Forecast-to-PL-Bridge — 需求预测误差的财务损失量化与成本优化

"""
Forecast-to-PL-Bridge — 需求预测误差财务损失量化
基于 Newsvendor 成本函数 (arXiv: 2603.16815)

依赖: numpy, scipy (标准科学计算库)
"""

from dataclasses import dataclass
import numpy as np
from scipy import stats


@dataclass
class CostParams:
    """成本参数"""
    holding_rate: float      # 年持货成本率（如 0.25 = 售价的 25%/年）
    stockout_rate: float     # 缺货惩罚率（如 0.40 = 售价的 40%）
    unit_price: float        # 产品售价（USD）
    review_period_days: int  # 补货周期（天）

    @property
    def h(self) -> float:
        """单位持货成本（每补货周期）"""
        return self.holding_rate * self.unit_price * self.review_period_days / 365

    @property
    def b(self) -> float:
        """单位缺货成本"""
        return self.stockout_rate * self.unit_price

    @property
    def critical_ratio(self) -> float:
        """临界比率（最优库存分位数）"""
        return self.b / (self.b + self.h)


def newsvendor_cost(demand_mean: float, demand_std: float,
                   order_qty: float, cost: CostParams) -> dict:
    """
    计算给定订货量的期望总成本

    Returns:
        dict: holding_cost, stockout_cost, total_cost, fill_rate
    """
    # 假设正态需求分布
    dist = stats.norm(loc=0, scale=1)  # 标准正态，z 已经标准化

    # 期望过剩库存 E[(Q-D)+] = (Q-μ)*Φ(z) + σ*φ(z)
    z = (order_qty - demand_mean) / demand_std
    expected_excess = (order_qty - demand_mean) * dist.cdf(z) + demand_std * dist.pdf(z)

    # 期望缺货量 E[(D-Q)+]
    expected_shortage = demand_mean - order_qty + expected_excess

    holding = cost.h * expected_excess
    stockout = cost.b * expected_shortage
    total = holding + stockout
    fill_rate = dist.cdf(order_qty)

    return {