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Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Vendor Managed Inventory and bullwhip reduction in a two
level supply chain
S.M. Disney and D.R. Towill
Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University,
Aberconway Building, Colum Drive, Cardiff, CF10 3EU, UK.
E-mail: DisneySM@Cadiff.a.cuk, Tel: +44(0)29 2087 6083, Fax: +44(0)29 2087
4301
Abstract
This paper compares the bullwhip properties of a Vendor Managed Inventory (VMI)
supply chain with those of a traditional “serially-linked” supply chain. The emphasis
of this investigation is the comparative impact the two structures have on the
“Bullwhip Effect” generated. Particular attention is paid to the manufacturer’s
production ordering activities as demonstrated using a simulation model based on
difference equations. Each of the four important sources of the Bullwhip Effect is
documented and considered in turn. The analysis shows that with VMI
implementation two sources of the Bullwhip Effect may be completely eliminated, i.e.
rationing and gaming or the Houlihan Effect, and the order batching effect or the
Burbidge Effect. VMI is also significantly better at responding to rogue changes in
demand due to the Promotion Effect or to price induced variations. However the
effect of VMI on demand signal processing induced bullwhip or the Forrester Effect is
less clear cut. The paper concludes that on balance VMI offers a significant
opportunity to reduce the Bullwhip Effect in real-world supply chains.
Key Words
Bullwhip Effect, Vendor Managed Inventory, Supply Chain Dynamics, Production
and Inventory Control.
1. Introduction
It is well established that removing an echelon in a supply chain can be of great
benefit in improving dynamic performance (Wikner, Towill and Naim, 1992). This is
because there is potential for a two-fold improvement. This is firstly due to
elimination of delays in both information and material flow. Secondly a decision-
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
making activity that customarily increases distortion in the order waveform as it is
flows upstream is eliminated (Towill and del Vecchio, 1994). VMI is one practical
way of seeking to obtain the benefits of echelon elimination. Hence the need for a
detailed investigation using the traditional supply chain as a benchmark to be bettered
via a suitable design. As Maloni and Benton (1997) have indicated, there exists a
large amount of literature on the concepts of supply chain partnerships projecting
extremely optimistic views about their promise as win-win partnerships without any
rigorous analysis to support the cause of optimism. This paper is a response to the
shortfall in research that adopts a more rigorous analytical approach to examine
supply chain partnership issues.
Performance Metric Traditional
Supply Chain
(1996)
New Supply
Chain Strategy
(NMS) (1998)
Supply Chain
Network with
PipeChain (2000)
Order lead time
(days)
(from customer’s
order entry to
delivery)
15 5 1
On Time Deliveries
(% of orders
delivered on time)
20% 98% 99.8%
Inventory Turnover
Rate
5 35 80
Total Overhead Cost
(index)
100 120 80
Table 1. Impact of the Change Supply Chain Strategy and Implementation of
NMS
PipeChain Version of VMI at Ericsson Radio Systems
(Source: Gustafsson and Norrman, 2001)
It is already known that when properly implemented, VMI healthily impacts the
bottom line, for example, as shown in Table 1 (Gustafsson and Norrman, 2001). Note
that there has been a two-stage programme of supply chain re-engineering supporting
the introduction of VMI. This is via changed responsibility for orders (NMS phase)
followed by total pipeline control (Pipechain phase). However there are both positive
and negative aspects of implementing the NMS/Pipechain mode of VMI. These are
listed in Table 2, and the downside is a warning to potential users falsely thinking that
implementation is straightforward and trivial. It is good to see that benefits are visible
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
within months. But in a global BPR Programme, Towill and McCullen (1999) have
observed significant improvements in supply chain performance occurring on a year-
by-year basis for some time after changeover. Hence to maximise impact it is
essential to ensure that adequate monitoring systems are in place. These will firstly
ensure that regeneration to previous working practices is avoided, and secondly to
help ensure that beneficial learning curve effects are forthcoming.
A. The Upside
Main benefits visible shortly after an implementation (months)
The investment pays off shortly (months)
The customers and suppliers in the network have gained a greater knowledge and
understanding of each others’ working processes and businesses
The software tool is fast to implement (weeks-month)
The users of the software tool rely on the system and find it logical and process
oriented
The work load for the people working with operative logistics has been less
fluctuating
B. The Downside
Although the concept is easy to understand, accepting the change of working
procedures and shift of responsibility takes time
Even though a standard interface is used to integrate the ERP systems it must be
adapted to the process. This should not be underestimated, it creates work and
takes time
The software tool does not fit certain businesses (e.g. short term relationships with
suppliers and seldom supply)
Table 2. Positive and Negative Experiences of Implementing NMS/PipeChain
Version of VMI at Ericsson Radio Systems
(Source: Gustafsson and Norrman, 2001)
The particular emphasis of this paper is the relative impact these two supply chain
structures have on the “Bullwhip Effect”, (Lee, Padmanabhan and Whang, 1997a and
b) generated in the supply chain, which is investigated using a simulation model.
Focussing on a one supplier, one customer relationship particular attention is given to
the manufacturer’s production scheduling activities. To achieve this aim, an overview
of a traditional supply chain and a VMI supply chain is given. The Bullwhip Effect is
then outlined and the various causes are highlighted. Next, the two supply chain
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
structures are compared with respect to the Bullwhip Effect, with each source being
investigated in turn in order to verify the research findings. This gives confidence to
the potential VMI system performance benefits via time-series displays readily
identified by managers as comparators with present day dynamic behaviour.
2. Using Bullwhip to Assess VMI Capability
The magnitude of the Enterprise Resource Planning (ERP) interface problem
currently facing the manufacturing industry is well known in the literature (Thaler,
1999). Table 3 lists some of the snags already noted by Lee and Whang (2000). It is
clear that substantial financial investment is required to move forward in this respect.
But who pays for the new communication system? Whereas the UK DTI/CBI
expectancy of partnering arrangements was of benefits to be equally shared (Towill
and Naim, 1993), present-day customer pressures have tended to negate this aim. For
example, Clark and Hammond (1997) infer that in much VMI experience to date,
cost-benefit analysis is arguably that the supplier bears the cost of implementation, but
the customer reaps the benefit. Similar conclusions may be drawn from the study by
Lamming (2001) on the Japanese supply chain relationships in recession. He states
that suppliers cannot now rely on retaining business in this new environment. Instead
they must work in innovative ways so as to enable their customers to concentrate on
real-time, market driven configuration of products coupled with minimum stocks in
their supply chains (Lamming, 2001). When implemented properly VMI is clearly a
step in the right direction.
