Ecom Inventory Health

Inventory Health Analysis

Overview

Inventory health balances two risks: stockouts (lost sales, unhappy customers) and overstock (carrying costs, obsolescence). This skill provides tools to measure, classify, and optimize inventory levels.

Framework

IRON LAW: Not All SKUs Deserve Equal Attention

ABC classification shows that ~20% of SKUs drive ~80% of revenue.
Treat A-items (top 20% revenue) with tight control and frequent review.
C-items (bottom 50% revenue) get simple rules and less attention.
Equal treatment of all SKUs wastes resources on low-impact items.

Key Metrics

ABC Classification

Safety Stock Calculation

Safety Stock = Z × σ_d × √(Lead Time)

Where:
- Z = service level factor (1.65 for 95%, 2.33 for 99%)
- σ_d = standard deviation of daily demand
- Lead Time = supplier lead time in days

Reorder Point

Reorder Point = (Average Daily Demand × Lead Time) + Safety Stock

Diagnosis Steps

Phase 1: Overall Health Check

• Calculate turnover and DOI for total inventory
• Compare to industry benchmarks
• Identify trend: improving or deteriorating?

Phase 2: ABC Classification

• Rank all SKUs by revenue contribution
• Classify into A/B/C
• Check: are A-items well-stocked? Are C-items over-stocked?

Phase 3: Problem Identification

• Overstock: DOI > 90 days, dead stock > 10%, carrying costs rising
• Stockout: Fill rate < 95%, lost sales reports, customer complaints
• Imbalance: A-items understocked while C-items overstocked

Phase 4: Optimization

• Set safety stock by ABC class
• Implement reorder points for A-items
• Liquidate dead stock (discount, bundle, donate)
• Reduce lead times through supplier negotiation

Output Format

# Inventory Health Report: {Business}

## Summary
| Metric | Current | Target | Status |
|--------|---------|--------|--------|
| Turnover | {X}x | {X}x | 🟢/🟡/🔴 |
| DOI | {X} days | {X} days | 🟢/🟡/🔴 |
| Fill Rate | {X%} | >95% | 🟢/🟡/🔴 |
| Dead Stock | {X%} | <10% | 🟢/🟡/🔴 |

## ABC Distribution
| Class | SKUs | Revenue % | Avg DOI | Issue |
|-------|------|----------|---------|-------|
| A | {N} | {%} | {days} | {stockout risk?} |
| B | {N} | {%} | {days} | ... |
| C | {N} | {%} | {days} | {overstock?} |

## Top Issues
1. {issue with specific SKUs and data}

## Recommendations
1. {action with expected impact}

Gotchas

• Seasonal products need separate treatment: Swimsuits in January will show as "dead stock" but shouldn't be liquidated. Use seasonal adjustment or analyze by season.
• Inventory turnover varies hugely by industry: Grocery: 20-50x/year. Fashion: 4-6x. Electronics: 6-12x. Always benchmark within industry.
• Low turnover ≠ bad if intentional: Strategic inventory (buying ahead of price increases, securing supply) may justify lower turnover.
• ABC classifications shift: A product that was A-class last year may be C-class this year. Reclassify quarterly.
• Carrying cost is often underestimated: Include: warehouse rent, insurance, obsolescence, capital cost (opportunity cost of money tied up), handling labor. Total is typically 20-30% of inventory value per year.

References

• For EOQ (Economic Order Quantity) model, see references/eoq-model.md
• For seasonal demand forecasting, see references/seasonal-forecasting.md

Example: 台灣戶外品牌庫存失衡診斷

Scenario

公司：TrailPeak 戶外裝備（台灣電商，主售登山與健行裝備） 時間：2026 年 Q1 結算後 用戶問題：

我們最近發現一個矛盾現象：登山背包和防水外套常常缺貨，客戶在抱怨，但整體倉庫幾乎快爆了。財務說我們的庫存金額比去年同期高了 40%，但業績只成長 12%。可以幫我看看哪裡出了問題嗎？

提供數據：

整體數據：

• 平均庫存（全年）：NTD 5,800,000
• 年總 COGS：NTD 6,426,000
• 訂單完成率（Fill Rate）：89%（最近 90 天）
• 缺貨事件：主要集中在 BP-01、JK-02

