7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Quantifying the Impact of a Supply Chain’s Design Parameters
on the Bullwhip Effect
Matloub Hussain, Paul R. Drake* and Dong M. Lee
University of Liverpool Management School
Liverpool, L69 7ZH, UK.
Tel: +(0)151-7953603
Email: drake@liv.ac.uk
*Corresponding author.
October 13-14, 2007
Rome, Italy
1
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Quantifying the Impact of a Supply Chain’s Design Parameters
on the Bullwhip Effect
ABSTRACT
This paper is concerned with understanding the effects of design parameters on demand
amplification in a model of a multi-echelon supply chain with information sharing. The model uses
the control theoretic concepts of variables, flows and feedback processes. Previous, similar studies
have used traditional operational research techniques such as mathematical programming and
stochastic process modeling and, as pointed out by Riddalls et al. (2000), differential equations
produce smooth outputs that are not suitable when modeling supply chains. A combination of
simulation and Taguchi Design of Experiments is applied here to quantify the impact of the supply
chain’s design parameters on its dynamic performance and the interactions that occur between the
parameters. This study presents an approach to determining the relative contribution of the design
parameters in controlling demand amplification (the Bullwhip Effect). The overall aim is to give
supply chain operations managers and designers a way to understand supply chain dynamics and the
effects of design parameters and their interactions.
Keywords: Bullwhip, Simulation, Taguchi Design of Experiments, Information Sharing.
INTRODUCTION
Supply chain dynamics has been studied for more than four decades. Since Forrester (1961)
discovered the fluctuation and amplification of demand moving upstream in the supply chain, there
has been a lot of research analyzing this phenomenon. Forrester (1961) pointed out that demand
amplification is due to the “system dynamics phenomenon” and can be tackled by reducing delays,
while Sterman (1989) through his “beer game” interprets the phenomenon as a consequence of
players’ irrational behaviours or misperceptions of feedback. Towill (1996) confirmed the findings
of Forrester that reducing delays and collapsing all cycle times improves the performance of the
system. Lee et al. (1997) found that demand amplification or the “Bullwhip Effect” was due to
demand signal processing, order batching, price variations and rationing and gaming and can be
reduced through information sharing. Slack and Lewis (2002) give a textbook introduction to its
causes and remedies. Its effects include inaccurate forecasting leading to periods of low capacity
utilization alternating with periods of having not enough capacity, i.e. periods of excessive inventory
caused by over production alternating with periods of stock-out caused by under production, leading
to inadequate customer service and high inventory costs.
Several supply chain models have been analyzed to quantify the Bullwhip Effect. For
example, Lee et al. (2000), while studying a two-tier supply chain, showed that manufacturer
inventory levels can be reduced dramatically by sharing point-of-sales data. Yu et al. (2001) used
information sharing to reduce the variability of demand placed on the supplier in a two-tier supply
chain model. Riddalls and Bennet (2002) investigated the use of pure delays in a single echelon of
Sterman’s beer game model and showed that transient inability to supply all that is demanded is an
important cause of amplification.
October 13-14, 2007
Rome, Italy
2
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
The multi-echelon supply chain model was developed originally by Forrester (1961). Towill
(1982) introduced a greater level of detail using the Inventory and Order Based Production Control
System (IOBPCS) to model each echelon in more detail, applying a basic periodic review algorithm
for issuing orders into the supply pipeline, based on current inventory deficit and incoming demand
from customers. Later, a work-in-progress feedback loop was added to the IOBPCS, “Let the
production targets be equal to the sum of an exponentially smoothed demand (over Ta time units)
plus a fraction (1/Tai) of the inventory error, plus a fraction (1/Tw) of the WIP error.”. This was then
termed the “Automatic Pipeline Inventory and Order Based Production Control System”
(APIOBPCS) (John et al., 1994). This model and the model used latterly by Riddalls and Bennett
(2002) form the basis of the echelon model (or building block) used here.