In a recent seminal paper, Buxey (2001) has argued that production strategy drives the
planning process. By having a clear view of what that strategy should be,
management decisions regarding order fulfilment, capacity requirements, workforce-
manning levels (and skills) become simpler and more transparent. The whole
business is then much more readily aligned with the production strategy. As Buxey
points out, the strategy is decided in the knowledge of customer requirements taking
both short term and medium term horizons into account. A careful review of the Case
Studies reported in Buxey (2001) suggests that generally the production strategy
selected is the simplest and most robust capable of satisfying requirements. It is clear
that VMI has much to offer in this scenario. Working closely with the end customer
reduces uncertainty that in turn enables simplicity and reliability of operations.
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
POTENTIAL
SNAGS
DESCRIPTION
MULTIPLE
STANDARDS
There are multiple industry-specific standards. So a company
with multiple business interests has to face dealing with
multiple standards.
INFLEXIBILITY
EDI is designed on a one-size-fits-all basis. It may not meet
the exact needs of any particular supply chain.
LIMITED
FUNCTION
EDI is primarily designed around transaction processing. It
may not cope with other kinds of information sharing such as
databases, bar codes, images etc.
FIXED
OPERATING
MODE
EDI is batch operated. It works only in operational windows.
COST
There is a high financial cost and high resource cost to
installing EDI. This discourages small and medium size
companies.
Table 3. Potential EDI Implementation Snags or Why VMI May Not Happen
Overnight
(Source: Authors Based on Lee & Whang, 2000)
We have selected Bullwhip as a measure of performance because it is a transparent
and readily identifiable metric that can be used to establish if a course of action has
been beneficial to the system. In that sense it is analogous to the use of elapsed time
as an independent and unambiguous metric used for assessing process re-engineering
programmes (Thomas, 1990; Stalk and Hout, 1990). Recent advances in costing the
bullwhip effect include predictions from an OR model developed by Metters (1997).
He concludes that avoidable on-costs range from 10% to 30% (depending on bullwhip
source) calculated at the manufacturing stage alone. As Fisher, Hammond,
Obermeyer and Raman (1997) point out, the on-costs throughout the chain can be
very substantial, especially where an artificially high load is placed on system
capacity. So in that sense the Metters (1997) figures can be regarded as
underestimates. However, in our search herein for generic solutions we concentrate
on bullwhip reduction alone. We believe it is a valid metric for VMI insight and
exploitation in customer/vendor negotiations and in subsequent system re-design. It is
simple enough to satisfy the Buxey (2001) need for basing production strategy around
rules-of-thumb. At the same time it is a meaningful driver towards cost reduction
(Metters, 1997).
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
3. Overview of a Traditional Supply Chain
A supply chain is a system consisting of material suppliers, production facilities,
distribution services, and customers who are all linked together via the downstream
feed-forward flow of materials (deliveries) and the upstream feedback flow of
information (orders), (Stevens, 1989). As shown in Figure 1, in a traditional supply
chain each “player” is responsible for his own inventory control and production or
distribution ordering activities. One fundamental characteristic and problem that all
players in a traditional supply chain (such as retailers, distributors, manufacturers, raw
material suppliers) must solve is “just how much to order the production system to
make (or the suppliers to supply) so as to enable a supply chain echelon to satisfy its
customers’ demands”. This is the production/inventory control problem.
Fabric
maker
Yarn
maker
Garment
maker
High
street
retailer
Flow of orders upstream
Flow of materials downstream
Customers
Order
fluctuations
are typically
+/-5%
Order
fluctuations
are typically
+/-10%
Order
fluctuations
are typically
+/-20%
Order
fluctuations
are typically
+/-40%
(hence
amplification
here+2x2x2=8
times greater
then marketplace
variability)
D
i
r
e
c
t
i
o
n
o
f
d
e
m
a
n
d
a
m
p
l
i
f
i
c
a
t
i
o
n
a
nd
i
n
c
r
e
a
s
i
n
g
v
a
r
i
a
b
i
l
i
t
y
a
n
d
u
n
c
e
r
t
a
i
n
t
y
a
s
t
h
e
w
a
v
e
f
o
r
m
m
o
v
e
s
up
s
t
r
e
a
m
Figure 1. Sequential Information Flow Causing Bullwhip in a “Traditional”
Clothing Supply Chain
(Source: Towill and McCullen, 1999, based on the description by Stalk and
Hout, 1990)
According to Axsä ter (1985), “the purpose of a production/inventory control system
(the method used to control inventory levels and production rates) is to transform
incomplete information about the market place into co-ordinated plans for production
and replenishment of raw materials”. The production/inventory control problem is
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
tackled by practitioners inspecting data relating to demands, inventory levels and
orders in the pipeline. Then, either in a structured, mathematical way (for example,
by using a decision support system with properly engineered, well designed
replenishment rules), or in a less formal way (by using their own experience and
judgement), they place orders up the supply chain. The structure of the traditional
supply chain shown in Figure 1 has developed partly as a result of the need for a
company to be in control of its own assets and partly because, until recently, it has
been uneconomic to pass vast amounts of information around the system. The
traditional supply chain is characterised by each player in the supply chain basing his
production orders or delivery orders solely on his sales to his customer, on his own
inventory levels and, sometimes, on WIP (pipeline) targets. Each echelon in the
supply chain only has information about what their customers want and not on which
products the end customer is actually buying today. The clothing supply chain shown
in Figure 1 typifies this state of affairs. It especially does not allow suppliers to gain
any insight into what their customers are ordering to cover their own Customer
Service Level (CSL) and cost requirements and what the customers are ordering to
satisfy immediate customer demand (Kaipia, Holmström and Tanskanen, 2002).
This lack of visibility of real demand leads to a double-guessing culture. It can and
does cause a number of problems in a supply chain if it is not properly designed and
even then fluctuations in the supply chain cannot be completely eliminated. Such a
state of affairs certainly causes the Forrester Effect, as a particular player over-orders
in response to genuine changes in demand to account for his inventory deviations that
result from the production/distribution lead-time. This over-ordering is then amplified
up the supply chain, creating wide (and wild) fluctuations in the demand signal as it
passes through the supply chain. Those shown in Fig. 1 are typical of real-world
supply chains (Olsmats, Edghill and Towill, 1988). As we shall see later, an
amplification of demand of 2:1 is typical as orders pass through a single supply chain
echelon. Our purpose herein is to look further into the causes of this phenomenon,
and to see how VMI helps to reduce this amplification on a source-by-source basis.
