1. Bullwhip Effect & Demand Information Sharing John Boylan & Mohammad Ali Buckinghamshire New University EPSRC Launch Meeting, 24 October 2007

2. Outline  Approaches to the Bullwhip Effect  Demand Information Sharing (DIS) and standard assumptions  Scenarios presented in current literature  Uncertainty Principles  New scenarios introduced

3. Bullwhip Effect Amplification of ‘noise’ as demand moves upstream Amplification of upstream inventory requirements

4. Approaches to the Bullwhip  Control Theory  System Dynamics  OR / Statistical approach : Share downstream demand information with upstream links Lee et al (2000) Chen et al (2000) Raghunathan (2003)

5. Demand Information Sharing Papers share the following assumptions: 1. Demand follows ARIMA process 2. Residual noise is Gaussian 3. Linear hierarchy, one node at each echelon 4. Inventory rule is ‘Order Up To’ (OUT)

6. 1. ARIMA process Advantages  Convenient mathematically  Can be insightful Disadvantages  Even if process is ARIMA, forecasting may not be ARIMA Alternatives  Assume ARIMA process but use a non-optimal method (eg SMA, SES)  Use state-space approach

7. 2. Gaussian Residual Noise Advantages  Leads to tractable results Disadvantages  May lead to low safety stocks if data is skewed  NB: depends on inventory rule Alternatives  Use non-standard ARIMA model with skewed noise distribution  For slow-moving items, use Integer ARMA models (with Poisson noise)

8. 3. Linear Hierarchy  Unrealistic to have single node at each echelon  Upstream propagation based on sum of demands: MA(q 1 ) + MA(q 2 ) = MA(max{q 1,q 2 }) AR(p 1 ) + AR(p 2 ) = ARMA(p 1 +p 2,max{p 1,p 2 })  Even if backward inference allows for identification of the process for total demand, it does not allow identification at each node

9. 4. ‘OUT’ Inventory Rule  OUT leads to Y t = D t + (S t – S t-1 )  If optimal (MMSE) forecasting method used: S t = m t +  -1 (p/(p+h))  √v Y t = D t + (m t – m t-1 ) Immediately apparent that Bullwhip or Anti-Bullwhip may occur

10. Upstream Translation of Demand (MMSE) ARIMA (p, d, q R ) ARIMA (p, d, q M ) where q M = max {p+d, q R -L} Manufacturer (Upstream Link) Retailer (Downstream Link) Forecasting Method MMSE Alwan et al (2003), Zhang (2004), Gilbert (2005)

11. Upstream Translation of Demand (SMA) ARIMA (p, d, q R ) ARIMA (p, d, q R +n) Manufacturer (Upstream Link) Retailer (Downstream Link) Forecasting Method SMA Where n is the number of historical terms used in forecasting

12. Upstream Translation of Demand (SES) ARIMA (p, d, q R ) ARIMA (p, d, t - 1) + term Manufacturer (Upstream Link) Retailer (Downstream Link) Forecasting Method SES Where t is the number of historical terms used in forecasting

13. Scenarios Current  No information sharing  Demand information sharing  Downstream Demand Inference New  No information sharing (estimation of noise term)  Centralised demand information sharing

14. Lead Time Forecast by Manufacturer AR(1)

15. No Information Sharing Take

16. Demand Information Sharing

17. Downstream Demand Inference

18. Uncertainty Principle I If the upstream member can identify the demand model at the downstream link, the demand value at the downstream link cannot be exactly calculated.

19. ARIMA (p, d, q M ) Principle I (applies when p+d<q M ) ARIMA (p, d, q R ) ARIMA (1, 0, 2 ) ARIMA (1, 0, 3 ) L=1 q M = max {p+d, q R -L } q M = q R -L = q R -1

20. Uncertainty Principles Principle II: “If the upstream member cannot identify the demand model at the downstream link, then the demand value at the downstream link can be exactly calculated, if a certain model is assumed from a restrictive subset of the possible models. ”

21. ARIMA (p, d, q M +L) … Principle II (applies when p+d=q M ) ARIMA (p, d, q M) ARIMA (p, d, 1) ARIMA (p, d, 0) ARIMA (p, d, q M +1) … ARIMA (p, d, q M )

22. New Scenario : No Information Sharing – estimation of noise There are two estimation methods for the above 1.Recursive Estimation MethodRecursive Estimation Method 2.Forecast Error MethodForecast Error Method

23. New Scenario: Centralised Demand Information Sharing

24. New Scenarios Introduced Current Literature Scenarios in our Research

25. Summary of Research  Downstream Demand Inference shown to be infeasible  No Information Scenario improved to include estimation of ‘noise’ term  Demand Information Sharing scenario enhanced by basing estimation on demand at retailer

26. Further Research  Issue of batching  Evaluation of multi-node supply chains  Inventory rules other than OUT  Challenging the nature of the rules