Finding the best operating conditions for a supply chain is complex due to the interactions
among the design parameters. Previous studies used traditional operational research techniques such
as mathematical programming, stochastic process modeling, heuristic methods and as pointed out by
Riddalls et al. (2000) differential equations produce a smooth output that is not suitable for the
modeling of all supply chains. Mathematical and control theoretic approaches can require an
academically advanced understanding of mathematics that many (if not most) supply chain
operations managers do not have. In contrast, the use of simulation methods involving simple
equations can help practitioners to understand the basic phenomena and to examine the effects of
parameters, interactions that occur and to search for the best combination of parameter values in
conjunction with Taguchi Design of Experiments.
This study differs from previous research in many ways. Previous studies have identified
several possible causes of the Bullwhip Effect but little attention has been given to measuring
quantitatively the impact of these causes on the Bullwhip Effect (Paik et al., 2007). Some studies
changed the value of one variable at a time and measured its effect on demand amplification. This
‘one-at-a time’ methodology reveals the effect of one factor with one particular set of values for the
other factors but does not provide the information for calculating the effects of the factor with any
values for the other factors. A more appropriate methodology is Taguchi’s Orthogonal Arrays
Technique in which levels of each factor are systematically varied and all possible combinations of
factor levels (parameter values) are considered. Furthermore, it measures quantitatively the effects
of the design parameters on demand amplification, the interactions among the parameters are
explored and the best combination of parameter values for mitigating the impact of demand
amplification is considered.
The remainder of this paper is organized as follows. First the methodology is introduced and
then the supply chain simulation model is presented. After that, the impact of the design parameters
on the dynamics of the inventory levels and order rates is studied and the orthogonal arrays
technique is applied to explore the impact of various levels of the design parameters on a measure of
demand amplification or the Bullwhip Effect.
Methodology.
The System Dynamics approach is used to analyze complex, dynamic and non-linear
interactions and to develop new structures and policies to obtain the improved behaviour of a
system. It allows one to visualize and solve a problem holistically. A System Dynamics computer
simulation model is developed here to study the time varying or dynamic behaviour of a supply
chain and thereby the Bullwhip Effect. The model uses levels, flows (or rates) and feedback
processes and is implemented using the iThink software package (http://www.iseesystems.com/).
October 13-14, 2007
Rome, Italy
3
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
A four-echelon supply chain is modeled and simulated, so it is the fourth echelon that
experiences the greatest demand amplification as it is farthest from the end-customer. The dynamics
of the inventory and order rate at the fourth echelon present the ‘worst-case’ scenario so the
Bullwhip Effect experienced at this echelon is studied in the work presented here. Taguchi and
analysis of variance (ANOVA) techniques are used to analyse the dynamic performance of the
fourth echelon with respect to its design parameters. As the design parameter values are varied, the
values are applied at all echelons.
The Model
iThink uses the four basic building blocks in Figure 1: Stock, represents something that
accumulates; Flow, an activity that changes the magnitude of the stock; Converter, modifies an
activity; Connector, transmits inputs and information. Figure 2 presents the discrete continuous
simulation model of a 4-echelon supply chain produced in iThink using these building blocks.
STOCK
CONVERTER
FLOW
CONNECTOR
Figure 1: Building blocks of iThink software.
