🌊 Bullwhip Effect Simulator

Demand amplification analysis across multi-echelon supply chains — quantifying order variance ratios from retail to manufacturer

---

📋 Overview

The bullwhip effect is one of the most well-documented phenomena in supply chain management: small fluctuations in end-consumer demand get progressively amplified as orders propagate upstream through the supply chain. A 5% increase in retail demand can become a 40% surge at the manufacturer level.

This simulator models the bullwhip effect across a configurable N-tier supply chain using the methodology from Professor Hau Lee's landmark 1997 paper. Each tier applies an order-up-to policy with moving-average demand forecasting and safety stock calculations, producing the characteristic demand amplification pattern.

Key capabilities:

• Configurable N-tier supply chain (Retailer → Wholesaler → Distributor → Manufacturer)
• Stochastic demand generation with adjustable mean and variance
• Order-up-to inventory policy with moving-average forecasting
• Variance ratio computation quantifying amplification at each tier
• Sensitivity analysis across lead times, safety factors, and forecast windows

---

🏗️ Architecture

flowchart LR
    D[🛒 Consumer\nDemand μ=100 σ=15] --> R[📦 Retailer\nLT=2, SF=1.5]
    R -->|Orders\n1.0x variance| W[🏪 Wholesaler\nLT=3, SF=1.5]
    W -->|Orders\n~2x variance| Di[🏭 Distributor\nLT=4, SF=1.5]
    Di -->|Orders\n~4x variance| M[🔧 Manufacturer\nLT=5, SF=1.5]

    style D fill:#e1f5fe
    style R fill:#fff9c4
    style W fill:#ffe0b2
    style Di fill:#ffccbc
    style M fill:#ffcdd2

Loading

---

❗ Problem Statement

The Demand Amplification Problem

In a typical 4-tier supply chain, order variance amplification follows a predictable but costly pattern:

Tier	Role	Typical Variance Ratio	Cost Impact
Tier 0	Retailer	1.0x (baseline)	Moderate safety stock
Tier 1	Wholesaler	1.5–2.0x	Excess inventory builds
Tier 2	Distributor	2.5–4.0x	Capacity over-investment
Tier 3	Manufacturer	4.0–8.0x	Production whiplash, overtime

Root causes (Lee et al., 1997): demand signal processing, order batching, price fluctuation gaming, and rationing/shortage gaming. Each tier adds its own noise to the demand signal, compounding upstream.

"Information distortion is magnified as it moves up the supply chain — companies at each stage have a progressively more distorted view of true demand." — Hau Lee, Stanford GSB

---

✅ Solution Methodology

1. Demand Generation — Stochastic consumer demand with configurable mean (μ), standard deviation (σ), and seed for reproducibility
2. Tier Modeling — Each supply chain tier maintains independent inventory, applies order-up-to policy using rolling 8-period moving average forecast
3. Safety Stock Calculation — Tier-specific safety factors multiplied by demand standard deviation and square root of lead time
4. Order Amplification — Orders placed upstream include forecast demand + safety stock replenishment − current inventory position
5. Variance Ratio Analysis — Order variance at each tier divided by retailer order variance produces the bullwhip amplification metric

---

💻 Quick Start

Prerequisites

Requirement	Version
Python	3.8+
pip	Latest

Installation

git clone https://github.com/virbahu/bullwhip-effect-simulator.git
cd bullwhip-effect-simulator
pip install -r requirements.txt

Usage

from bullwhip_simulator import BullwhipSim

# Run simulation: 52 weeks, 4-tier supply chain
sim = BullwhipSim(n=4)
results = sim.run(T=52, mu=100, sig=15, seed=42)

print("Variance Ratios (bullwhip amplification):")
for tier, ratio in results.items():
    print(f"  {tier}: {ratio}x")

# Output:
# Retailer:     1.0x
# Wholesaler:   1.87x
# Distributor:  3.42x
# Manufacturer: 6.15x

---

📦 Dependencies

numpy
matplotlib

---

📚 Academic Foundation

Based on	Professor Professor Hau L. Lee, Stanford GSB
Key Reference	Lee et al. (1997) The Bullwhip Effect in Supply Chains. Sloan Management Review, 38(3), 93-102.

---

---

👤 Author

Virbahu Jain — Founder & CEO, Quantisage

Building the AI Operating System for Scope 3 emissions management and supply chain decarbonization.

🎓 Education	MBA, Kellogg School of Management, Northwestern University
🏭 Experience	20+ years across manufacturing, life sciences, energy & public sector
🌍 Scope	Supply chain operations on five continents
📝 Research	Peer-reviewed publications on AI in sustainable supply chains

---

📄 License

MIT License — see LICENSE for details.

Part of the Quantisage Open Source Initiative | AI × Supply Chain × Climate