mcm-mfp/kmin_effectiveness.py

"""
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
import os

try:
    import matplotlib

    # 允许在无GUI环境生成图片
    matplotlib.use("Agg")
    import matplotlib.pyplot as plt

    _HAS_MPL = True
except ModuleNotFoundError:
    plt = None
    _HAS_MPL = False

# 参数
C_OPT = 250
N_TOTAL = 730
ALPHA = 0.6
BETA = 0.2
N_SIMS = 2000
RANDOM_SEED = 606
OUTPUT_DIR = "data"


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():
    """加载数据"""
    df = pd.read_excel('prob/MFP Regular Sites 2019.xlsx')
    df = df.drop(columns=['Unnamed: 10', 'Demand per Visit == the number of clients serviced on that visit'])
    df['TotalDemand'] = df['Average Demand per Visit'] * df['Number of Visits in 2019']
    return df.sort_values('TotalDemand').reset_index(drop=True)


def allocate_visits(df, k_min_real, n_total, c_opt):
    """
    根据实数k_min分配访问次数

    k_min=2.7: floor=2, ceil=3, 70%站点得2次, 30%站点得3次
    低需求站点优先获得较低的k_min（已按TotalDemand排序）
    """
    df = df.copy()
    n = len(df)

    k_floor = int(np.floor(k_min_real))
    k_ceil = int(np.ceil(k_min_real))
    frac = k_min_real - k_floor  # 获得ceil的比例

    # 分配最低次数：低需求站点得floor，高需求站点得ceil
    n_ceil = int(round(n * frac))
    n_floor = n - n_ceil

    k_base = np.array([k_floor] * n_floor + [k_ceil] * n_ceil)
    df['K_base'] = k_base

    # 计算剩余运力
    n_reserved = k_base.sum()
    n_free = n_total - n_reserved

    if n_free < 0:
        return None

    # 按需求权重分配剩余运力
    df['Weight'] = df['TotalDemand'] / df['TotalDemand'].sum()
    df['AllocatedVisits'] = (k_base + n_free * df['Weight'].values).round().astype(int)
    df['AllocatedVisits'] = np.maximum(df['AllocatedVisits'], k_base)

    # 调整总数
    diff = n_total - df['AllocatedVisits'].sum()
    if diff != 0:
        sorted_idx = df['Weight'].sort_values(ascending=(diff < 0)).index.tolist()
        for idx in sorted_idx[:abs(diff)]:
            df.loc[idx, 'AllocatedVisits'] += int(np.sign(diff))

    return df


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

    method = (method or "mc").lower()
    if method not in {"mc", "analytic"}:
        raise ValueError("method must be 'mc' or 'analytic'")

    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

        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)

        base = annual_eff / np.maximum(D, 1)
        score = np.clip(base - alpha * unmet - beta * waste, 0, 1)

        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': 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': 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),
    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, 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)


def plot_results(results):
    """绘制k_min-有效性曲线"""
    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(4, 2, figsize=(12, 13))

    # 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(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')
    ax.legend()
    ax.grid(True, alpha=0.3)

    # 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(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')
    ax.grid(True, alpha=0.3)

    # 3. 总服务客户数
    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(selected_k, color='r', ls='--')
    ax.set_xlabel('k_min')
    ax.set_ylabel('Served Families (×1000)')
    ax.set_title('Total Served vs k_min')
    ax.legend()
    ax.grid(True, alpha=0.3)

    # 4. 最小有效性
    ax = axes[1, 1]
    ax.plot(results['k_min'], results['min_eff'], 'g-', lw=2)
    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')
    ax.grid(True, alpha=0.3)

    # 5. 未满足需求 vs 浪费
    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(selected_k, color='gray', ls='--')
    ax.set_xlabel('k_min')
    ax.set_ylabel('Families (×1000)')
    ax.set_title('Unmet Demand vs Wasted Capacity')
    ax.legend()
    ax.grid(True, alpha=0.3)

    # 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(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()
    os.makedirs(OUTPUT_DIR, exist_ok=True)
    plt.savefig(os.path.join(OUTPUT_DIR, 'kmin_effectiveness.png'), dpi=150)
    plt.close(fig)

    return selected_k, selected_eff


def main():
    # 1. 加载数据
    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]...")
    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()
    best_k = results.loc[best_idx, 'k_min']
    best_eff = results.loc[best_idx, 'effectiveness']
    if _HAS_MPL:
        plot_results(results)
    else:
        print("\n未检测到 matplotlib，跳过绘图（仍会保存CSV结果）。")

    # 4. 输出最优结果
    print(f"\n最优 k_min = {best_k:.1f}")
    print(f"最优有效性 = {best_eff:.4f}")

    # 5. 生成最优方案
    df_opt = allocate_visits(df, best_k, N_TOTAL, C_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})")
    print(f"  总服务: {metrics['total_served']:,.0f} / {metrics['total_demand']:,.0f} ({metrics['serve_ratio']:.1%})")
    print(f"  未满足: {metrics['total_unmet']:,.0f} 家庭次")
    print(f"  浪费: {metrics['total_waste']:,.0f} 家庭次")
    print(f"  访问次数: [{df_opt['AllocatedVisits'].min()}, {df_opt['AllocatedVisits'].max()}]")

    # 6. 保存
    os.makedirs(OUTPUT_DIR, exist_ok=True)
    results.to_csv(os.path.join(OUTPUT_DIR, 'kmin_effectiveness_data.csv'), index=False)
    sites_out.to_csv(os.path.join(OUTPUT_DIR, "kmin_effectiveness_sites.csv"), index=False)
    print("\n已保存到 data/: kmin_effectiveness.png, kmin_effectiveness_data.csv, kmin_effectiveness_sites.csv")


if __name__ == '__main__':
    main()