At the material flow level, each echelon or tier constitutes one inventory and one time delay
(factory). Each echelon operates individually based on demand information gained from downstream
(towards the end-customer). This situation is the same as that modeled in the beer game, where a
brewery and a distribution centre try to cope with changes in demand. The input to the factory is the
order rate (ORATE). Production is controlled by feeding forward the exponentially smoothed sales
(SSALES) and feeding back the error in the inventory and the work-in-progress to determine the
ORATE with the aim of keeping the inventory at a desired level. The error in the inventory (EINV)
is the difference between the desired inventory (DINV) and the actual inventory (AINV). DINV is
adaptive. In this case it is simply equal to the current (one week’s) sales. The work in progress
(WIP) is the accumulation of orders that have been placed on the factory but not yet completed and
the desired WIP is DWIP. The error in the WIP (EWIP) is the difference between the desired WIP
(DWIP) and the actual WIP (WIP). Ti is a divisor applied to the inventory deficit to control the rate
of recovery and Tw is a divisor that controls the WIP replenishment rate. In summary:
October 13-14, 2007
Rome, Italy
DINV = SSALES
(1)
EINV = DINV-AINV
(2)
DWIP = Tp x SSALES
(3)
EWIP = DWIP-WIP
(4)
ORATE = SSALES + EINV/Ti + EWIP/Tw
(5)
4
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Alpha 4
Ti 4
SSales
ORate
TIER1 - THE RETAILER
Actual
Inv entory 1
Factory 1
~
ComRate
Sales
EInv
N
EWIP
Tw 3
DInv
DWIP
Tp 4
Alpha 4
TIER2 - THE WAREHOUSE
SSales 2
Ti 4
Actual
Inv entory 2
Factory 2
ORate 2
ComRate 2
Sales 2
EInv 2
EWIP 2
N
N
Tw 3
DInv 2
DWIP 2
Tp 4
IEP 1
IEP 2
Alpha 4
Ti 4
SSales 3
TIER3 - THE DISTRIBUTOR
Actual
Inv entory 3
ORate 3
ComRate 3
Sales 3
Factory 3
EInv 3
EWIP 3
Tw 3
N
DInv 3
Tp 4
IEP 1
DWIP 3
IEP 2
Alpha 4
Ti 4
TIER4 - THE MANUFACTURER
SSales 4
Actual
Inv entory 4
ORate 4
ComRate 4
Sales 4
Factory 4
EInv 4
Tw 3
EWIP 4
N
DInv 4
Tp 4
DWIP 4
IEP 1
IEP 2
Figure 2: iThink Model of Multi-Echelon Supply Chain.
October 13-14, 2007
Rome, Italy
5
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Initial Analysis of Effects of Parameters
In the model used here there are five control or design parameters at each echelon:
i.
ii.
iii.
iv.
v.
information enrichment percentage (IEP);
time to adjust inventory (Ti);
time to adjust WIP (Tw);
production (or pipeline) delay (Tp);
sales exponential smoothing (forecasting) constant α.
In the initial simulations, Tp is set equal to six weeks as in the work of Riddalls et al. (2002)
and levels around this value are chosen for the Taguchi Design of Experiments. A constraint in
exponential smoothing is that  must lie in the range 0 to 1. Typically, values between 0.2 and 0.8
are used as beyond this range the performance approaches that of no exponential smoothing (=1) or
the smoothed variable remaining constant (=0). Figures 3 and 4 illustrate the effect of varying 
with Ti=Tw=8 and IEP=100%. Typical values used for Ti and Tw elsewhere in the literature are
between 4 and 12, so this range is used in the Taguchi experiments presented below. Depending on
the values of other parameters, small values of Ti can lead to instability.
The retailer shares end-customer demand with the manufacturer that then bases its
production on the weighted sum of end-customer demand and incoming orders from the distributor
(the next echelon in the supply chain). With full information enrichment (IEP=100%) the
manufacturer bases production solely on end-customer demand whilst with no information
enrichment (IEP=0%) production is based solely on the incoming orders from the distributor.
Production can be based on a combination using IEP% of end customer demand plus (100 – IEP)%
of the incoming orders from the distributor; in the iThink model these percentages are referred to as
IEP1 and IEP2 respectively. The simulation results in Figures 5 and 6 show information sharing
damps the peaks in the responses whilst effectively matching settling times. The effect on the
ORATE would be most beneficial to a manufacturing business as the very large fluctuations in
ORATE seen without information sharing would be highly destructive and costly to achieve. The
cost of improving the ORATE is the damping of the inventory response. Whilst the large reduction
in the peak inventory deficit is a good thing, there is a much longer time to replenish the inventory
up to the desired level, causing a much greater period during which there is a risk of stock-out if any
other increases in demand or other supply problems occur. Figures 5 and 6 suggest that a
compromise may be the best solution. In particular, when IEP=75%, the inventory response is much
faster, whilst retaining the benefit of a greatly reduced peak deficit and only a small overshoot of the
desired level. Finding IEP=75% may be better agrees with the results of Jones et al. (1997). So in
the Taguchi Design of Experiments presented below, the IEP levels are chosen around 75%. As
100% information sharing should be investigated to test basing production on end-customer sales
alone, the third value chosen is 50% to keep a constant difference between the levels, i.e. a linear
increase.
