algo-sc-bullwhip

# Bullwhip Effect Analysis

## Overview

The bullwhip effect describes how small fluctuations in consumer demand amplify progressively at each upstream stage of the supply chain. A 5% retail demand increase can become a 40% order spike at the manufacturer. Caused by demand signal processing, order batching, price fluctuations, and rationing/shortage gaming.

## When to Use

**Trigger conditions:**
- Diagnosing why supplier orders are far more volatile than end-consumer demand
- Quantifying demand amplification across supply chain tiers
- Designing strategies to reduce order variability

**When NOT to use:**
- When demand is genuinely volatile (not amplified) — the issue is demand forecasting
- For single-echelon inventory optimization (use EOQ or safety stock)

## Algorithm

```
IRON LAW: Demand Variability Amplifies at EACH Upstream Stage
Bullwhip ratio = Var(orders) / Var(demand). A ratio > 1 at any stage
confirms the bullwhip effect. The four root causes (Lee et al., 1997):
1. Demand signal processing (forecasting with moving averages)
2. Order batching (periodic review, MOQs)
3. Price fluctuations (forward buying during promotions)
4. Rationing and shortage gaming (inflating orders during scarcity)
```

### Phase 1: Input Validation
Collect: end-consumer demand time series AND order time series at each supply chain stage (retailer → distributor → manufacturer → supplier).
**Gate:** At least 2 tiers of order data, minimum 26 periods.

### Phase 2: Core Algorithm
1. Compute variance of demand at each tier
2. Compute bullwhip ratio per tier: BWR_i = Var(orders_i) / Var(orders_{i-1})
3. Identify contribution of each cause: batch size analysis, promotion calendar overlap, forecast method evaluation
4. Quantify cost: excess inventory carrying cost, expediting cost, capacity misallocation

### Phase 3: Verification
Check: BWR > 1 at upstream stages (confirms bullwhip). Correlate order spikes with identifiable causes (promotions, forecast updates, batch cycles).
**Gate:** Bullwhip quantified and root causes identified.

### Phase 4: Output
Return bullwhip ratios with root cause attribution and mitigation recommendations.

## Output Format

```json
{
  "bullwhip_ratios": [{"tier": "retailer→distributor", "ratio": 1.8}, {"tier": "distributor→manufacturer", "ratio": 2.3}],
  "root_causes": [{"cause": "order_batching", "contribution_pct": 40}, {"cause": "demand_signal_processing", "contribution_pct": 35}],
  "metadata": {"periods": 52, "tiers_analyzed": 3}
}
```

## Examples

### Sample I/O
**Input:** Consumer demand CV=0.10, Retailer orders CV=0.18, Distributor orders CV=0.32
**Expected:** BWR retailer=3.24 (0.18²/0.10²), BWR distributor=3.16 (0.32²/0.18²). Strong bullwhip confirmed.

### Edge Cases
| Input | Expected | Why |
|-------|----------|-----|
| BWR < 1 | Smoothing effect | Information sharing or VMI may dampen variability |
| Promotional periods | Spike in BWR | Forward buying amplifies orders |
| Single tier only | Cannot measure amplification | Need at least 2 tiers for comparison |

## Gotchas

- **Data granularity**: Weekly vs monthly data can show different bullwhip magnitudes. Use consistent time buckets across tiers.
- **VMI and CPFR**: Vendor-managed inventory and collaborative planning reduce bullwhip by sharing demand data. But they require trust and IT integration.
- **Information sharing ≠ bullwhip elimination**: Even with POS data sharing, lead times and batch constraints still cause some amplification.
- **Shortage gaming is hardest to fix**: During shortages, customers inflate orders. When supply recovers, cancellations flood in. Only committed-quantity allocations prevent this.
- **Measurement challenges**: True consumer demand is often unobserved (only POS data). Lost sales from stockouts are invisible, understating true demand variability.

## References

- For Lee-Padmanabhan-Whang formal model, see `references/bullwhip-model.md`
- For information sharing strategies, see `references/information-sharing.md`