SIMULATION-BASED ANALYSIS OF THE BULLWHIP EFFECT UNDERDIFFERENT INFORMATION SHARING STRATEGIES
Yuri A. Merkuryev and Julija J. Petuhova
Rik Van Landeghem and Steven Vansteenkiste
Department of Modelling and Simulation
Department of Industrial Management
Riga Technical University
University of Ghent
1 Kalku Street
LV-1658 Riga, Latvia
B-9052 Zwijnaarde, Belgium
E-Mail: email@example.com, firstname.lastname@example.org
customer demand and can base the forecast of demand on theKEYWORDS
actual end customer demand data, instead of on the orders
Bullwhip effect, Supply chain simulation, Information
from the downstream stage. We will compare the different
sharing strategies, Inventory control policies.
strategies from the point of view of the bullwhip effect.
The bullwhip effect is an important observation inABSTRACT
supply chains and suggests that the demand variability
increases as one moves up a supply chain, towards the
This paper describes the impact of two different information
manufacturer or supplier of raw materials.
sharing strategies – decentralized and centralized
In the second section, the background, the importance of
information – combined with two inventory control policies
the bullwhip effect as research topic will be demonstrated.
– min-max and stock-to-demand inventory control – on the
The section 3 on conceptual models will treat the logical and
bullwhip effect. To investigate and measure this impact,
mathematical formulation of the model. The section 4 on
simulation models are developed using the Arena 5.0
model logic in Arena is about the features specific for the
software package for a four-stage supply chain, consisting of
Arena implementation. The experiments and their results are
a single retailer, wholesaler, distributor and manufacturer.
described in section 5.
The experiments with the developed models are described
and the results are analyzed.BACKGROUNDINTRODUCTION
As markets tend to be more and more customer-oriented, the
uncertainty connected with end customer demand and its
Inventory control plays an important role in supply chain
consequences in the supply chain have become an important
management. It is concerned with how much and when to
subject for research. The bullwhip effect is caused by this
order from the supplier. The first policy that will be used in
uncertainty, and several researchers have identified causes to
the simulation models presented in this paper is min-max
this effect and have tried to propose methods to minimize it.
inventory control. It is a variant of the classical reorder point
Chen et al. 1998 and Lee and Padmanabhan 1997 have
model. The main concept of this policy is that the inventory
discussed the main causes of the bullwhip effect. In this
level is continuously monitored and as soon as the inventory
paper, we will try to reduce the bullwhip effect using
level drops below the reorder point a replenishment order
information sharing strategies (centralized information) and
will be triggered. The second policy, stock-to-demand
breaking order batches (changing the frequency of reordering
inventory control, is a variant of the periodic review model.
using two inventory control policies).
The inventory level will be reviewed at predetermined time
Due to the uncertainty and complexity inherent in a
intervals. At this review times, an order will be placed to get
supply chain and in inventory control systems, simulation
the inventory back up to a target level.
was found a suitable tool to analyze the bullwhip effect
In order to determine the parameters of the inventory
(Banks and Malave 1984). Especially the combination of the
control policy, one needs to forecast demand. The amount of
high-level simulation tool Arena and the procedural
information available for a company in the supply chain will
programming language Visual Basic for Applications
determine the accuracy of the forecast of mean demand and
(VBA), proved its usefulness to simulate the systems
of the forecast of the standard deviation of demand.
presented in this paper. The model logic can be represented
According to Simchi-Levi et al. 2000, each stage in the
comprehensibly in Arena, while the more complex
supply chain forecasts demand based on the orders it gets
calculation algorithms can be programmed in VBA.
from the downstream stage in the decentralized information
sharing strategy. By downstream we mean in the direction of
the end customer. In the centralized information sharing
strategy, all stages have access to data about actual endProceedings 14th European Simulation Symposium
A. Verbraeck, W. Krug, eds. (c) SCS Europe BVBA, 2002
This demand forecast will be calculated as the moving
average of the demand during the last ten periods. The same
The combination of two information sharing strategies and
observations will be used for estimation of the standard
two inventory control policies results in four models. The
deviation of demand.
four-stage supply chain used in these models, can be seen in
In the min-max inventory control policy, a
Figure 1, where the solid lines represent the models with a
replenishment order will be placed as soon as the inventory
centralized information structure; the striped lines are
level drops below the reorder point. The order size is the
specific for the models with a decentralized information
difference between a target level, and the effective inventory
structure. This figure illustrates that in the decentralized
level. It is important to remark that replenishment triggering
information structure, the demand forecast is based on the
will be based on the effective inventory level, which is the
orders a stage gets from the downstream stage. In the models
quantity on hand plus the quantity on order minus the
with centralized information structure, the demand forecast
unshipped backorders to customers or the quantity allocated
is based on the actual end customer demand.