October 13-14, 2007
Rome, Italy
6
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
180
150
160
AINV 4
Alpha .2
0
10
20
30
40
50
60
70
-50
Alpha .5
Alpha .8
ORATE 4
50
Alpha .2
Alpha .5
140
Alpha .8
120
-150
-250
100
0
Weeks
Figure 3: Effect of α on AINV 4
10
20
30
40
Weeks
50
60
70
Figure 4: Effect of α on ORATE.
300
300
100
IEP= 25%
0
10
20
30
40
50
60
70
IEP= 50%
-100
IEP= 0%
Orate 4
AINV 4
IEP= 0%
IEP= 25%
200
IEP= 50%
IEP= 75%
IEP= 75%
IEP= 100%
IEP= 100%
-300
100
0
-500
10
20
Weeks
30
40
50
60
70
Weeks
Figure 5: Impact of IEP on AINV 4.
Figure 6: Impact of IEP on ORATE 4.
Measuring the Bullwhip Effect
Different approaches can be applied to measure the Bullwhip Effect. A common approach is
to divide the coefficient of variation of orders placed by the coefficient of variation of orders
received (Fransoo and Wouters, 2000):
Bullwhip = Cout / Cin
where
Cout =  (Dout(t, t+T))/(Dout(t, t+T))
and
Cin =  (Din(t, t+T))/(Din(t, t+T)).
Dout(t, t+T) and Din(t, t+T) are the factory orders and completions during the time interval (t, t+T).
Since demand is deterministic, Cin is constant and only Cout needs to be considered in the analysis.
October 13-14, 2007
Rome, Italy
7
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Taguchi Design of Experiments.
The arguably ubiquitous Taguchi approach is used to identify the effects of different levels of
the design parameters on the measure of the Bullwhip Effect, the interactions that occur and
ultimately the best values. The technique is used to obtain the maximum information with the
minimum number of experiments (Shang et al, 2004). This is valuable in studying supply chain
dynamics as there are a large number of possible parameter value combinations. The choice of
orthogonal array size used in the design of experiment depends on the total degrees of freedom
(DOF) required for the parameters and their interactions. In this study, the DOF for five control
factors with three levels is 5 x (3-1) +1= 11. This leads to choosing the L18 (35) array in Table 1
that defines, for each experiment, the level of each factor (parameter) to be used. The factor levels
used in the experiments reported here are given in Table 2.
Experimental Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Tp
1
1
1
2
2
2
3
3
3
1
1
1
2
2
2
3
3
3
IEP
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
Α
1
2
3
1
2
3
2
3
1
3
1
2
2
3
1
3
1
2
Ti
1
2
3
2
3
1
1
2
3
3
1
2
3
1
2
2
3
1
Tw
1
2
3
2
3
1
3
1
2
2
3
1
1
2
3
3
1
2
Table 1: Inner Arrays ( L18 )
Factor
Level 1
Level 2
Level 3
4
6
8
Information Enrichment Percentage (IEP)
50%
75 %
100%
Alpha (α)
0.2
0.5
0.8
Time to adjust Inventory (Ti)
4
8
12
Time to adjust WIP (Tw)
4
8
12
Production (Pipeline) Delay (Tp)
Table 2: Factors and Levels
October 13-14, 2007
Rome, Italy
8
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Statistical Analysis of Results
The effect of a design parameter on the measured response when the parameter’s value is
changed from one level to another is known as a ‘main effect’ and is calculated for a particular level
of a factor by examining the orthogonal array, the factor assignment, and the experimental results
(Roy, 2001). For example, to calculate the average effect of information sharing (IEP) at Level 1, all
results of IEP at Level 1 are averaged. Figure 7 shows that the Bullwhip Effect measurement is most
sensitive to Tp and Ti is the next most significant factor. The least sensitivity is seen with IEP,
although it must remembered that the experimental range is 50-100% and not 0-100%. It is observed
that reducing Tp minimizes the Bullwhip Effect and this result verifies the time compression
paradigm and the importance of compressing Tp to reduce demand amplification. Increasing the
value of Ti reduces the Bullwhip Effect. Decreasing  increases the damping effect of the
exponential smoother, so it is not surprising that it also reduces the Bullwhip Effect, as does
reducing Tw. An interesting finding is that increasing the information enrichment percentage to
100% reduces the Bullwhip measure used here; there is no optimum around 75% as intimated earlier
and in the work of Jones et al. (1997).
