Bullwhip Effect & Demand Information Sharing

John Boylan & Mohammad AliBuckinghamshire New University

EPSRC Launch Meeting, 24 October 2007

Outline

Approaches to the Bullwhip Effect Demand Information Sharing (DIS) and

standard assumptions Scenarios presented in current literature Uncertainty Principles New scenarios introduced

Bullwhip Effect

Amplification of ‘noise’ as demand moves upstream

Amplification of upstream inventory requirements

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)

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)

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

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)

3. Linear Hierarchy

Unrealistic to have single node at each echelon Upstream propagation based on sum of

demands: MA(q1) + MA(q2) = MA(max{q1,q2})

AR(p1) + AR(p2) = ARMA(p1+p2,max{p1,p2})

Even if backward inference allows for identification of the process for total demand, it does not allow identification at each node

4. ‘OUT’ Inventory Rule

OUT leads to

Yt = Dt + (St – St-1)

If optimal (MMSE) forecasting method used: St = mt + -1(p/(p+h)) √v

Yt = Dt + (mt – mt-1)

Immediately apparent that Bullwhip or Anti-Bullwhip may occur

Upstream Translation of Demand (MMSE)

ARIMA (p, d, qR)

ARIMA (p, d, qM)

where qM = max {p+d, qR-L}

Manufacturer(Upstream Link)

Retailer(Downstream Link)

Forecasting Method

MMSE

Alwan et al (2003), Zhang (2004), Gilbert (2005)Alwan et al (2003), Zhang (2004), Gilbert (2005)

Upstream Translation of Demand (SMA)

ARIMA (p, d, qR)

ARIMA (p, d, qR +n)

Manufacturer(Upstream Link)

Retailer(Downstream Link)

Forecasting Method

SMA

Where n is the number of historical terms used in forecasting

Upstream Translation of Demand (SES)

ARIMA (p, d, qR)

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

Scenarios

Current No information

sharing Demand information

sharing Downstream

Demand Inference

New No information

sharing (estimation of noise term)

Centralised demand information sharing

1 11 (1 )ˆ 1 1

(Manufacturer's Lead Time Forecast)

L L

t t tY y

Lead Time Forecast by Manufacturer AR(1)

1ˆ ˆ( ) (Demand at Manufacturer)t t t ty d D D

1 (Demand at Retailer)t t td d

1(1 )ˆ (Retailer's Lead Time Forecast)1

L

t tD d

No Information Sharing

0t

1 11 (1 )ˆ 1 1

L L

t t tY y

11ˆ

1

L

t tY y

Take

t

1 1

is known, thus can be calculated

1 (1 )ˆ 1 1

t

L L

t t t

d

Y y

1 11 (1 )ˆ 1 1

L L

t t tY y

Demand Information Sharing

t

1 1

ˆ is unknown, but can be estimated

1 (1 )ˆ ˆ 1 1

t

L L

t t t

d

Y y

1 11 (1 )ˆ 1 1

L L

t t tY y

Downstream Demand Inference

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.

ARIMA (p, d, qM)

Principle I(applies when p+d<qM)

ARIMA (p, d, qR)

ARIMA (1, 0, 2)

ARIMA (1, 0, 3)

L=1

qM = max {p+d, qR-L}

qM = qR-L = qR-1

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.”

ARIMA (p, d, qM+L)…

Principle II (applies when p+d=qM)

ARIMA (p, d, qM)

ARIMA (p, d, 1)

ARIMA(p, d, 0)

ARIMA(p, d, qM+1)…

ARIMA(p, d, qM)

New Scenario : No Information Sharing – estimation of noise

1 11 (1 )ˆ 1 1

L L

t t tY y

t

1 1

ˆ is unknown but can be calculated

1 (1 )ˆ ˆ 1 1

t

L L

t t t

d

Y y

There are two estimation methods for the above1. Recursive Estimation Method

2. Forecast Error Method

New Scenario: Centralised Demand Information Sharing

1 11 (1 )ˆ 1 1

L L

t t tY y

11ˆ

1

L

t t tY d

New Scenarios Introduced

Current Literature

t t

NIS

Y , 0 t t

NIS-Est

ˆY ,

t

DIS

Y , t t t

CDIS

d ,

Scenarios in our Research

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

Further Research

Issue of batching Evaluation of multi-node supply chains Inventory rules other than OUT Challenging the nature of the rules