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task3/03_allocation.py
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task3/03_allocation.py
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"""
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Task 3 - Step 3: 第一站点最优分配计算
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=====================================
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输入: 02_pairing.xlsx (选中的配对列表)
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输出: 03_allocation.xlsx (含最优分配量q*的配对列表)
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最优分配公式:
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q* = (σ_j * μ_i + σ_i * (Q - μ_j)) / (σ_i + σ_j)
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鲁棒性约束:
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q_final = clip(q*, μ_i - σ_i, Q - μ_j + σ_j)
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物理意义:
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- 波动大的站点需要更多"缓冲"
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- 当σ_j >> σ_i时，q* → μ_i（精确分配给站点i）
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- 当σ_i >> σ_j时，q* → Q - μ_j（为站点j预留更多）
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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 scipy import stats
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# ============================================
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# 参数设置
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# ============================================
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INPUT_FILE = '02_pairing.xlsx'
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OUTPUT_FILE = '03_allocation.xlsx'
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Q = 400 # 卡车容量
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K_ROBUST = 1 # 鲁棒性水平 (84%保护)
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# ============================================
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# 读取数据
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# ============================================
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print("=" * 60)
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print("Task 3 - Step 3: 第一站点最优分配计算")
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print("=" * 60)
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# 读取选中的配对
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df_pairs = pd.read_excel(INPUT_FILE, sheet_name='selected_pairs')
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print(f"\n读取配对数据: {len(df_pairs)} 对")
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# ============================================
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# 计算最优分配
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# ============================================
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print(f"\n" + "-" * 40)
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print("计算最优分配 q*")
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print("-" * 40)
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def optimal_allocation(mu_i, sigma_i, mu_j, sigma_j, Q=400):
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"""
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计算双站点访问时第一站点的最优分配量
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公式: q* = (σ_j * μ_i + σ_i * (Q - μ_j)) / (σ_i + σ_j)
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"""
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if sigma_i + sigma_j == 0:
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# 边界情况：两站点都无波动
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return mu_i
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q_star = (sigma_j * mu_i + sigma_i * (Q - mu_j)) / (sigma_i + sigma_j)
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return q_star
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def robust_allocation(q_star, mu_i, sigma_i, mu_j, sigma_j, Q=400, k=1):
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"""
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应用鲁棒性约束
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约束: μ_i - k*σ_i ≤ q ≤ Q - μ_j + k*σ_j
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"""
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q_lower = max(0, mu_i - k * sigma_i)
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q_upper = min(Q, Q - mu_j + k * sigma_j)
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# 确保上下界合理
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if q_lower > q_upper:
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# 如果约束冲突，取中点
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q_final = (q_lower + q_upper) / 2
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else:
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q_final = np.clip(q_star, q_lower, q_upper)
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return q_final, q_lower, q_upper
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def expected_service(q, mu, sigma):
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"""
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计算截断期望 E[min(D, q)]
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E[min(D, q)] = μ * Φ(z) - σ * φ(z) + q * (1 - Φ(z))
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where z = (q - μ) / σ
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当q > μ时，大部分时候D < q，期望接近μ
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当q < μ时，经常D > q，期望接近q但略低
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"""
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if sigma == 0:
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return min(mu, q)
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z = (q - mu) / sigma
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phi_z = stats.norm.pdf(z)
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Phi_z = stats.norm.cdf(z)
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return mu * Phi_z - sigma * phi_z + q * (1 - Phi_z)
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# 计算每个配对的分配
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results = []
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for idx, row in df_pairs.iterrows():
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mu_i = row['mu_i']
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sigma_i = row['sigma_i']
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mu_j = row['mu_j']
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sigma_j = row['sigma_j']
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# 计算最优分配
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q_star = optimal_allocation(mu_i, sigma_i, mu_j, sigma_j, Q)
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# 应用鲁棒性约束
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q_final, q_lower, q_upper = robust_allocation(
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q_star, mu_i, sigma_i, mu_j, sigma_j, Q, K_ROBUST
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)
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# 计算期望服务量
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E_Si = expected_service(q_final, mu_i, sigma_i)
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E_Sj = expected_service(Q - q_final, mu_j, sigma_j)
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E_total = E_Si + E_Sj
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# 计算分配比例
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alloc_ratio = q_final / Q if Q > 0 else 0
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results.append({