Centralized information: all stages have access
to end customer demand data
Decentralized information: all stages base their
forecast on the direct customer’s demand
Figure 1: Conceptual Model
Based on Ballou 1999, the reorder point (ROP) and target
difference between the target level and the effective inventory
level can be calculated as:
level at the review time. According to Ballou 1999, the targetROP
level can be calculated as:d
Tr – the review period;
2 * d
– economic order quantity;
Tss – the safety time.HoldingCost
This safety time represents the safety stock, and is
d – the forecast of average weekly demand;
expressed as a number of weeks of average demand. Its value
LT – the lead time;
is a managerial decision.
Z – the safety stock factor, based on a defined in-stock
probability during the lead time;SIMULATION MODELS IN ARENA
σd – estimation of the standard deviation of the weekly
The general structure of the Arena models is identical for all
The target level is calculated as the reorder point plus the
four models. However, the calculation of the demand forecast
economic order quantity (EOQ), where OrderCost is the fixed
and the inventory, as well as the reordering trigger is different
cost for placing an order and HoldingCost is the cost to hold
for different models, as was indicated in the previous section.
an item in stock during one week.
Certain model parameters had to be chosen. End
Under the stock-to-demand inventory control policy,
customer demands arrive with fixed time-intervals of one
stages will place orders with their suppliers in accordance
week. Their size is variable and is derived from a normal
with a predetermined review period. The order size is the
distribution with mean = 100 and standard deviation = 30. A
constant lead time of 2 weeks will be assumed. No order
processing delay is taken into account, so all demand events
demand will be based on demand data from the ten previous
are treated immediately by the upstream stage. We also will
assume no capacity constraints for the manufacturer. The
estimation of average demand and of standard deviation of
Trigger the code in VBA block 9
if another order shouldDecide
if there are open
This code removes the order arrival
arrive at this time moment. If
backorders that should be
event from the schedule, checks if
the entity; if not, go
treated. If yes, signal value 2
another order should arrive now
to the next decide-block.
for recalculation of backorders
and updates the inventory level and
and then dispose the entity.
quantity on order for the retailer.
As s ig n 3 9
De c i d e i f Re t d e m an d
s h ou l d s ti ll b e h e ld
Si g n a l o rd e r a rri v a l
De c i d e 3 0
a t wh o l e s a l e r
Reset the total size of all
orders arrived in this
L e a d Ti m e
Di s tri b u to r to
W h o l e s a l e r
F re e Re t De m a n d
As s i g n 4 0Delay
for the lead time.
If no backorders should be treated,signal
value 20 to allow the retailer
Schedule the order arrival in
demand for this period to arrive.
array in VBA block 17
Add the arriving order size to the total of
orders arrived in this period. This variable
will then be used in the backorder
recalculation to check if the arriving order
was large enough to cover the total open
Figure 2: Submodel of Order Shipment to Wholesaler
If several events are scheduled to occur at a certain stage
the implementation of this procedure in Arena.
at the same simulation time, there is a fixed order in which the
Implementation in Arena of an order shipment procedure
events should be processed:
from the distributor to the wholesaler is shown in Figure 2.
1. order or backorder arrival from upstream stage
Another important choice to be made concerned
stockouts. In these models, stockouts will not lead to lost
2. fulfilling of backorders (only if an order has arrived)
sales, but to backorders. We thus assume that we have loyal
3. new demand fulfilling.
customers. The calculation of backorders was modeled in
As Arena’s simulation engine didn’t always process the
An example of the backordering procedure
events in this order (Kelton et al. 2002); a procedure had to be
implementation for the wholesaler in Arena can be seen in
developed to guarantee that events are processed in the
mentioned order. Wait and Signal blocks formed the basis of
to the waiting demand from retailer that
backorder has been (re)processed (signal value 20).
The total of all backorders will beDecide
if the arrived order at the wholesaler is
represented by one entity. This decide-
large enough to cover the total backorders. Ifblock
checks if there is already an entity
yes, ship the order; if no loop back and divide
waiting in the hold block that represents
it again into a part that can be shipped and a
the total backorders. If yes, the active
entity is dispose
d, if no, the active entity
will represent the backorders and
proceed to the hold block.
Only one entity to 0 Tr ue
Wait for order
0 Tr ue
Backlog larger than
trigger backlog loop at
to the waiting
demand from retailer
until an order
that backorder has been
arrives at the wholesaler
(wait for value 2).
the order size of the order
shipped to the retailer (= the total
open backorders) and reset the
total open backorders.