4. The Bullwhip Effect
The “Bullwhip Effect” is a new term (but not a new phenomenon since it has been
debated in the literature for over four decades) coined by Lee, Padmanabhan and
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Whang (1997a, b). It refers to the scenario where the orders to the supplier tend to
have larger fluctuations than sales to the buyer. This distortion subsequently
propagates upstream in an amplified form. Generally speaking, the further upstream
the echelon, the more distorted and amplified is the waveform. Lee et al (1997a and
b) state that there are five fundamental causes of Bullwhip; non-zero lead-times,
demand signalling processing, price variations, rationing and gaming, and order
batching. In any practical supply chain these may all be present and interact as shown
in Fig. 2. Note that we consider both zero lead-time and demand signal processing to
be the essence of the well-known Forrester effect (Forrester, 1961). It is our intention
in this paper to show how each of these bullwhip sources is affected by the
introduction of VMI. This will be done using a dynamic model of a particular VMI
system capable of representing current industrial practice.
T
h
e
B
u
l
l
w
h
i
p
E
f
f
e
c
t
Price fluctuations
or the Promotion
Effect
Rationing
and gaming or the
Houlihan Effect
Order
batching or the
Burbidge Effect
Demand signal
processing and
non-zero
lead-times or the
Forrester Effect
Figure 2. Four Major Causes of the Bullwhip Effect
(Source: Disney and Towill, 2001)
Demand signal processing has in the past been called the “Demand Amplification” or
the “Forrester Effect” after Jay Forrester (1961) who encountered the problem and
subsequently demonstrated it via DYNAMO simulation. The Forrester Effect is also
encompassed by Sterman’s bounded rationality, (Sterman, 1989), terminology that is
common in the field of psychology as used to describe players sub-optimal but
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
seemingly rational decision making behaviour. This particular source of bullwhip
was fully understood and the phenomenon well described and publicised by Stalk and
Hout (1990). It is thus clear that the Boston Consultancy Group were fully conversant
with the existence of bullwhip problems, which they then studied further and
proposed solutions specific via a dynamic simulation.
Order batching is also known as the Burbidge Effect (Burbidge, 1991). It refers to the
practise of placing orders up the supply chain (or on the various manufacturing
processes) in batches. The philosophy behind this action is to gain economies of scale
in set-up activities (such as setting up a specific machine or placing and receiving an
order). It is often the result of the application of an Economic Order Quantity
calculation or similar technique. Burbidge discusses the problems this causes on the
shop floor in considerable detail. To deal with these problems Towill (1997) outlined
the contributions of Forrester and Burbidge for avoiding the Bullwhip Effect brought
together in an integrated approach termed “Forridge”. The Input-Output diagram in
Figure 3 highlights the root causes of demand amplification that can be attributed to
either the Forrester Effect or the Burbidge Effect and in some cases both.
Supply
chain
Avoidable demand
amplification
F
orrester
Effect
Burbidge
Effect
Figure 3. “FORRIDGE” Input-output diagram of demand amplification
resulting from evidence provided by Jay Forrester and Jack Burbidge
(Source: Towill, 1997)
Within the production context, rationing and gaming, or the Houlihan Effect was
highlighted by Houlihan (1987) who recognised that as shortages or missed deliveries
occur in traditional supply chains, customers overload their schedules or orders. This
in turn places more demands on the production system that inevitably leads to more
unreliable deliveries. Customers then increase their safety stock target in a vicious
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
circle that further distorts the demand signal, giving rise to the Bullwhip Effect.
Houlihan has summarised this phenomenon as the Flywheel effect as shown in Fig. 4.
This simple diagram conveys, in terms readily recognised by top management, the
dilemma facing production schedulers in “traditional” supply chains, such as
previously reported in an automotive sector Case Study (Edghill, Olsmats and Towill,
1988). It deserves to be much more widely known and used.
Price variations or the Promotion Effect refers to the practise of offering products at
reduced prices so as to stimulate demand. Assuming an elastic demand, this creates
temporary increases in orders where customers take advantage of this opportunity and
forward buy or “stock up”. However this has serious impacts on the dynamics of the
supply chain, as when the price is released from the discounted level, demand slumps,
creating a perceived need for further discounting in order to stimulate demand. A
famous real-world example is due to Fisher et al (1997), with the resulting time-series
being shown in Fig. 5.
As can be seen, the enticement of a discount offered by Campbells Soups to the
retailer caused an unpredictable change in behaviour to which all suppliers have to
Capacity overload
Demand distortion
Safety stock increase
Shortages
Over-ordering
Unreliable delivery
Fig. 4. The Houlihan Flywheel Describing One Aspect of Bullwhip
(Houlihan, 1988)
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
respond. This produces a typical bullwhip profile with demand being amplified as it
is passed upstream. As can be seen from Fig. 5, this self-induced bullwhip requires a
peak capacity well over twice the average demand. The resultant on-costs are
considerable for all ‘players’ in the chain, including overtime, shift premiums, quality
variances, and additional distribution, handling and storage charges. Furthermore,
actual point-of-sales data suggests that adaptive level scheduling would be sufficient
to meet real demand.
CASES OF CHICKEN NOODLE
SOUP (X10 )
July 1st June 30th
WEEKS
0 10 20304050
SHIPMENTS
ACTUAL
CONSUMPTION
FALSE DEMAND
PEAK INDUCED
BY SUPPLIER
DISCOUNT!
0
4
8
6
2
5
Fig. 5. Example of a Price Discount Induced Bullwhip Recorded in
Campbell’s Soups Supply Chain
(Source: Fisher, Hammond, Obermeyer and Raman, 1997)
5. Measuring The Bullwhip Effect in Real Supply Chains
Many authors have recently supported using statistical measures of the Bullwhip
Effect, for example, Chen, Ryan and Simchi-Levi (2000). Herein ORATE refers to
the orders placed on our supplier and CONS represents sales or consumption by our
customer. The bullwhip effect metric of choice is then:
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
2
2
2
2
/
/
CONS
ORATE
CONS
CONS
ORATEORATE
Bullwhip
……Eq 1
Where;
2
is the unconditional variance of the orders (subscript ORATE) and
consumption (CONS).
is the unconditional mean of the orders (subscript ORATE) and
consumption (CONS).