---

Analysis

Phase 1：整體健康檢查

庫存周轉率：

Turnover = COGS / 平均庫存 = 6,426,000 / 5,800,000 = 1.11x/年

庫存天數（DOI）：

DOI = 365 / 1.11 = 329 天

評估：戶外裝備行業健康周轉率約 4–6x/年（DOI ≈ 60–90 天）。TrailPeak 目前 DOI 高達 329 天，是健康值的 3–5 倍，庫存嚴重積壓。

Fill Rate 89% 遠低於目標 95%，印證客戶投訴有據。

---

Phase 2：ABC 分類

依年銷售額排序：

A 類（2 SKU，佔 25%）→ 貢獻 65.3% 收入 B 類（3 SKU，佔 37.5%）→ 貢獻 25% 收入 C 類（3 SKU，佔 37.5%）→ 貢獻 9.7% 收入

---

Phase 3：各 SKU 庫存天數計算

DOI (per SKU) = 期末庫存 / (年 COGS / 365)

根本問題確認：A 類高轉速品嚴重缺貨，C 類低轉速品大量積壓。

---

Phase 4：安全庫存計算（A 類）

服務水準目標：95%（Z = 1.65）

BP-01（50L 登山背包，前置期 21 天）：

Safety Stock = 1.65 × 3.2 × √21 = 1.65 × 3.2 × 4.58 = 24.2 ≈ 25 件
Reorder Point = (14 × 21) + 25 = 294 + 25 = 319 件

JK-02（Gore-Tex 外套，前置期 28 天）：

Safety Stock = 1.65 × 2.8 × √28 = 1.65 × 2.8 × 5.29 = 24.4 ≈ 25 件
Reorder Point = (11 × 28) + 25 = 308 + 25 = 333 件

目前 BP-01 庫存以 COGS 換算約 126 件，JK-02 約 61 件。JK-02 已接近 Reorder Point，BP-01 尚有緩衝但前置期達 21 天需立即採購。

---

Result

# Inventory Health Report: TrailPeak 戶外裝備

## Summary
| Metric | Current | Target | Status |
|--------|---------|--------|--------|
| Turnover | 1.1x | 4-6x | 🔴 |
| DOI | 329 天 | 60-90 天 | 🔴 |
| Fill Rate | 89% | >95% | 🔴 |
| Dead Stock % | BT-06/SC-07/SX-08 估計 >5 年存量 | <10% SKU | 🔴 |

## ABC Distribution
| Class | SKUs | Revenue % | Avg DOI | Issue |
|-------|------|----------|---------|-------|
| A | 2 | 65.3% | 26 天 | 嚴重缺貨，低於安全庫存 |
| B | 3 | 25.0% | 754 天 | 積壓 2 年以上 |
| C | 3 | 9.7% | 2,085 天 | 死庫存，佔壓大量現金 |

## Top Issues

1. **A 類缺貨危機**：BP-01 和 JK-02 合計貢獻 65% 營收，但 DOI 僅 22–29 天，低於
   前置期（21–28 天），表示目前補貨頻率已無法保住 95% 服務水準。
   → 立即觸發採購：BP-01 補單 300+ 件，JK-02 補單 300+ 件。

2. **C 類死庫存佔壓資金**：SX-08（登山襪）DOI 達 3,187 天，以目前銷速需 8.7
   年才能清完；BT-06、SC-07 亦超過 3 年。三者庫存合計 NTD 3,230,000，
   佔整體庫存 47%，年倉儲與資金成本（25% 估計）= NTD 807,500/年白燒。

3. **採購結構性錯誤**：高銷速 A 品缺貨、低銷速 C 品積壓，顯示採購決策未依
   ABC 分級，可能使用統一的「固定批量」或「按廠商最小訂量」模式。

## Recommendations

1. **立即補貨 A 類（本週）**
   - BP-01：下單 400 件（覆蓋 21 天前置期 + 25 件安全庫存 + 緩衝）
   - JK-02：下單 380 件；若廠商 MOQ 問題，與供應商談縮短前置期至 21 天
   - 預期效果：Fill Rate 從 89% 恢復至 ≥95%，Q2 停損估計 NTD 400,000+ 失單

