit = np.minimum(d, c_opt)
-    annual_eff = k * eff_per_visit
+    method = (method or "mc").lower()
+    if method not in {"mc", "analytic"}:
+        raise ValueError("method must be 'mc' or 'analytic'")
 
-    # 缺货率、浪费率
-    unmet = np.maximum(0, D - annual_eff) / np.maximum(D, 1)
-    waste = np.maximum(0, k * c_opt - D) / np.maximum(k * c_opt, 1)
+    if method == "analytic":
+        # 正态分布需求：单次期望有效服务 = E[min(max(N(d, std),0), 容量)]
+        eff_per_visit = expected_clipped_normal(d, d_std, lower=0.0, upper=float(c_opt))
+        annual_eff = k * eff_per_visit
 
-    # 有效性得分
-    base = annual_eff / np.maximum(D, 1)
-    score = np.clip(base - alpha * unmet - beta * waste, 0, 1)
+        unmet = np.maximum(0, D - annual_eff) / np.maximum(D, 1)
+        waste = np.maximum(0, k * c_opt - annual_eff) / np.maximum(k * c_opt, 1)
 
-    n = score.size
-    bottom_n = max(1, int(np.ceil(n * 0.10)))
-    bottom10_mean = float(np.sort(score)[:bottom_n].mean())
+        base = annual_eff / np.maximum(D, 1)
+        score = np.clip(base - alpha * unmet - beta * waste, 0, 1)
 
-    # 总服务客户数 = Σ min(供给能力, 需求)
-    total_served = np.minimum(k * c_opt, D).sum()
-    total_demand = D.sum()
+        n = score.size
+        bottom_n = max(1, int(np.ceil(n * 0.10)))
+
+        total_served = np.minimum(annual_eff, D).sum()
+        total_demand = D.sum()
+
+        return {
+            'mean': float(score.mean()),
+            'min': float(score.min()),
+            'bottom10_mean': float(np.sort(score)[:bottom_n].mean()),
+            'gini_eff': float(gini_coefficient(score)),
+            'std': float(score.std()),
+            'total_unmet': float((D - annual_eff).clip(min=0).sum()),
+            'total_waste': float((k * c_opt - annual_eff).clip(min=0).sum()),
+            'total_served': float(total_served),
+            'total_demand': float(total_demand),
+            'serve_ratio': float(total_served / total_demand) if total_demand > 0 else 0.0
+        }
+
+    # Monte Carlo：每次访问的需求 ~ Normal(mu, sigma)，重复 n_sims 次取均值
+    n_sims = int(n_sims)
+    if n_sims <= 0:
+        raise ValueError("n_sims must be > 0")
+
+    rng = np.random.default_rng(seed)
+    n_sites = len(df)
+    annual_eff_sims = np.zeros((n_sites, n_sims), dtype=float)
+
+    for i in range(n_sites):
+        k_i = int(k[i])
+        if k_i <= 0:
+            continue
+
+        mu_i = float(d[i])
+        sigma_i = float(d_std[i])
+        if sigma_i <= 0:
+            demand = np.full((n_sims, k_i), mu_i, dtype=float)
+        else:
+            demand = rng.normal(mu_i, sigma_i, size=(n_sims, k_i))
+        demand = np.clip(demand, 0, None)
+        annual_eff_sims[i, :] = np.minimum(demand, float(c_opt)).sum(axis=1)
+
+    D2 = D.reshape(-1, 1)
+    cap2 = (k * c_opt).reshape(-1, 1)
+
+    unmet = np.maximum(0, D2 - annual_eff_sims) / np.maximum(D2, 1)
+    waste = np.maximum(0, cap2 - annual_eff_sims) / np.maximum(cap2, 1)
+    base = annual_eff_sims / np.maximum(D2, 1)
+    score_sims = np.clip(base - alpha * unmet - beta * waste, 0, 1)
+
+    # 每个站点的期望得分（跨模拟平均）
+    avg_score = score_sims.mean(axis=1)
+    bottom_n = max(1, int(np.ceil(n_sites * 0.10)))
+
+    total_served_sims = np.minimum(annual_eff_sims, D2).sum(axis=0)
+    total_unmet_sims = np.maximum(0, D2 - annual_eff_sims).sum(axis=0)
+    total_waste_sims = np.maximum(0, cap2 - annual_eff_sims).sum(axis=0)
+    total_demand = float(D.sum())
+    total_served = float(total_served_sims.mean())
 