We may expect, as we are considering a single customer and supplier that the
unconditional means are identical and thus they cancel. There is already a
considerable amount of evidence in the literature that bullwhip exists in real-world
supply chains (as distinct from simulation model results). Fransoo and Wouters
(2000) used statistical techniques to measure the Bullwhip Effect experienced in a
grocery supply chain. They considered the practical aspects of using the standard
deviation ratios (rather then the variance) as a bullwhip measure and concluded that
four Bullwhip metrics should be used. These focus on:
a specific product for a specific outlet;
a specific product demand aggregated across all outlets;
aggregated products for individual outlets;
aggregated outlets against aggregate products.
Fransoo and Wouters (2000) highlight the fact that each bullwhip measure is useful
for investigating somewhat different circumstances. For example, Table 4
summarises the Bullwhip metrics estimated in their particular grocery supply chain.
The four methods of calculation clearly enables bullwhip to be associated in turn with
specific products and/or specific outlets as required by the systems designer.
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Coefficient of Variation
Estimated for
Product Outlet Bullwhip Weighted Average
Bullwhip
Individual Products and
Aggregated Outlets
1 A 2.449
4.20925
2 A 4.796
1 B 4.796
2 B 4.796
Aggregate Products and
Aggregate Outlets
1 (A+B) 2.796
3.6205
2 (A+B) 4.472
Aggregate products and
Individual Outlets
(1+2) A 4.583
4.619
(1+2) (B) 4.712
Aggregate Products and
Aggregate Orders
(1+2) (A+B) 4.712 4.712
Table 4. Bullwhip Found in a Grocery Supply Chain
(Fransoo and Wouters 2000)
Note that Bullwhip Factors yield important insights into the real-world behaviour of
the different ‘players’ in the chain. This is shown in Table 5, based on a European
retail supply chain (Holmström, 1997). He analysed the orders flowing upstream
from the retail outlets right through the various echelons and ultimately back to the
factory. Using the bullwhip measure (Eq 1) Holmström studied in depth a traffic
building (high volume, low margin) product and a low traffic (low volume, high
margin) product. This established that the downstream players (shops and
wholesalers) are the biggest culprits in the particular sense of bullwhip generation.
Furthermore the decision-makers exhibit little difference in their attitude to ordering
policies for either the low margin or the high margin products, with Bullwhip Factors
at around 3 to 1 at each stage. Not so the factory scheduler who clearly matches the
ordering policy to SKU. He visibly treats the two products differently, and
significantly dampens down the demand volatility in the factory orders placed for the
high volume product. This is most likely to have been achieved via some version of
level scheduling (Suzaki, 1987). In contrast, the same scheduler is quite prepared to
induce further substantial bullwhip into the system when considering the low volume
product. Finally, deliveries from the factory also exhibit some bullwhip but it is of a
smaller order of magnitude than that generated by the downstream ‘players’
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Supply Chain
Echelon
High Volume Low Margin
Product
Low Volume High Margin
Product
Coefficient of
Variation
Comments on
Waveforms
Coefficient of
Variation
Comments on
Waveforms
Retailer
2.60 Primarily
Forrester Effect
3.14 Primarily
Forrester Effect
Wholesaler
2.88 Forrester and
Burbidge
Effects
3.05 Forrester and
Burbidge
Effects
Factory
Planner
0.72 Levelled
Scheduling
2.39 Pronounced
Burbidge Effect
Factory
Production/
Distribution
1.67 Forrester and
Burbidge
Effects
1.25 Pronounced
Burbidge Effect
Table 5. Actual Demand Amplification Recorded within a Real-World Supply
Chain
(McCullen and Towill, 2001, based on results by Holmström, 1997)
The composite Bullwhip Factor over the entire retail chain is obtained here by
multiplying together the bullwhip at each stage. The result is 9:1 for the high volume
product, but nearly 29:1 for the low volume product. These results show that
“demonstrator” bullwhip values of 2 or 3 to 1 per stage as recorded by Sterman (1989)
during the playing of the MIT Beer Game are realistic benchmarks. This is good to
verify, as critics of the game have doubted its real-world relevance. In terms of
generation of insight the retail supply chain results puts the value of the game into a
new and enhanced perspective. Inspection of the time series presented by Holmström
(1997) also enables some comment to be made on likely causes of the bullwhip in this
retail supply chain. Those in Table 5 follow from the observations by McCullen and
Towill (2001). They argue that Forrester Effects appear to dominate downstream
ordering, with Burbidge Effects becoming much more evident as the waveform
propagates upstream.
6. Overview of a VMI Supply Chain
In recent years, many companies have been compelled to improve their supply chain
operations by sharing demand and inventory information with their suppliers and
customers. Different industries have coined different terms for VMI, but all are based
essentially on the same idea. VMI is a supply chain strategy whereby the vendor or
supplier is given the responsibility of managing the customer’s stock. For clarity the
term “distributor” for the customer in the VMI relationship and “manufacturer” for
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
the supplier or vendor is the VMI relationship will be used. VMI has become more
popular in the grocery sector in the last 15 years due to the success of retailers such as
Wal-Mart. Additionally, it is only relatively recently that the necessary information
and communication technology has become economically available to enable the
strategy, although Holmström (1998) has shown that it can be readily enabled via fax
or emails and spreadsheets. As proof, Disney, Holmström, Kaipia and Towill (2001)
have implemented VMI in a real-world supply chain using data available from a
popular ERP system and a spreadsheet based decision support system.
Moreover, VMI is not a new philosophy. It was initially discussed by Magee (1958,
pp 298) in a presentation of a conceptual framework for designing a production
control system. Quoting directly from the text (as it prophetically and very concisely
portrays what we believe VMI actually is):
“Frequently there is argument as to who should control inventories. For
example, should it be the sales organisation or (some) other unit that draws on
the stocks and wants to be sure they are there, or the operation that supplies
the stock point and wants to feed it economically? There is probably no
resolution to this question as stated; the difficulty is that both have a legitimate
interest. It is possible to restate the question slightly and reach a solution. The
user has to be sure the material he needs is there. He has corresponding
responsibility to state what his maximum and minimum requirements will be.
Once these limits are accepted as reasonable, the supplier has the
responsibility of meeting demand within these limits, making whatever use he
can of the flexibility the inventory provides. Thus both have a share in the
responsibility for and control over a stock unit. One specifies what the
maximum and minimum demands on the stock unit will be; the other has the
responsibility of keeping the stock unit replenished but not overloaded as long
as demand stays within the specified limits”, Magee (1958, pp298).