2. **C 類死庫存清倉（30 天內啟動）**
   - SX-08 登山襪：搭配 BP-01 購買滿額贈，或打包「入門登山組」折扣套組
   - BT-06 登山靴、SC-07 炊具：5 折促銷或聯絡戶外社群 / 二手平台清倉
   - 目標：90 天內回收 NTD 1,500,000 現金，釋出倉位給 A 類備貨
   - 注意：CP-05 帳篷為季節性品（Q2 露營旺季），暫不促銷，待 4–5 月自然消化

3. **建立分級採購制度（下季前上線）**
   - A 類：設定 Reorder Point 自動觸發（BP-01: 319 件，JK-02: 333 件）
   - B 類：月底盤點，依當月實際銷量調整下季備貨
   - C 類：採 Min/Max 策略（Max = 60 天存量），不提前大批採購

Iron Law 驗證：A 類 2 個 SKU 佔 65% 收入卻只剩 26 天庫存，C 類 3 個

SKU 佔 10% 收入卻堆了 2,000+ 天庫存。根本原因是「等量對待所有 SKU」——

用同一套補貨邏輯處理背包和登山襪，導致資源錯置。

EOQ Model — Economic Order Quantity

EOQ answers one question: given a fixed annual demand and known costs, what order size minimizes total inventory cost?

It is most useful for A-class items with relatively stable demand. For C-class items with erratic demand, a simple min/max rule is usually sufficient.

---

Core Formula

EOQ = √( 2 × D × S / H )

Where:
- D  = Annual demand (units/year)
- S  = Ordering cost per order (固定費用，每次下單的成本, e.g., admin, shipping setup)
- H  = Annual holding cost per unit (= unit cost × carrying cost %)

Total Annual Cost at EOQ:

TAC = (D / Q) × S  +  (Q / 2) × H

     └─ ordering cost ─┘  └─ holding cost ─┘

At Q = EOQ, ordering cost = holding cost (they balance exactly).

---

Worked Example

Scenario: An e-commerce shop sells a phone case (SKU: PC-001).

Step 1: Compute EOQ

EOQ = √( 2 × 1,200 × 600 / 37.5 )
    = √( 1,440,000 / 37.5 )
    = √( 38,400 )
    = 196 units  ≈ 200 units (round to a practical lot size)

Step 2: Orders per year

Orders/year = D / EOQ = 1,200 / 200 = 6 orders/year
              → roughly one order every 2 months

Step 3: Verify total cost

Ordering cost = (1,200 / 200) × 600 = NT$3,600/year
Holding cost  = (200 / 2) × 37.5   = NT$3,750/year
TAC           = NT$7,350/year

At EOQ the two halves are nearly equal — this is the mathematical minimum.

Comparison: What if they ordered 500 units at a time?

Ordering cost = (1,200 / 500) × 600 = NT$1,440/year
Holding cost  = (500 / 2) × 37.5   = NT$9,375/year
TAC           = NT$10,815/year  (+47% vs EOQ)

Over-ordering roughly doubles holding cost while under-saving ordering cost.

---

Sensitivity: EOQ Is Robust to Estimate Errors

EOQ's biggest practical strength is flatness near the optimum. The total cost curve is shallow — a 50% error in your inputs moves total cost by far less than 50%.

Implication: don't spend days perfecting your S and H estimates. A rough EOQ beats gut instinct ordering by a wide margin.

---

Connecting EOQ to Reorder Point

EOQ tells you how much to order. The reorder point (from SKILL.md) tells you when to order.

Reorder Point = (Avg Daily Demand × Lead Time) + Safety Stock

Order Cycle   = EOQ / Avg Daily Demand  (days between orders)

Continuing the example (lead time = 14 days, σ_d = 5 units, service level 95%):

Avg daily demand  = 1,200 / 365 ≈ 3.3 units/day
Safety stock      = 1.65 × 5 × √14 ≈ 31 units
Reorder Point     = 3.3 × 14 + 31  ≈ 77 units

So the operating rule for PC-001 is:

• When stock drops to 77 units, place an order for 200 units.

---

When EOQ Assumptions Break Down

EOQ requires four assumptions. When they fail, the model needs adjustment or replacement.

