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