VMI comes in many different forms. Familiar names are Quick Response (QR), (Lee,
So and Tang, 2000), Synchronised Consumer Response (SCR), Continuous
Replenishment (CR), Efficient Consumer Response (ECR), (Cachon and Fisher,
1997), Rapid Replenishment (RR), Collaborative Planning, Forecasting and
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Replenishment (CPFR), Holmström et al, (2000) and Centralised Inventory
Management (Lee, Padmanabhan and Whang, 1997a), the terminology depending on
sector application, ownership issues and scope of implementation. However, in
essence, they are all specific applications of VMI that is summarised conceptually in
Figure 6. This is the system to be used to benchmark bullwhip reduction.
VMI
Controls
Business
Ta rgets
Infinite
Material
Stocks
Vending
Stocks(DINV)
Finished
Goods
Stocks (FINV)
Sales (CONS)
Factory
Production lead-time
Distribution lead-time
Despatch
This Number
Set GIT
Stock
Set Target
Stock, R
Completions Despatches
Set Target
Stock (TINV)
S
e
r
v
i
c
e
L
e
v
e
l
s
Production
Orders
Deliveries
T
o
t
a
l
S
y
s
t
e
m
S
t
o
c
k
(
S
I
N
V
)
F
a
c
t
o
r
y
O
r
d
e
r
R
a
t
e
(
O
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A
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)
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(
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)
GIT
Figure 6. Overview of the VMI Scenario
Note that we do not consider those supply chain scenarios that exploit only the data
about end consumer demand in the ordering decisions to be true VMI. We term this
kind of supply chain as possessing “information sharing” and it is a distinct (but
equally valid) strategy. However, the lack of customer inventory information in the
suppliers ordering decision makes it a fundamentally different system. Examples of
information sharing can be found in Yu, Yan and Cheng (2001), Chen, Drezner, Ryan
and Simchi-Levi (2000), Lee, So and Tang (2000) and Mason-Jones and Towill
(1997).
7. Description of the VMI Supply Chain Simulation Model
The difference equations required to model our version of the VMI scenario are
shown in Appendix 1. These difference equations can quickly be turned into a
mathematical model of the VMI supply chain by using z-transforms. The formulation
and exploitation of such a mathematical model is not presented in this contribution
due to space restrictions but can be found in Disney (2001) and Disney and Towill
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
(2001 and 2002). Herein, the difference equation representation will be exploited.
The difference equations may be quickly realised by interested readers in
“spreadsheet” applications such as Microsoft Excel. Difference equations can also be
implemented in standard computer languages with relative ease, as shown in Disney
and Towill, (2001). The specific “flavour” of VMI that the difference equations
represent in Appendix 1 is termed VMI-APIOBPCS, or Vendor Managed Inventory,
Automatic Pipeline, Inventory and Order Based Production Control System.
The VMI term in VMI-APIOBPCS reflects the most significant fact about a VMI
supply chain, i.e. that the distributor (the customer in the VMI relationship) passes
inventory information and Point of Sales (POS) data to their suppliers rather than
orders, (Kaipia et al (2002), Cottrill (1997)). The actual inventory at the customer is
then compared to a re-order point that has been agreed on by both parties. This re-
order point is set to ensure adequate availability without building up excessive stocks.
It triggers a replenishment order that is delivered to the customer if the actual
inventory is below the re-order point in each planning period. Each party also agrees
the order-up-to point, O. The dispatches between the two echelons are equal to the
order-up to level, O, minus the re-order point, R, and the dispatches can be of a
constant or varying size within this framework.
The re-order point is set dynamically so as to reflect perceived changes in demand.
This is done by exponentially smoothing (over Tq time units) the sales signal and
multiplying it by a constant (G) that ensures appropriate customer service levels at the
distributor, taking into account the transportation lead-time between the two parties in
the supply chain. Exponential smoothing was chosen as the forecasting mechanism
because it is; simple to implement in computer systems (requiring less data storage),
readily understood and the most favoured technique by both industrialists and
academics. It should be noted that the net change in the re-order point from one time
period to another is added to the sales signal and the vendor treats this a demand. So,
when demand is increasing and the distributors re-order point grows, the supplier or
vendor treats the stock (re-order point) requirements at the distributor as demand and
incorporates that into his forecasts and stock levels, as he clearly should do.
Obviously, the negative argument also applies, i.e. when the re-order point is reducing
in size over time, demand signals to the manufacture reflect this.
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
The APIOBPCS term reflects the components of the structure of the ordering decision
at the VMI supplier. In words it is “let our production orders be equal to the sum of
three components; the forecasted demand, (exponential smoothed over Ta time units),
a fraction (1/Ti) of the difference between target stock and actual stock and a fraction
(1/Tw) of the difference between target WIP and actual WIP.
8. Description of the Traditional Supply Chain Simulation Model
The APIOBPCS model, John, Naim and Towill (1994), was chosen to represent a
traditional supply chain. This was due to a number of reasons. Firstly it was felt
important that it is desirable that like (APIOBPCS) is compared to like as much as
possible (VMI-APIOBPCS) in order to gain as much understanding as possible on the
fundamental structure of VMI. Secondly APIOBPCS was chosen for VMI and the
traditional supply chain, as it is recognised as good practice, incorporates all
commonly available forms of information, represents human behaviour (Sterman,
1989 and Naim and Towill, 1995) and is a well-understood member of the IOBPCS
(Towill, 1982) family. The APIOBPCS model can be expressed in words as outlined
in the previous section. It incorporates three variables;
Ta, a parameter that describes how quickly demand is tracked in the
forecasting mechanism,
Ti, a parameter that describes of much of the discrepancy between actual
inventory and target inventory levels should be added to the production/
distribution order rate and
Tw, a parameter that describes how much of the discrepancy between actual
WIP and target WIP levels should be added to the production/ distribution
order rate.
Individual echelons, or APIOBPCS models, can be linked together to form a supply
chain, by coupling the ORATE signal of the consuming echelon to the CONS signal
of the supplying echelon, as recognised by Burns and Sivazlian (1978) and further
exploited by Towill and del Vecchio (1994). The difference equations required to
model a two-level APIOBPCS supply chain (for example in a spreadsheet) are shown
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
in Appendix 2. Like the VMI model the production and distribution delays are
arbitrarily assumed to be of four time units.