The next step is to explore the interactions among the parameters. Interaction here refers to
factors behaving differently in the presence of other factors such that the trend of influence changes
when the levels of the other factors change. Simple but powerful “interaction graphs” (Figures 8-11)
are used to determine the severity of the interactions between control parameters. If the lines in the
graph are parallel there is no interaction between the parameters, whilst non-parallel lines indicate
interaction with intersecting lines indicating strong interaction (Antony, 2001). Four important
interactions are observed in this analysis. Figure 8 shows the strong interaction between IEP and α.
The value of information sharing is affected significantly by the forecasting error generated due to
inaccurate forecasts. It is important to note that information sharing decreases the sensitivity to α.
The next significant interaction occurs between Ti and α as shown in Figure 9. A third important
interaction is observed between Ti and Tw as shown in Figure 10. Smaller values of Ti yield quicker
responses but poor filtering properties and smaller values of Tw result in larger settling times. Figure
11 shows the small interaction between α and Tw.
400
Output Varaince
300
200
100
Figure 7: The plot of main effect response
October 13-14, 2007
Rome, Italy
9
2
1
3
Tw
Tw
Tw
Ti3
Ti2
Ti1
Al p
ha
1
Al p
ha
2
Al p
ha
3
IEP
3
IEP
2
IEP
1
Tp
1
Tp
2
Tp
3
0
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
500
400
300
Aalpha 1
200
Alpha 2
Alpha 3
100
Output Varaince
Output Varaince
400
Ti 2
200
Ti 3
100
0
0
IEP 1
IEP 2
Alpha 1
IEP 3
Figure 8: Interaction between IEP & α
Alpha 2
Alpha 3
Figure 9: Interaction between α & Ti
400
300
Tw 1
200
Tw 2
Tw 3
100
Output Varaince
400
Output Varaince
Ti 1
300
0
300
Tw 1
200
Tw 2
Tw 3
100
0
Ti 1
Ti 2
Ti 3
Figure 10: Interaction between Ti & Tw
Alpha 1
Alpha 2
Alpha 3
Figure 11: Interaction between α & Tw
In order to discover which of the effects are statistically significant, analysis of variance
(ANOVA) is performed to quantify the contribution of each parameter to the total variation in the
experimental data. The ANOVA results (Table 3) show that Tp makes the largest contribution to the
variation in the measurement of the Bullwhip Effect, with a contribution of 37 % and next is Ti, with
the two parameters accounting for 64% of the variation. The percentage contribution of the
remaining three parameters is much smaller. The F-ratios can also be used to see the relative
significance of the parameters.
Little research has been carried out to identify ‘optimal’ or ‘good practice’ values and
relationships among the different design parameters of supply chains. The best parameter levels
within the range of values considered here are given in Table 4; this is in the context of minimizing
the chosen measure of the Bullwhip Effect. It is found that Tp should be made as small as possible,
which verifies the value of the time compression paradigm for reducing bullwhip. According to the
October 13-14, 2007
Rome, Italy
10
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
measure chosen here 100% information enrichment is preferred. This is contrary to the initial
analysis and the results of Jones et al. (1997). This suggests that further study of how the Bullwhip
Effect should be measured is required. The result indicates the use of a small  and Tw, which will
give faster responses to change, whilst the largest Ti is used to control excessively large fluctuations
in the ORATE by damping the reaction to errors in the inventory.