Assign the total open backorders as to
the entity as the demand size attribute
and reset the total open backorders
variable prior to recalculation of the
Figure 3: Wholesaler Submodel: Backordering ProcedureRESULTS
It is important that the simulation results are independents
from the empty-and-idle initial state. In addition, there is no
predetermined starting and finishing point for a simulation
run of the system under study. Therefore the simulation study
conducted is a non-terminating system study. After the
determination of the warm-up period, all models were run for
- the arithmetic average of the standard
ten replications, each replication lasting for 10,000 weeks.
As measures of performance for these experiments, the
deviations of demand between stages and σs,i – the standard
standard deviations of demand between stages, the service
deviation of demand between stage s-1 and s.
levels at all stages, and a measure for the bullwhip effect over
Here stage s=0 is the end customer and stage s=5
the entire supply chain will be calculated.
represents the manufacturer’s production facility, while stage
The standard deviations of demand between stages
s=4 is the manufacturer’s stock point.
identify if the bullwhip effect is present. If this is the case, a
This measure takes into account differences in standard
measure for the bullwhip effect over the entire supply chain is
deviation of demand between stages; these differences give an
indication of the seriousness of the bullwhip effect.
The measure of the bullwhip effect over the entire supply
The results of the simulation runs are represented in
chain for the i-th replication can be calculated as
Tables 1, 2 and 3. The standard deviations of demand are also
shown in Figure 4.
Table 1: Standard Deviations of Demand between Stages over all Replications
Standard deviation of demand
End customer demand
Table 2: Overall Measure of the Bullwhip Effect for each Replication
Overall measure bullwhip effect
Table 3: Service Levels for all Stages over all Replications
information structure give better results. The models using a
stock-to-demand inventory control reveal better results than
A first important conclusion to be drawn from the
the models with min-max inventory control from the point of
experiments is that in all four alternatives, the bullwhip
view of the bullwhip effect. This is mainly due to the choice
effect is present. This means that we cannot eliminate the
of the review period, which was chosen as one week, leading
bullwhip effect by sharing end customer demand
to more frequent reordering and thus less batching of orders.
information, not even when we order every week. Under
both inventory control policies, the models with centralized
100Standard deviation of demand
Figure 4: Standard Deviations of Demand between Stages
We can say that the model with centralized informationBIOGRAPHY
structure and stock-to-demand inventory control gave the best
is Habilitated Doctor of Engineering,
An important remark to the conclusions drawn above, is
Professor of the Institute of Information technology at Riga
that no cost consideration was taken into account.
Technical University, Head of the Department of Modelling
An important disadvantage of the measure of the
and Simulation. His professional interests include a
bullwhip effect over the entire supply chain is that it does not
methodology and practical implementation of discrete-event
take into account whether this difference is positive or
simulation, supply chain modelling and management, and
negative. Further research will be aimed at the elimination of
education in the areas of modelling, simulation and logistics
management. He is Programme Director of the curriculum
“Industrial Logistics Management” at Riga TechnicalREFERENCES
University. Prof Merkuryev has wide experiences in
performing research and educational projects in the
Ballou R.H. 1999. Business logistics management
simulation area, at both national and European levels. He
International Inc., New Jersey.
regularly participates in organising international conferences
Banks, J. and C.O. Malave. 1984. “The simulation of inventory
in the simulation area. For instance, he is Track Co-Chair for
systems: an overview”. Simulation
, No.42(Aug), 283-290.
Chen, F.; Z. Drezner; J. Ryan; and D. Simchi-Levi. 1998. “The
“Simulation in Logistics, Traffic and Transport” at the annual
bullwhip effect: managerial insights on the impact of
European Simulation Symposium. Prof. Merkuryev has about
forecasting and information on variability in a supply chain”.
180 scientific publications, including 2 books. He is a Board
Kelton, W.D.; R.P. Sadowski; and D.A. Sadowski. 2002. Simulation
member of the European Council of the Society for Computerwith Arena
. McGraw-Hill Inc., New York.
Simulation International, President of the Latvian Simulation
Lee, H.L. and V. Padmanabhan. 1997. “The bullwhip effect in
Society, and Board member of the Latvian Transport
supply chains”. Sloan management review
, No.38(Mar), 93-
Development and Education Association.
Simchi-Levi, D.; P. Kaminsky; and E. Simchi-Levi. 2000. Designingand managing the supply chain
. McGraw-Hill Inc., Boston.