9. Impact of VMI on the Promotions Induced Bullwhip
To investigate the impact of VMI on the promotions induced Bullwhip Effect, the
Factory Order Rate response of the two supply chain structures to a step input will be
used. This produces a very “rich picture” of the associated system dynamics.
Understanding the dynamic response to a step input will thereby yield insight into
how the system will be affected by various promotions. As there are an infinite
number of designs for VMI and traditional supply chains that might be compared,
previous best practise designs will be used to compare the two supply chains via the
step response. The following designs were chosen to represent good designs of a
traditional supply chain with a production lead-time of 4 time periods;
John et al (1994) recommended settings (Ta=8, Ti=4, Tw=8). This was derived
using classical control theory and simulation and may be considered to a fairly
conservative deign.
Disney et al (1997) recommended settings (Ta=8, Ti=4, Tw=15). This was based
on a Genetic Algorithms search, using Laplace transforms, simulation with the
aim of minimising the Forrester Effect, inventory holding, selectivity, whilst
maximising robustness to errors in estimation of WIP levels and production lead-
times.
Naim and Towill (1995) values of (Ta=8, Ti=4, Tw=4). These were derived from
inspecting Sterman’s (1989) Beer Game derived optimum settings. This may be
considered to a reactive version of the John et al (1994) settings.
Disney (2001) recommended settings (Ta=4, Ti=7, Tw=28). This was based on
the full solution based search using z-transforms and simulation aimed at
balancing the Forrester Effect and inventory holding requirements.
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Operational Setting Parameters of “Optimum” VMI System
G
~
W
#
Ta Ti Tq Tw
1 0.01 1 3 1 3
1 1 6 7 6 42
1 100 18 23 6 63
4 0.01 1 14 1 14
4 1 4 14 4 63
4 100 22 27 6 63
~
G =Re-order point level
#
W=Weighting function used in optimisation routine to trade-off production capacity
requirements against stock requirements
Table 6. Sample Optimum Parameter Values for VMI System Simulation
As outlined earlier, the VMI strategy has 5 key parameters
Tq - the forecasting parameter used to generate the re-order point,
G - the gain on the forecast generated by Tq use to calculate the re-order point,
Ta - the forecasting parameter used to forecast demand by the manufacturer,
Ti – the fraction of inventory error accounted for in a single order and
Tw – the fraction of the WIP error accounted for in a single order
that determine the dynamic response of the system. The terms Ta, Ti, Tq and Tw
depend on the parameter G that is independently set to reflect the desired CSL given
the transportation lead-time between the manufacturer and the distributor, via the re-
order point equation. A full-scale optimisation procedure (Disney (2001) and Disney
and Towill (2002)) has been applied to these parameters for a range of ratios of
production adaptation costs (due to the Forrester Effect) to the associated inventory
holding costs and for different values of the re-order point G. The resulting optimal
parameter settings for Ta, Ti, Tq and Tw for the case when G= 1 and 4 are shown in
Table 6. There is a complex relationship between these parameters for example;
higher values of G generally induce more bullwhip into the manufacturer’s orders.
Furthermore, higher values of Tq help to reduce the bullwhip experienced by the
manufacturer but at the expense of longer inventory settling time. It is not our
intention to explore this here. In this Section it is sufficient to illustrate the VMI
system step response for the case where production adaptation and inventory holding
costs were given equal importance, for the two designs chosen to represent good
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
solutions for a VMI supply chain. Hence the “best practice” settings for the VMI
supply chain used were;
The optimum parameter setting when the distributor has a re-order point level
set at 1 planning periods average demand, (i.e. G=1, Ta=6, Ti=7, Tq=6,
Tw=42)
The optimum parameter setting when the distributor has a re-order point level
set at 4 planning periods average demand, (i.e. G=4, Ta=4, Ti =14, Tq=4,
Tw=63)
It can be seen from inspection of Figure 7 that the VMI design outperforms the
traditional supply chain, with less peak overshoot, faster settling time and a generally
quicker response.
0
0.5
1
1.5
2
2.5
3
3.5
-10 0 10 20 30 40
Time
ORATE
VMI, Ta=6, Ti=7, Tq=6, Tw=42, G=1
VMI, Ta=4, Ti=14, Tq=4, Tw=63, G=4
APIOBPCS, Ta=8, Ti=4, Tw=8
APIOBPCS, Ta=8, Ti=4, Tw=15
APIOBPCS, Ta=8, Ti=4, Tw=4
APIOBPCS, Ta=4, Ti=7, Tw=28
Figure 7. Impact of VMI on the Promotions Bullwhip Effect
10. Impact of VMI on System Induced Bullwhip Effect
We now estimate the impact of VMI on Forrester source induced bullwhip. In Table
7 we have compared VMI and traditional supply chains across a range of performance
metrics. The peak ORATE overshoot is the simple measure of bullwhip already met
in Fig. 7. Note that for completeness Table 7 includes three optimal solutions for each
of the two values of G (1 and 4). These are for ratios of production
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
adaptation/inventory holding costs W = 0.01; W = 1.0; and W = 100. The reason for
this is that W = 0.01 approximates an agile system; W = 100 approximates a lean
(level scheduling) system; whilst W = 1.0 is a compromise solution. As noted by
Christopher and Towill (2000) there are occasions where “agile” is the best business
solution, and where “lean” is the best business solution, and where some “mix” is
required.
For the optimal VMI supply chains, the bullwhip is reasonably unaffected by varying
W for a given value of G. This is because the optimisation programme (Disney,
2001) drives the VMI parameters to yield the best possible response. (As we have
seen in Table 6, the parameter settings to achieve this goal are substantially different.)
If the peak ORATE overshoot is 2.5, then X is a bullwhip effect of 150% and so on.
So comparing the optimal VMI system with the nearest equivalent traditional supply
chain i.e. G = 1, W = 1.0, and with VMI optimal parameter setting, we see VMI
reduces the bullwhip effect from 144% to 69%. Some authors (for example Chen,
Ryan and Simchi-Levi [2000]) use the ratio of order and sales variance as a bullwhip
measure, others (for example Fransoo and Wouters (2000) have been using ratios
involving the standard deviation. Whilst both conceptually similar, the variance ratio
is preferred as this can be calculated directly from a system’s transfer function,
Disney and Towill (2001) or efficiently enumerated with difference equations. Hence
in Table 6 we have included an estimate of variance obtained via evaluation of system
noise bandwidth (Towill, 1982). This bullwhip measure has been reduced from 0.93
(Traditional supply chain) to 0.46 (VMI system), a factor of 2 to 1. So on both
bullwhip measures using VMI is a great improvement in coping with Forrester
sourced bullwhip.