     return {
-        'mean': score.mean(),
-        'min': score.min(),
-        'bottom10_mean': bottom10_mean,
-        'std': score.std(),
-        'total_unmet': (D - annual_eff).clip(min=0).sum(),
-        'total_waste': (k * c_opt - D).clip(min=0).sum(),
+        'mean': float(avg_score.mean()),
+        'min': float(avg_score.min()),
+        'bottom10_mean': float(np.sort(avg_score)[:bottom_n].mean()),
+        'gini_eff': float(gini_coefficient(avg_score)),
+        'std': float(avg_score.std()),
+        'total_unmet': float(total_unmet_sims.mean()),
+        'total_waste': float(total_waste_sims.mean()),
         'total_served': total_served,
         'total_demand': total_demand,
-        'serve_ratio': total_served / total_demand
+        'serve_ratio': float(total_served / total_demand) if total_demand > 0 else 0.0
     }
 
 
-def analyze_kmin_range(df, k_range=np.arange(1.0, 10.1, 0.1)):
+def analyze_kmin_range(
+    df,
+    k_range=np.arange(1.0, 10.1, 0.1),
+    method="mc",
+    n_sims=N_SIMS,
+    seed=RANDOM_SEED,
+):
     """扫描k_min范围，计算有效性"""
     results = []
+    n_sites = len(df)
+    site_cols = [f"visits_{i+1:02d}" for i in range(n_sites)]
 
     for k_min in k_range:
         df_alloc = allocate_visits(df, k_min, N_TOTAL, C_OPT)
         if df_alloc is None:
             continue
 
-        metrics = calc_effectiveness(df_alloc)
-        results.append({
+        metrics = calc_effectiveness(df_alloc, method=method, n_sims=n_sims, seed=seed)
+        row = {
             'k_min': k_min,
             'effectiveness': metrics['mean'],
             'min_eff': metrics['min'],
             'bottom10_eff': metrics['bottom10_mean'],
+            'gini_eff': metrics['gini_eff'],
             'std_eff': metrics['std'],
             'unmet': metrics['total_unmet'],
             'waste': metrics['total_waste'],
             'total_served': metrics['total_served'],
             'total_demand': metrics['total_demand'],
             'serve_ratio': metrics['serve_ratio']
-        })
+        }
+
+        # 追加每个站点在该 k_min 下的访问次数（按 df 当前排序的站点顺序）
+        alloc = df_alloc["AllocatedVisits"].astype(int).tolist()
+        row.update({col: v for col, v in zip(site_cols, alloc)})
+
+        results.append(row)
 
     return pd.DataFrame(results)
 
@@ -146,18 +304,26 @@ def plot_results(results):
     if not _HAS_MPL:
         raise RuntimeError("缺少依赖: matplotlib（无法绘图）。请先安装 matplotlib 再运行绘图部分。")
 
-    fig, axes = plt.subplots(3, 2, figsize=(12, 10))
+    fig, axes = plt.subplots(4, 2, figsize=(12, 13))
 
-    # 找最优点
-    best_idx = results['effectiveness'].idxmax()
-    best_k = results.loc[best_idx, 'k_min']
-    best_eff = results.loc[best_idx, 'effectiveness']
+    # 红线选点：基尼系数第一次 < 0.2 的 k_min（若不存在则回退到均值有效性最优点）
+    gini_candidates = results.loc[results["gini_eff"] < 0.2, "k_min"]
+    if len(gini_candidates) > 0:
+        selected_k = float(gini_candidates.iloc[0])
+        selected_label = f'First Gini<0.2: k_min={selected_k:.1f}'
+    else:
+        best_idx = results['effectiveness'].idxmax()
+        selected_k = float(results.loc[best_idx, 'k_min'])
+        selected_label = f'Best mean eff: k_min={selected_k:.1f}'
+
+    selected_idx = (results["k_min"] - selected_k).abs().idxmin()
+    selected_eff = float(results.loc[selected_idx, "effectiveness"])
 