---

EOQ with Quantity Discounts

When suppliers offer price breaks, compare total cost including purchase cost at each price tier.

Procedure:

1. Calculate EOQ at each unit price. 2. Check if the computed EOQ is feasible (≥ the minimum quantity for that tier). 3. If feasible: compute TAC = purchase cost + ordering cost + holding cost. 4. If not feasible: use the minimum quantity for that tier, compute TAC. 5. Pick the tier with the lowest TAC.

Example extension — Supplier offers:

Compute TAC for each tier (D = 1,200, S = 600, carrying rate = 25%):

Tier 1 (NT$150, H = 37.5):

• EOQ = 200 (feasible: 200 < 300 ✓)
• TAC = 1,200 × 150 + 3,600 + 3,750 = NT$187,350

Tier 2 (NT$140, H = 35):

• EOQ = √(2 × 1,200 × 600 / 35) = 202 → not feasible (need 300+), use Q = 300
• TAC = 1,200 × 140 + (1,200/300)×600 + (300/2)×35 = 168,000 + 2,400 + 5,250 = NT$175,650

Tier 3 (NT$130, H = 32.5):

• EOQ = 210 → not feasible (need 600+), use Q = 600
• TAC = 1,200 × 130 + (1,200/600)×600 + (600/2)×32.5 = 156,000 + 1,200 + 9,750 = NT$166,950 ← lowest

Decision: Order 600 units at a time despite holding more inventory — the price discount outweighs the extra holding cost.

---

Python Snippet

import math

def eoq(D: float, S: float, H: float) -> float:
    """
    D: annual demand (units)
    S: ordering cost per order (currency)
    H: annual holding cost per unit (currency)
    Returns: EOQ (units)
    """
    return math.sqrt(2 * D * S / H)

def total_annual_cost(D: float, S: float, H: float, Q: float,
                      unit_cost: float = 0.0) -> float:
    """Includes optional purchase cost."""
    return (D / Q) * S + (Q / 2) * H + D * unit_cost

def reorder_point(avg_daily_demand: float, lead_time: float,
                  safety_stock: float) -> float:
    return avg_daily_demand * lead_time + safety_stock


# --- Example ---
D, S, unit_cost, carrying_rate = 1200, 600, 150, 0.25
H = unit_cost * carrying_rate

q = eoq(D, S, H)
print(f"EOQ: {q:.0f} units")
print(f"Orders/year: {D/q:.1f}")
print(f"TAC: {total_annual_cost(D, S, H, q, unit_cost):,.0f}")

Output:

EOQ: 196 units
Orders/year: 6.1
TAC: 187,350

---

ABC Class Application

Per the parent skill's Iron Law, not all SKUs deserve EOQ analysis.

For a 500-SKU catalogue: roughly 100 A-items justify rigorous EOQ. The remaining 400 B/C items can use simplified rules. This matches the Pareto principle in SKILL.md.

---

Common Mistakes

• Using retail price instead of COGS for H: H must be based on the cost you have tied up, not the selling price.
• Forgetting capital cost in H: Carrying cost % should include the opportunity cost of capital (typically 10-15% of the 20-30% total). Underestimating H overstates EOQ and leads to over-ordering.
• Applying EOQ to seasonal items without adjustment: A coat with demand concentrated in Oct-Feb will have very different optimal order quantities in each season than an annual EOQ implies. Segment by season or use a rolling 90-day demand window.
• Treating EOQ as the only input to order quantity: Supplier minimums, shelf capacity, expiry dates, and container fill rates are hard constraints that override the EOQ optimum. Use EOQ as a starting point and adjust upward to the nearest feasible quantity.
• Recalculating too infrequently: If demand or costs shift significantly, the EOQ shifts too. Recalculate A-item EOQs quarterly or when a major demand change occurs.

Seasonal Demand Forecasting for Inventory Health

Seasonal products break two assumptions baked into the base formulas: constant average demand and stable variance. This document shows how to detect seasonality, compute seasonal indices, adjust safety stock seasonally, and avoid liquidating product that is merely "off-season".

---

1. Detecting Seasonality Before Acting

Before applying any seasonal model, confirm the pattern is real and recurring.