11. The Impact of VMI on the Houlihan Effect
In the VMI supply chain the responsibility for managing the stock at the customer’s
premises clearly lies with the manufacturer. Therefore, the Houlihan Effect is
completely eliminated as the manufacturer is generating the despatches in the supply
chain rather than the distributor. With this configuration it is not possible to “game”
against yourself. VMI has the advantage that on-time delivery does not need to be
monitored, because for as long as there is stock availability at the distributor, no one
cares (including the end customer) if a delivery is missed. In fact, it is unlikely that
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI:
10.1108/01443570310476654.
System
Performance
Optimal VMI supply chain Traditional supply chain
G=0 G=1 G=4
Design 1
“G=0, W=1
equivalent”
Design 2
John et al (1994)
Design 3
Disney et al
(1997)
Ta Ti Tw Ta Ti Tw Ta Ti Tw
W=1 W=0.01 W=1 W=100 W=0.01 W=1 W=100 4 7 28 8 4 8 8 4 15
Bullwhip Measures
Peak ORATE
overshoot
1.6 2.5 1.69 1.21 2.45 1.70 1.22 2.44 2.48 2.99
Noise
Bandwidth/
0.45 5.52 0.46 0.08 4.96 0.59 0.09 0.93 1.1 2.32
2
(calculated
from real time
series)
0.5 5.63 0.5 0.11 5.07 0.62 0.12 1.01 1.31 3.18
Table 7. Impact of VMI on Forrester Sourced Bullwhip Effect
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
the distributor would even know if a delivery is on time, as he does not even generate
orders to compare against shipments.
VMI has another unique advantage over the traditional supply chain; it aligns the
necessary measures of performance required in the VMI supply chain to the customer
expectations, which has also been noticed by Kaipia, Holmström and Tanskanen
(2002). This comes from the fact that the only two measures that are important in the
VMI supply chain (at least in a logistical sense), are whether there is a lost sale due to
a stock-out at the distributor and how much inventory there is in the supply chain, as
this influences the costs to the end consumer. So clearly VMI eliminates one very
common source of bullwhip. It is also arguably the most tenuous and irritating source
of bullwhip. More often than not it is enflamed by secrecy, lack of trust, and the
general adversarial nature of “traditional” supply chains.
12. The Impact of VMI on the Burbidge Effect
The Burbidge Effect in a traditional supply chain can be avoided by despatching every
time period only the requirements for that time period. However, it is often the case
that under such conditions the transportation (or receiving facilities) cost is hugely
inflated. Thus, companies often resort to a batching mentality, thereby introducing a
huge source of Bullwhip Effect into the supply chain. If only the current time
period’s requirements are despatched then, as shown in Fig. 8, the amount transported
will need to change every time period. So there is an apparent conflict between
reducing bullwhip and obtaining economies of scale on transportation costs.
However, the way a VMI supply chain copes with the Burbidge Effect in an
innovative manner, is also shown in Figure 8. This is because VMI allows batching
to occur in the transportation activity between the manufacturer and the distributor,
without introducing the order batching effect into the production order rate. This is
enabled by VMI because of the way the information flow is structured. Recall that in
a VMI supply chain the stock position at the distributor is compared to a re-order
point and if the stock position is below the re-order point then a despatch quantity is
transported to the distributor. This is one side of an IF…. THEN rule. Capturing the
other side of the IF…. THEN rule is done by adding to the distributor’s stock the
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
010203040
Time
Despatches
Traditional Supply Chain
VMI Supply Chain
Figure 8. Impact of VMI on Burbidge Sourced Bullwhip ‘Effect. Comparison
of transportation despatches between the manufacturer and the distributor
echelons in the two supply chain types
goods in transit between the two parties and the manufacturer’s stock position. When
these three stock positions are summed up together the batching disappears from the
supply chain dynamics. This can be easily verified by implementation of the
difference equations in Appendix 1 and 2. It should noted that to account for different
demand rates the frequency of deliveries changes (rather then the size of those
deliveries), in a VMI supply chain, thus permitting much better scope for gaining
economies of scale in transportation and packaging without introducing the Bullwhip
Effect.
13. Discussion of Results
Our simulation model suggests that VMI offers significant opportunities for reducing
the Bullwhip Effect in supply chains. Table 8 summarises the findings in terms of the
four reported sources of bullwhip.
Two sources (The Houlihan and Burbidge Effect) of the Bullwhip Effect may be
completely eliminated by the adoption of VMI in a supply chain. The Houlihan
Effect is sidestepped because of the change in responsibilities in the relationships and
it is unlikely that rationing and gaming effects will be introduced by the manufacturer
on himself. The Burbidge or order batching effect is eliminated by VMI because of
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
the balancing effect of the information flows in the supply chain. The influence of
price variations or the Promotion Effect on the dynamics of the supply chain is also
greatly reduced by the use of VMI.
Approximately 50% less overshoot is generated in a VMI supply chain when demand
shifts to a new level due to a step change in demand rates. Finally the Forrester Effect
in the VMI supply chain exhibits much less variation than a traditional supply chain,
although a traditional supply chain can be designed to reduce the Forrester Effect at
the expense of other criteria, for example stockholding. Importantly however, VMI
requires typically only approximately 50% of the inventory holding in the supply
chain (Disney and Towill, 2001). Thus this paper argues that VMI can significantly
improve the dynamics of supply chains and it simultaneously offers an effective
mechanism for solving the Bullwhip problem.