     # 1. 有效性均值
     ax = axes[0, 0]
     ax.plot(results['k_min'], results['effectiveness'], 'b-', lw=2)
-    ax.axvline(best_k, color='r', ls='--', label=f'Best k_min={best_k:.1f}')
-    ax.scatter([best_k], [best_eff], c='r', s=100, zorder=5)
+    ax.axvline(selected_k, color='r', ls='--', label=selected_label)
+    ax.scatter([selected_k], [selected_eff], c='r', s=100, zorder=5)
     ax.set_xlabel('k_min')
     ax.set_ylabel('Mean Effectiveness')
     ax.set_title('Mean Effectiveness vs k_min')
@@ -167,7 +333,7 @@ def plot_results(results):
     # 2. 最低10%有效性均值
     ax = axes[0, 1]
     ax.plot(results['k_min'], results['bottom10_eff'], 'm-', lw=2)
-    ax.axvline(best_k, color='r', ls='--')
+    ax.axvline(selected_k, color='r', ls='--')
     ax.set_xlabel('k_min')
     ax.set_ylabel('Bottom 10% Mean Effectiveness')
     ax.set_title('Bottom 10% Mean Effectiveness vs k_min')
@@ -177,7 +343,7 @@ def plot_results(results):
     ax = axes[1, 0]
     ax.plot(results['k_min'], results['total_served'] / 1000, 'c-', lw=2)
     ax.axhline(results['total_demand'].iloc[0] / 1000, color='gray', ls=':', label='Total Demand')
-    ax.axvline(best_k, color='r', ls='--')
+    ax.axvline(selected_k, color='r', ls='--')
     ax.set_xlabel('k_min')
     ax.set_ylabel('Served Families (×1000)')
     ax.set_title('Total Served vs k_min')
@@ -187,7 +353,7 @@ def plot_results(results):
     # 4. 最小有效性
     ax = axes[1, 1]
     ax.plot(results['k_min'], results['min_eff'], 'g-', lw=2)
-    ax.axvline(best_k, color='r', ls='--')
+    ax.axvline(selected_k, color='r', ls='--')
     ax.set_xlabel('k_min')
     ax.set_ylabel('Min Effectiveness')
     ax.set_title('Worst Site Effectiveness vs k_min')
@@ -197,7 +363,7 @@ def plot_results(results):
     ax = axes[2, 0]
     ax.plot(results['k_min'], results['unmet'] / 1000, 'r-', lw=2, label='Unmet')
     ax.plot(results['k_min'], results['waste'] / 1000, 'b-', lw=2, label='Waste')
-    ax.axvline(best_k, color='gray', ls='--')
+    ax.axvline(selected_k, color='gray', ls='--')
     ax.set_xlabel('k_min')
     ax.set_ylabel('Families (×1000)')
     ax.set_title('Unmet Demand vs Wasted Capacity')
@@ -207,17 +373,30 @@ def plot_results(results):
     # 6. 有效性标准差
     ax = axes[2, 1]
     ax.plot(results['k_min'], results['std_eff'], color='tab:orange', lw=2)
-    ax.axvline(best_k, color='gray', ls='--')
+    ax.axvline(selected_k, color='gray', ls='--')
     ax.set_xlabel('k_min')
     ax.set_ylabel('Std Effectiveness')
     ax.set_title('Effectiveness Std vs k_min')
     ax.grid(True, alpha=0.3)
 
+    # 7. 基尼系数
+    ax = axes[3, 0]
+    ax.plot(results['k_min'], results['gini_eff'], color='tab:purple', lw=2)
+    ax.axhline(0.2, color='gray', ls=':', lw=1)
+    ax.axvline(selected_k, color='r', ls='--')
+    ax.set_xlabel('k_min')
+    ax.set_ylabel('Gini Coefficient')
+    ax.set_title('Gini (Effectiveness) vs k_min')
+    ax.grid(True, alpha=0.3)
+
+    # 8. 空白占位（避免最后一格空图框太挤）
+    axes[3, 1].axis('off')
+
     plt.tight_layout()
     plt.savefig('kmin_effectiveness.png', dpi=150)
     plt.close(fig)
 