Minimum data requirement: at least 2 full years of weekly or monthly sales. One year is not enough — you cannot separate seasonality from a one-time spike.

Quick visual check: plot monthly sales for each SKU as a line chart. If peaks and troughs fall in roughly the same calendar months across both years, seasonality is present.

Quantitative screen — Coefficient of Variation (CV) and Peak-to-Trough Ratio:

CV = σ_monthly / μ_monthly

Peak-to-Trough Ratio = max(monthly sales) / min(monthly sales)

Important: high CV alone could mean demand is erratic (random noise), not seasonal. The pattern must repeat across years. If peaks shift month-to-month each year, use a different forecasting approach (e.g., event-driven).

---

2. Seasonal Index Method (Ratio-to-Moving-Average)

This is the standard decomposition method. It separates demand into:

Demand = Trend × Seasonal Index × Irregular

For inventory purposes you need the Seasonal Index (SI) per period.

Step-by-step procedure

Input: Monthly sales data, ≥ 2 years, one SKU at a time.

Step 1 — Compute 12-month centered moving average (CMA)

For each month t:

CMA(t) = [ 0.5×S(t-6) + S(t-5) + ... + S(t) + ... + S(t+5) + 0.5×S(t+6) ] / 12

The 0.5 weighting on the endpoints centers the average exactly on month t.

This removes seasonality and leaves Trend × Irregular.

Step 2 — Compute raw seasonal ratios

Raw Ratio(t) = S(t) / CMA(t)

Step 3 — Average ratios by calendar month

Collect all Raw Ratio(t) values for January across all years, take the median (more robust than mean):

SI(Jan) = median( Raw Ratio for all Januaries )
SI(Feb) = median( Raw Ratio for all Februaries )
... (12 values total)

Step 4 — Normalize so indices sum to 12.00

Adjustment = 12.0 / sum(all 12 SI values)
SI_normalized(m) = SI(m) × Adjustment

After normalization: sum(SI_normalized) = 12.0, and the annual average SI = 1.0.

---

Worked Example: Outdoor Sunscreen SKU

Monthly sales (units), 2 years:

Annual average monthly demand (use for comparison):

μ = (6,470 + 6,595) / 2 / 12 = 546 units/month

After computing CMA and ratios (abbreviated for brevity), normalized seasonal indices:

Seasonal forecast for next July (assuming flat trend, average monthly base = 550):

Forecast(Jul) = Base × SI(Jul) = 550 × 2.18 = 1,199 units

---

3. Seasonal Safety Stock

The base formula from SKILL.md:

Safety Stock = Z × σ_d × √(Lead Time)

This uses a single σ_d (standard deviation of daily demand). For seasonal products, σ_d varies month-to-month. Using the annual average σ_d causes:

• Overstock in off-peak months (safety stock set too high)
• Stockouts in peak months (safety stock set too low)

Seasonal safety stock formula

Compute σ_d separately for each month (or season), then apply:

Safety Stock(m) = Z × σ_d(m) × √(Lead Time)

Where σ_d(m) is the standard deviation of daily demand during month m, estimated from historical data for that calendar month.

Practical shortcut using seasonal indices

If you have limited history, estimate monthly σ_d from annual σ_d:

σ_d(m) ≈ σ_d_annual × SI(m)

This assumes the coefficient of variation is roughly constant across seasons — a reasonable approximation when you lack month-level data.

Continued worked example — sunscreen, 95% service level (Z = 1.65), Lead Time = 14 days:

Suppose annual σ_d = 18 units/day.

Using the annual average safety stock of 111 units in July means you are running at effectively only 66% service level during peak. Using 242 units in January means ~$200–300 of unnecessary carrying cost per SKU.

---

4. Seasonal Reorder Point

From SKILL.md:

Reorder Point = (Average Daily Demand × Lead Time) + Safety Stock

For seasonal products, both terms must use the current-month values:

ROP(m) = [ μ_d × SI(m) × Lead Time ] + Safety Stock(m)

Where μ_d is the annual average daily demand and SI(m) is the month-specific index.

