docs(10_Wiki): 위키 전체 재구성 — Topic_* 폴더를 4개 카테고리로 통합 + 대규모 중복 제거

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+---
+id: wiki-2026-0508-replenishment
+title: Replenishment
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [Inventory Replenishment, Stock Replenishment, 재고보충]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [supply-chain, inventory, operations, forecasting, optimization]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: Python
+  framework: pandas/scipy/forecasting
+---
+
+# Replenishment
+
+## 매 한 줄
+> **"매 right item, right quantity, right time."**. Replenishment 매 inventory 가 demand 의 동안 stockout 의 X 의 process 의 maintaining. 1934 Wilson EOQ 부터 modern AI-driven probabilistic forecasting (Amazon, Walmart 의 LSTM/Transformer demand models) 까지 evolved.
+
+## 매 핵심
+
+### 매 핵심 levers
+- **Reorder Point (ROP)**: trigger threshold = `lead_time_demand + safety_stock`.
+- **Order Quantity**: how much (EOQ, min-max, fixed).
+- **Review period**: continuous (Q-system) 의 X periodic (P-system).
+- **Safety Stock**: buffer 의 demand/lead-time variability 의.
+
+### 매 modern signals
+- Probabilistic demand forecast (quantiles, 의 X point estimate).
+- Lead time variance (supplier reliability score).
+- Cross-location pooling (omnichannel inventory).
+- Substitution + promotion lift modeling.
+
+### 매 응용
+1. Retail (Walmart, Costco 의 daily auto-replenishment).
+2. E-commerce FBA (Amazon 의 fulfillment center distribution).
+3. Manufacturing MRP (BOM-driven component replenishment).
+4. Healthcare (vaccine, drug 의 cold-chain replenishment).
+
+## 💻 패턴
+
+### EOQ (Economic Order Quantity)
+```python
+import math
+
+def eoq(annual_demand: float, order_cost: float, holding_cost_per_unit: float) -> float:
+    """Wilson formula. Min total cost = order + holding."""
+    return math.sqrt(2 * annual_demand * order_cost / holding_cost_per_unit)
+
+# Example: 10K units/yr, $50/order, $2/unit/yr holding
+print(eoq(10_000, 50, 2))  # 707 units per order
+```
+
+### Reorder Point with Safety Stock
+```python
+from scipy.stats import norm
+
+def reorder_point(daily_demand_mean, daily_demand_std,
+                  lead_time_days, service_level=0.95):
+    z = norm.ppf(service_level)
+    lead_time_demand = daily_demand_mean * lead_time_days
+    safety_stock = z * daily_demand_std * math.sqrt(lead_time_days)
+    return lead_time_demand + safety_stock, safety_stock
+```
+
+### Min-Max (s, S) Policy
+```python
+def min_max_order(on_hand: int, on_order: int, s: int, S: int) -> int:
+    """매 inventory_position <= s 일 때 S 까지 order."""
+    inv_pos = on_hand + on_order
+    return max(0, S - inv_pos) if inv_pos <= s else 0
+```
+
+### Probabilistic Forecast → Newsvendor
+```python
+import numpy as np
+
+def newsvendor_quantile(unit_cost, sale_price, salvage=0):
+    """Critical ratio = (p - c) / (p - s)."""
+    return (sale_price - unit_cost) / (sale_price - salvage)
+
+def order_qty_from_forecast(demand_samples: np.ndarray, critical_ratio: float):
+    return float(np.quantile(demand_samples, critical_ratio))
+
+# 1000 Monte Carlo demand samples → optimal order
+samples = np.random.gamma(shape=4, scale=25, size=1000)
+cr = newsvendor_quantile(unit_cost=10, sale_price=25, salvage=3)
+print(order_qty_from_forecast(samples, cr))
+```
+
+### LSTM Demand Forecast (modern)
+```python
+import torch.nn as nn
+
+class DemandLSTM(nn.Module):
+    def __init__(self, n_features=8, hidden=64):
+        super().__init__()
+        self.lstm = nn.LSTM(n_features, hidden, num_layers=2,
+                            dropout=0.2, batch_first=True)
+        self.head = nn.Linear(hidden, 3)  # P10, P50, P90 quantiles
+
+    def forward(self, x):
+        out, _ = self.lstm(x)
+        return self.head(out[:, -1])
+```
+
+### Multi-Echelon Allocation
+```python
+def fair_share_allocation(forecasts: dict, total_supply: float) -> dict:
+    """Allocate constrained supply across stores proportional to forecast."""
+    total_demand = sum(forecasts.values())
+    if total_supply >= total_demand:
+        return forecasts.copy()
+    ratio = total_supply / total_demand
+    return {loc: f * ratio for loc, f in forecasts.items()}
+```
+
+### KPI Dashboard
+```python
+def replenishment_kpis(history: list[dict]) -> dict:
+    stockouts = sum(1 for d in history if d["on_hand"] == 0)
+    fill_rate = sum(d["fulfilled"] for d in history) / sum(d["demanded"] for d in history)
+    avg_inv = sum(d["on_hand"] for d in history) / len(history)
+    return {
+        "service_level": 1 - stockouts / len(history),
+        "fill_rate": fill_rate,
+        "avg_inventory": avg_inv,
+        "inventory_turns": sum(d["demanded"] for d in history) / avg_inv,
+    }
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Stable demand, known lead time | EOQ + ROP |
+| Highly variable demand | Probabilistic forecast + newsvendor |
+| Many SKUs, low value | Min-Max (s, S) |
+| Perishable / fashion | Newsvendor (single-period) |
+| Multi-location, constrained supply | Fair-share / DRP |
+| Modern e-commerce scale | ML demand model + RL ordering policy |
+
+**기본값**: Probabilistic LSTM forecast → newsvendor quantile order. 매 P50 forecast + ROP 의 단순 baseline 의 X.
+
+## 🔗 Graph
+- 부모: [[Supply Chain Management]] · [[Operations Research]]
+- Adjacent: [[Reinforcement Learning]] · [[MRP]]
+
+## 🤖 LLM 활용
+**언제**: SKU master data 의 cleansing, supplier email parsing, anomaly explanation, what-if scenario 의 narrative.
+**언제 X**: 매 actual demand forecasting 의 LLM 의 X — purpose-built time-series models (Prophet, NeuralForecast, Chronos) 의 use.
+
+## ❌ 안티패턴
+- **Point forecast only**: P50 만 사용 의 X — quantiles 의 사용 의 service level tuning 의 가능.
+- **Static safety stock**: lead time 의 variance 의 ignore 의 X.
+- **Local optimization**: 각 store 의 independent ordering — pooling 의 lost.
+- **Bullwhip ignored**: downstream order 의 upstream 의 amplification 의 monitor 의 필요.
+- **Excel-only**: 1000+ SKU 의 manual review 의 scale 의 X.
+
+## 🧪 검증 / 중복
+- Verified (Silver/Pyke "Inventory Management" textbook, AWS Forecast docs).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — replenishment policy + ML forecasting patterns |