-    return best_k, best_eff
+    return selected_k, selected_eff
 
 
 def main():
@@ -225,10 +404,19 @@ def main():
     df = load_data()
     print(f"站点数: {len(df)}, 总运力: {N_TOTAL}")
     print(f"总需求: {df['TotalDemand'].sum():,.0f} 家庭次")
+    site_name_col = "Site Name" if "Site Name" in df.columns else None
+    sites_out = pd.DataFrame(
+        {
+            "site_idx": np.arange(1, len(df) + 1, dtype=int),
+            "site_name": df[site_name_col].astype(str).values if site_name_col else [f"Site_{i+1:02d}" for i in range(len(df))],
+            "total_demand": df["TotalDemand"].values,
+        }
+    )
 
     # 2. 扫描k_min
     print("\n扫描 k_min ∈ [1.0, 10.0]...")
-    results = analyze_kmin_range(df)
+    print(f"使用 Monte Carlo 平均：n_sims={N_SIMS}, seed={RANDOM_SEED}")
+    results = analyze_kmin_range(df, method="mc", n_sims=N_SIMS, seed=RANDOM_SEED)
 
     # 3. 绘图
     best_idx = results['effectiveness'].idxmax()
@@ -245,7 +433,7 @@ def main():
 
     # 5. 生成最优方案
     df_opt = allocate_visits(df, best_k, N_TOTAL, C_OPT)
-    metrics = calc_effectiveness(df_opt)
+    metrics = calc_effectiveness(df_opt, method="mc", n_sims=N_SIMS, seed=RANDOM_SEED)
 
     print(f"\n最优方案统计:")
     print(f"  有效性: {metrics['mean']:.4f} (min={metrics['min']:.4f})")
@@ -256,7 +444,8 @@ def main():
 
     # 6. 保存
     results.to_csv('kmin_effectiveness_data.csv', index=False)
-    print("\n已保存: kmin_effectiveness.png, kmin_effectiveness_data.csv")
+    sites_out.to_csv("kmin_effectiveness_sites.csv", index=False)
+    print("\n已保存: kmin_effectiveness.png, kmin_effectiveness_data.csv, kmin_effectiveness_sites.csv")
 
 
 if __name__ == '__main__':

kmin_effectiveness_data.csv

@@ -0,0 +1,92 @@
+k_min,effectiveness,min_eff,bottom10_eff,gini_eff,std_eff,unmet,waste,total_served,total_demand,serve_ratio,visits_01,visits_02,visits_03,visits_04,visits_05,visits_06,visits_07,visits_08,visits_09,visits_10,visits_11,visits_12,visits_13,visits_14,visits_15,visits_16,visits_17,visits_18,visits_19,visits_20,visits_21,visits_22,visits_23,visits_24,visits_25,visits_26,visits_27,visits_28,visits_29,visits_30,visits_31,visits_32,visits_33,visits_34,visits_35,visits_36,visits_37,visits_38,visits_39,visits_40,visits_41,visits_42,visits_43,visits_44,visits_45,visits_46,visits_47,visits_48,visits_49,visits_50,visits_51,visits_52,visits_53,visits_54,visits_55,visits_56,visits_57,visits_58,visits_59,visits_60,visits_61,visits_62,visits_63,visits_64,visits_65,visits_66,visits_67,visits_68,visits_69,visits_70
+1.0,0.6341145571330261,0.0,0.0,0.3576469174594097,0.44121099409856696,7211.9349775511755,52958.89819394406,95261.06502244883,102473.0,0.9296211199286528,1,1,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,5,6,6,6,7,8,8,9,9,10,10,10,11,11,11,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,20,20,21,21,23,25,29
+1.1,0.631881646766723,0.0,0.0,0.3595928073033041,0.44071458493703186,7339.685342065542,52748.84063760984,95133.31465793446,102473.0,0.9283744465169798,1,1,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,5,6,6,6,7,8,8,9,9,9,10,10,10,11,11,11,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,20,21,21,22,24,26,29
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kmin_effectiveness_sites.csv