Factor
Production Delay ( Tp )
Information Enrichment Percentage (IEP)
Exponential smoothing constant ()
Time to adjust Inventory ( Ti )
Time to adjust WIP ( Tw)
Error
Total
DOF
2
2
2
2
2
7
17
Sum of Squares
256454
69063
103297
187016
83875
5612
705317
Variance
28227
34532
51649
93508
41937
802
F-Ratios
160
43
64
117
52
Pure Sum
254850
67460
101694
185412
82271
P
37%
9%
14%
27%
12%
1%
100%
Table 3: Results of ANOVA
Factor
Production (pipeline) Delay (Tp)
Information Enrichment Percentage (IEP)
Exponential smoothing constant (α)
Time to adjust inventory (Ti)
Time to adjust WIP (Tw)
Level
1
100%
0.2
12
4
Level description
4
3
1
3
1
Table 4. Factors at optimal condition
Conclusion
This paper has demonstrated the use of simulation and the Taguchi Design of Experiments
technique to quantify the effects of design parameters in controlling the Bullwhip Effect in supply
chains. An approach to gaining an understanding of the relative contributions of design parameters
and the interactions between them has been presented as an aid to those concerned with designing
and managing supply chain operations. This initial study paves the way for a more detailed study
into controlling the Bullwhip Effect and to extending the supply chain model to incorporate capacity
constraints and order batching, as these are know to be further sources of demand amplification.
References
Antony, J. (2001), Improving the manufacturing process quality using design of experiment: A case
study, International Journal of Production & Operations Management, 21, pp. 812- 822.
Forrester, J.W. (1961), Industrial dynamics, MIT Press and John Wiley & Sons, Inc., New York.
October 13-14, 2007
Rome, Italy
11
7th Global Conference on Business & Economics
ISBN : 978-0-9742114-9-7
Fransoo, J. and Wouters, M.J.F. (2000), Measuring the bullwhip effect in the supply chain, Supply
Chain Management: An International Journal, 5, pp. 78-89
John, S., Naim, M. M. and Towill, D. R. (1994), Dynamic analysis of a WIP compensated decision
support system, International Journal of Manufacturing System Design, 1, pp. 283-97
Jones, S.M. and Towill, D.R. (1997), Information enrichment: Designing the supply chain for
competitive advantage, Supply Chain Management, 2, pp. 137-148.
Lee, H.L., Padmanabhan, V. and Whang, S. (1997), Information distortion in the supply chain: The
Bullwhip Effect, Management Science, 43, pp. 546-559.
Lee, H.L., So, K.C. and Tang, C.S. (2000), The Value of information sharing in a two level supply
chain, Management Science, 46, pp. 626-643.
Li, G., Yan, H., Wang, S. and Xia,Y. (2005), Comparative analysis on value of information sharing
in supply chains, Supply Chain Management, 10, pp. 34-46.
Paik, S.K. and Bagchi, P.K. (2007), Understanding the causes of the bullwhip effect in a supply
chain, International Journal of Retail & Distribution Management, 35, pp. 308-324.
Riddalls, C.E., Bennett, S. and Tipi, N.S. (2000), Modeling the dynamics of supply chains,
International Journal of System Science, 31, pp. 969- 976.
Riddalls, C.E. and Bennett, S. (2002), The stability of supply chains, International Journal of
Production Research, 40, pp. 459- 475.
Roy, R, K. (2001), Design of experiments using the Taguchi approach, Wiley-Interscience, USA
Shang, J, S., Li, S., Tadikamalla, P. (2004), Operational design of supply chain system using the
Taguchi method, response surface methodology, simulation and optimization, International Journal
of Production Research, 42, pp. 3823-3849.
Sterman, J. (1989), Modeling managerial behaviour: misperception of feedback in a dynamic
decision making experiment, Management Science, 35, pp. 321-339.
Towill, D.R.. (1982), Dynamic analysis of an inventory and order based production control system,
International Journal of Production Research, 20, pp. 369-383.
Towill, D.R. (1996), Time compression and supply chain management- a guided tour, Supply Chain
Management, 1, pp. 15-27.
Yu, Z., Yan, H. and Cheng, T.C.E. (2001), Benefits of information sharing with supply chain
partnerships, Industrial Management and Data Systems, 101, pp. 114-119.
October 13-14, 2007
Rome, Italy
12