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**row.to_dict(),
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'q_star': q_star,
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'q_lower': q_lower,
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'q_upper': q_upper,
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'q_final': q_final,
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'q_ratio': alloc_ratio,
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'E_Si': E_Si,
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'E_Sj': E_Sj,
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'E_total': E_total,
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'efficiency': E_total / (mu_i + mu_j) if (mu_i + mu_j) > 0 else 0
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})
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df_allocation = pd.DataFrame(results)
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# ============================================
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# 统计信息
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# ============================================
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print(f"\n分配统计:")
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print(f" - q* 范围: [{df_allocation['q_star'].min():.1f}, {df_allocation['q_star'].max():.1f}]")
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print(f" - q_final 范围: [{df_allocation['q_final'].min():.1f}, {df_allocation['q_final'].max():.1f}]")
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print(f" - 分配比例范围: [{df_allocation['q_ratio'].min():.2%}, {df_allocation['q_ratio'].max():.2%}]")
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print(f" - 平均分配比例: {df_allocation['q_ratio'].mean():.2%}")
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print(f"\n期望服务量统计:")
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print(f" - E[S_i] 范围: [{df_allocation['E_Si'].min():.1f}, {df_allocation['E_Si'].max():.1f}]")
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print(f" - E[S_j] 范围: [{df_allocation['E_Sj'].min():.1f}, {df_allocation['E_Sj'].max():.1f}]")
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print(f" - E[total] 范围: [{df_allocation['E_total'].min():.1f}, {df_allocation['E_total'].max():.1f}]")
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print(f" - 平均效率: {df_allocation['efficiency'].mean():.2%}")
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# 检查是否有被约束裁剪的情况
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clipped_lower = (df_allocation['q_final'] <= df_allocation['q_lower'] + 0.01).sum()
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clipped_upper = (df_allocation['q_final'] >= df_allocation['q_upper'] - 0.01).sum()
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print(f"\n鲁棒性约束影响:")
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print(f" - 触及下界: {clipped_lower} 对")
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print(f" - 触及上界: {clipped_upper} 对")
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print(f" - 未被裁剪: {len(df_allocation) - clipped_lower - clipped_upper} 对")
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# ============================================
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# 显示关键配对的分配
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# ============================================
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print(f"\n" + "-" * 40)
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print("高价值配对的分配方案 (Top 10)")
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print("-" * 40)
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display_cols = ['site_i_name', 'site_j_name', 'mu_i', 'mu_j', 'q_final', 'E_Si', 'E_Sj', 'E_total']
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df_top = df_allocation.nlargest(10, 'value')[display_cols].copy()
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df_top['site_i_name'] = df_top['site_i_name'].str[:25]
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df_top['site_j_name'] = df_top['site_j_name'].str[:25]
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print(df_top.to_string(index=False))
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# ============================================
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# 保存结果
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# ============================================
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with pd.ExcelWriter(OUTPUT_FILE, engine='openpyxl') as writer:
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# Sheet 1: 完整分配结果
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df_allocation.to_excel(writer, sheet_name='allocation', index=False)
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# Sheet 2: 简化视图
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simple_cols = ['site_i_id', 'site_j_id', 'site_i_name', 'site_j_name',
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'mu_i', 'mu_j', 'sigma_i', 'sigma_j', 'k_i', 'k_j',
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'q_final', 'E_Si', 'E_Sj', 'E_total', 'value']
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df_allocation[simple_cols].to_excel(writer, sheet_name='allocation_simple', index=False)
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# Sheet 3: 参数记录
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params = pd.DataFrame({
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'parameter': ['Q', 'K_ROBUST'],
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'value': [Q, K_ROBUST],
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'description': ['卡车容量', '鲁棒性水平(k*σ)']
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})
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params.to_excel(writer, sheet_name='parameters', index=False)
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# Sheet 4: 汇总统计
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summary = pd.DataFrame({
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'metric': ['total_pairs', 'avg_q_ratio', 'avg_E_total', 'avg_efficiency',
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'min_E_total', 'max_E_total', 'clipped_lower', 'clipped_upper'],
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'value': [len(df_allocation),
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df_allocation['q_ratio'].mean(),
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df_allocation['E_total'].mean(),
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df_allocation['efficiency'].mean(),
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df_allocation['E_total'].min(),
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df_allocation['E_total'].max(),
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clipped_lower, clipped_upper]
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})
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summary.to_excel(writer, sheet_name='summary', index=False)
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print(f"\n结果已保存至: {OUTPUT_FILE}")
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print(" - Sheet 'allocation': 完整分配结果")
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print(" - Sheet 'allocation_simple': 简化视图")
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print(" - Sheet 'parameters': 参数记录")
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print(" - Sheet 'summary': 汇总统计")
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print("\n" + "=" * 60)
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