Sunscreen example, July, μ_d = 546/30 = 18.2 units/day:

ROP(Jul) = (18.2 × 2.18 × 14) + 242
         = 555 + 242
         = 797 units

In January:

ROP(Jan) = (18.2 × 0.23 × 14) + 25
         = 59 + 25
         = 84 units

Set your replenishment triggers accordingly — they should be updated at the start of each month (or each quarter for slower-moving products).

---

5. ABC Classification for Seasonal Products

The SKILL.md Iron Law — 20% of SKUs drive 80% of revenue — still holds, but seasonal products must be reclassified by season, not by annual total alone.

Problem with annual-only ABC

A swimsuit SKU may generate $0 revenue in Nov–Mar and $150,000 in Apr–Sep. Classified on annual revenue, it ranks as A. But in January, treating it as an A-item (tight control, high safety stock) wastes capital.

Seasonal ABC approach

Run ABC classification on a rolling 13-week revenue window updated monthly:

Revenue_rolling(SKU, month m) = Σ sales revenue for weeks (m-12) to m

Classify each month independently. A swimsuit becomes:

• A-class: Apr–Sep (peak season)
• C-class: Oct–Mar (off-season, hold minimal or zero stock)

Implementation shortcut — use seasonal index thresholds:

---

6. Pre-Season Inventory Build Plan

For highly seasonal SKUs (Peak-to-Trough > 4×), you cannot rely on in-season replenishment if lead time is long. You must build inventory before peak.

Build quantity formula

Build Target = Σ Forecast(m) for all peak months + Peak Safety Stock − Current Stock

Peak months = months where SI(m) ≥ 1.0

Decision rule for build timing: place the buy Lead Time days before the first peak month (SI ≥ 1.0).

Sunscreen example — planning for May–Aug peak, current stock = 400 units, lead time = 45 days:

Forecast peak demand = (550×1.56) + (550×1.98) + (550×2.18) + (550×1.97)
                     = 858 + 1,089 + 1,199 + 1,084
                     = 4,230 units

Peak Safety Stock    = 242 units (July value, the highest)

Build Target         = 4,230 + 242 − 400 = 4,072 units

Order placement      = April 1 (first peak month May 1, minus 45-day lead time → March 17; round up to April 1 for supplier cut-off)

---

7. End-of-Season Liquidation Trigger

Seasonal products that are not sold by end of peak season become carry-over inventory — a major source of dead stock and write-downs.

Liquidation decision rule

At the start of the final month of peak season (SI drops below 1.0 next month):

Expected Remaining Demand = Σ Forecast(m) for remaining off-peak months
Expected Remaining Demand = Base × Σ SI(m) for off-peak months

If Current Stock > 2 × Expected Remaining Demand, begin liquidation (discount, bundle, channel clearance).

Sunscreen example — entering October, current stock = 620 units:

Off-peak forecast (Oct–Mar):
= 550 × (0.65 + 0.37 + 0.28 + 0.23 + 0.26 + 0.49)
= 550 × 2.28
= 1,254 units  ← still meaningful demand off-season

Threshold = 2 × 1,254 = 2,508 units
620 < 2,508 → no liquidation needed; carry over normally

If stock were 3,000 units: 3,000 > 2,508 → liquidate the excess 746 units before April to avoid a second year of carry costs.

---

8. Pitfalls Specific to Seasonal Forecasting

Index calculation requires ≥ 2 years: with one year you cannot separate trend from seasonality. If you only have one year, use industry seasonal indices as a prior and adjust as data accumulates.

Promotional spikes inflate indices: a flash sale in July inflates SI(Jul) permanently. Scrub known promotional periods before computing indices, or they will inflate next year's July safety stock unnecessarily.

Lead time length relative to seasonal swing: if lead time (14 days) is short relative to the seasonal cycle (monthly), seasonal safety stock is the right tool. If lead time is 6 months (e.g., ocean freight from Asia for fashion), you are forecasting the entire season at order time — use a pre-season buy model with a single probability distribution over total season demand, not monthly rolling reorders.

Newly launched SKUs have no history: use category-level seasonal indices from similar established SKUs as a proxy. Do not use flat indices (SI = 1.0) for a known seasonal category — this guarantees stockouts at peak.

Seasonal index drift: fashion and lifestyle categories shift their peak month over time (e.g., "back to school" moving earlier). Recompute indices annually; do not reuse indices older than 2 years.