Source of the
Bullwhip
Effect
Traditional Supply Chain VMI Supply Chain
Price variations
(Promotion
Effect)
Requires 50% increase in capacity
to provide desired Customer
Service Levels
Step responses show that
VMI produces
approximately 50% less
overshoot when responding
to step inputs
Rationing and
gaming
(Houlihan
Effect)
Can make a significant contribution
to Bullwhip in a traditional supply
chain
Completely avoided by VMI
supply chains because of the
change in the nature of the
relationships in the supply
chain
Demand signal
processing
(Forrester
Effect)
The Forrester Effect can be reduced
in a traditional supply chain but it
comes at the cost of twice as much
system inventory holding
In a well designed system it
is easy to substantially
reduce bullwhip to about the
level of a single echelon
supply chain
Order batching
(Burbidge
Effect)
Can make a significant contribution
to Bullwhip in a traditional supply
chain. However, it can be avoided
if deliveries occur every time
period and variable batch sizes are
used
Completely avoided by VMI
supply chains due to the
structure of the information
flows
Table 8. The Impact of VMI on the Bullwhip Effect in Supply Chains
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Our analysis herein has concentrated on the case of a single VMI customer and a
single supplier. We have not considered the case of multiple (VMI and non-VMI)
customers and interacting values streams in the manufacturer. This is a different
problem altogether, but we note that Waller, Johnson and Davies (1999) have
considered such a case. Furthermore, as Burbidge (1991) was at pains to point out,
interacting value streams should be avoided if at all possible and Towill and
McCullen (1999) have shown that BPR principles emerging from a simple generic
model can indeed be exploited in a real world supply chain scenario. We have also
not considered here the impact on tardy or inaccurate information flows on VMI
performance.
14. Conclusions
Our analysis has shown that by adopting VMI can have positive impacts on the
bullwhip problem in supply chains. We have investigated each of the potential
sources of bullwhip identified by Lee et al (1997a and b) and shown that it is possible
to completely avoid two causes of bullwhip altogether. It is also possible to reduce
the impact of other sources of bullwhip. It is clear that VMI can be of great benefit to
the vendor or supplier in a VMI relationship if they correctly use inventory and sales
information in the production and inventory control decision-making process.
However there is relatively little discussion of this in the literature, which has often
focussed on benefits for the customer in the VMI relationship. In our approach has
highlighted that VMI offers benefits for low volume products, which typically suffer
from Burbidge effects, and high volume products that typically suffer from the
Forrester effect.
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
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Appendix 1. The Difference Equations Required to Simulate the VMI-APIOBPCS
Model When Inventory is Treated Separately and Transportation Despatches are
Modelled Explicitly
Description Difference Equations Eq. No
Forecasted Re-order point at
the distributor
)R)CONS*((G
Tq+1
1
+RR
1-tt1-tt
(1.1)
Order-up-to point at the
distributor
ttt
TQRO
,
(1.2)
Distributor's inventory level
Ttt1tt
DESCONSDINVDINV
,
(1.3)
Goods In Transit between
factory and distributor
1Tti
ti
it
DESGIT
, where T is the transportation lead-time,
(1.4)
Despatches
1t1t1-t
1t1t1-t1t
t
RGITDINV if 0
RGITDINV if TQ
DES
,
(1.5)
Transport quantity
ttt
ETQor CONSTQ
, nominally set to equal 4
(1.6)
System inventory levels
t
R
tttt
DINV GIT FINVSINV
,
(1.7)
Factory inventory levels
tt1tt
DESCOMRATEFINVFINV
,
(1.8)
Virtual consumption
ttt
dSSCONSVCON
,
(1.9)
Net changes in the
distributor's re-order point
1ttt
RRdSS
,
(1.10)
Forecasted consumption for
the factory
AVCON AVCON
T
a
VCON AVCON
t-1 t t-1t
1
1
(),
(1.11)
Desired WIP
pT*AVCONDWIP
tt
,
(1.12)
Actual WIP
tt1tt
COMRATEORATEWIPWIP
,
(1.13)
Error in WIP
ttt
WIPDWIPEWIP
(1.14)
Order rate
Tw
EWIP
Ti
EINV
AVCONORATE
1-t1-t
1-tt
,
(1.15)
Completion rate
,ORATECOMRATE
(Tp)-tt
(1.16)
Error in system inventory
levels
ttt
SINVTINV=EINV
.
(1.17)
Typical Test Input
0> tif 10
0< tif 0
CONS
t
, for a step input
(1.18)
Typical Target inventory
0=TINV
t
(1.19)
Disney, S.M. and Towill, D.R., (2003) “Vendor-managed inventory and bullwhip reduction in a two-level supply chain”, International Journal of
Production and Operations Management. Vol. 23, No. 6, pp625–651. ISSN: 0144-3577. DOI: 10.1108/01443570310476654.
Appendix 2. Difference Equations Required for the Two Level APIOBPCS
(Traditional Supply Chain) Simulation Model
These difference equations (where the subscript 1 denoted the distributor variables
and subscript 2 denotes the manufacturer variables) are for modelling a two level
APIOBPCS model are;
Description Difference Equations Eq. No
Distributor's actual WIP
tt1tt
COMRATEORATEWIPWIP
,
(2.1)
Distributor's completion rate
,ORATECOMRATE
)(Tp-tt
1
(2.2)
Distributor's desired WIP
1tt
pT*AVCONDWIP
,
(2.3)
Distributor's error in system
inventory levels
ttt
SINVTINV=EINV
.
(2.4)
Distributor's error in WIP
ttt
WIPDWIPEWIP
(2.5)
Distributor's forecasted
consumption for the factory
)AVCONCONS(
Ta1
1
AVCONAVCON
1-tt
1
1-t
t
(2.6)
Distributor's inventory levels
t
CONSCOMRATEAINVAINV
t1tt
,
(2.7)
Distributor's order rate
1
1-t
1
1-t
1-tt
Tw
EWIP
Ti
EINV
AVCONORATE
,
(2.8)
Distributor's typical target
inventory
0=TINV
t
(2.9)
Manufacturer's Actual WIP
tt1tt
MCOMRATEMORATEMWIPMWIP
,
(2.10)
Manufacturer's Completion rate
,MORATEMCOMRATE
)(Tp-tt
2
(2.11)
Manufacturer's Desired WIP
2tt
pT*MAVCONMDWIP
,
(2.12)
Manufacturer's error in
inventory levels
ttt
MAINVMTINV=MEINV
.
(2.13)
Manufacturer's Error in WIP
ttt
MWIPMDWIPMEWIP
(2.14)
Manufacturer's forecasted
consumption for the
manufacturer
)MAVCONORATE(
Ta1
1
MAVCONMAVCON
1-tt
2
1-t
t
,
(2.15)
Manufacturer's Inventory levels
tt1tt
ORATEMCOMRATEMAINVMAINV
,
(2.16)
Manufacturer's Order rate
2
1-t
2
1-t
1-tt
Tw
MEWIP
Ti
MEINV
MAVCONMORATE
,
(2.17)
Manufacturer's typical target
inventory
0=MTINV
t
(2.18)
Typical test input
0> tif 10
0< tif 0
CONS
t
, for a step input
(2.19)