@@ -0,0 +1,71 @@
+site_idx,site_name,total_demand
+1,MFP Senior - Woodsedge Apartments,172.0
+2,MFP Senior - Harry L Apartments,197.0
+3,MFP Senior - Cayuga Meadows,233.0
+4,MFP Senior - Wells Apartments,235.0
+5,MFP Senior - Lincoln Court,260.0
+6,MFP Senior - Park Terrace Congregate Apartments,268.0
+7,MFP Senior - Ellis Hollow,272.0
+8,MFP Senior - Jefferson Village,273.0
+9,MFP Senior - Springview Apartments,331.0
+10,MFP Senior - Addison Place Apartments,331.0
+11,MFP Senior - Conifer Village,338.0
+12,MFP Senior - Carpenter Apartments,342.0
+13,"MFP Senior - Elizabeth Square, Waverly",348.0
+14,MFP Senior - North Shore Towers,350.0
+15,MFP Senior - Village Square/Manor,411.0
+16,MFP Senior - Long Meadow Senior Housing,417.0
+17,MFP Senior - East Hill Senior Living,478.0
+18,"MFP Senior - Northern Broome Senior Center, Whitney Point",560.0
+19,MFP Senior - Metro Plaza Apartments,563.0
+20,MFP Senior - Bragg,602.0
+21,MFP Nichols-The Creamery,612.0
+22,MFP Senior - Corning Senior Center,675.0
+23,MFP Senior - Flannery,679.0
+24,MFP Senior - Titus Towers,728.0
+25,MFP Senior - Villa Serene,767.0000000000001
+26,MFP Senior - Dayspring,849.0
+27,MFP Schuyler Outreach,972.0
+28,MFP Troupsburg,1041.0
+29,MFP Senior - CFS Lakeview,1120.0
+30,MFP College Ithaca College,1245.0
+31,MFP Lamphear Court,1260.0
+32,MFP Bradford,1345.0
+33,MFP Danby,1442.0
+34,MFP Saint Mary Recreation Center,1483.0
+35,MFP College Corning Community College,1506.0
+36,MFP College TC3 -College,1569.0
+37,MFP Montour Falls-Schuyler County Human Services Complex,1643.0
+38,MFP Millport,1660.0
+39,MFP Beaver Dams,1707.0
+40,MFP Birnie Transportation Services,1707.0
+41,MFP Prattsburgh,1734.0
+42,MFP First Assembly Of God Church,1752.0
+43,MFP Canisteo,1770.0
+44,MFP Conklin- Maines Community Center,1838.0
+45,MFP Deposit,1879.0
+46,MFP Erin,1913.0
+47,MFP Lansing,1991.0
+48,MFP Salvation Army Ithaca,1993.0
+49,MFP Campbell,2022.0
+50,MFP Boys and Girls Club,2108.0
+51,MFP Woodhull,2112.0
+52,MFP Owego VFW,2115.0
+53,MFP Tuscarora,2119.0
+54,MFP Van Etten,2137.0
+55,MFP Wayland,2165.0
+56,MFP Reach for Christ Church Freeville,2200.0
+57,MFP American Legion - Binghamton,2202.0
+58,MFP Windsor,2210.0
+59,MFP Whitney Point,2228.0
+60,MFP Redeemer Lutheran Church,2306.0
+61,MFP Lindley,2329.0
+62,MFP Rehoboth Deliverance Ministry,2359.0
+63,MFP Colesville,2368.0
+64,MFP Richford,2925.0000000000005
+65,MFP Rathbone,2959.9999999999995
+66,MFP Bath,3074.0
+67,MFP The Love Church,3112.0
+68,MFP Endwell United Methodist Church,3423.0
+69,MFP Avoca,3775.0
+70,MFP Waverly,4363.0