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Serial versus divergent supply chain networks: a comparative analysis of
the bullwhip effect
Roberto Domínguez Cañizares1 and Jose M. Framiñán1
Roberto Dominguez1, Jose M. Framinan2, Salvatore Cannella3
1 Industrial Management, School of Engineering, University of Seville, Ave. Descubrimientos
s/n, Seville, E41092, Spain; tel: (+34) 954488137; e-mail: rdc@us.es (corresponding author)
2 Industrial Management, School of Engineering, University of Seville, Ave. Descubrimientos
s/n, Seville, E41092, Spain; tel: (+34) 954487214; e-mail: framinan@us.es
3 tel: (+39) 3386263359; e-mail: salvatore.cannella@ist.utl.pt
The amplification of demand variation in a supply chain network (SCN) is a well-known phenomenon called the
bullwhip effect, which creates inefficiencies due to high variation in the order quantities placed between
companies, leading to a flow of a larger number of units than the actual need, increasing stock and generating
stock-outs. Since this phenomenon has been recognized as one of the main obstacles for improving SCN
performance, recently it has received a lot of attention by SCN managers and researchers. One of the most
common simplifying assumptions in the literature is to assume that the SCN adopts a serial structure. The
present work addresses a comparative analysis of the bullwhip effect between a serial SCN and a more complex
divergent SCN. To do so, we adopt the framework proposed by Towill et al. (2007), and analyze the response of
both SCNs under two different input demands: a stationary demand and an impulse demand. The results reveal
that there are not significant differences in terms of bullwhip effect between both SCNs for a stationary demand.
Nevertheless, we show how for a violent disturbance in customer demand there is a great different between the
two SCNs.
Keywords: Bullwhip Effect, Serial Supply Chain, Divergent Supply Chain, Simulation, Multi-Agent Systems,
Shock Behavior.
Published in:
International Journal of Production Research, 52 (7), pp. 2194-2210. 2014.
doi: 10.1080/00207543.2013.860495
1. Introduction
The amplification of demand variation in a Supply Chain Network (SCN) is called the
bullwhip effect (Lee et al., 1997), and it can be defined as the tendency to see an increase in
variability in the replenishment orders with respect to the true demand due to distortion in the
demand information as we move upstream in the SCN (Nepal et al., 2012). As consequence,
orders placed by upstream nodes exhibit a higher variability as compared to that of orders
placed by their downstream partners (Chatfield and Pritchard, 2013). This phenomenon has
many undesirable effects such as increasing stock and generating stock-outs (Adenso-Diaz et
al., 2012).
The bullwhip effect is relevant both for individual companies that face an unnecessarily
variable demand as well as for the entire SCN (Zotteri, 2012). Moreover, the most recent
economic downturn has no doubt created a lot of bullwhips around the world (Lee, 2010). For
instance, the electronics manufacturing sector has experienced something akin to the bullwhip
effect in terms of larger sales declines occurring further upstream (Dvorak, 2009). More
specifically, in the last quarter of 2008, consumer demand had declined 8 percent, while
product shipments fell 10 percent and chip sales fell 20 percent. These data suggest that
electronics retailers, wholesalers and manufacturers responded differently to the decline in
consumer demand (Dooley et al., 2010).
Since the bullwhip effect has been long recognized as one of the main obstacles for improving
the performance of a SCN, it has received in the last years a lot of attention by managers and
researchers (Li, 2012). More specifically, several studies have been generated in the last
decade to better understand the causes, economics consequences and remedies to the bullwhip
effect. In order to analyze this phenomenon under real business world conditions, increasingly
complex mathematical representations of SCNs (such as multi-product scenarios, stochastic
lead times, production/distribution capacity constraints, reverse logistic and so on) have been
developed. However, several assumptions are commonly made to simplify the analysis
(Chatfield and Pritchard, 2013), being one of the most relevant what it can be labeled as a
“serial structure model”, i.e. each echelon k in the system has a single successor k+1 and a
single predecessor k-1. Undoubtedly, the serial SCN system analysis has represented and
continues to represent a powerful technique for studying the dynamics of the bullwhip effect,
but this assumption is seldom verified in real SCNs (Bhattacharya and Bandyopadhyay,
2011). The main reason for the adoption of this modeling structure is probably due to the fact
that most of the studies dealing with supply chain dynamics are based on classical operational
research methods, continuous time differential equation models, and discrete time difference
equation models. Classical operational research methods approaches are not always able to
cope with the characteristics of dynamics SCNs (Riddalls et al., 2000; Long et al., 2011).
Analogously, continuous time and discrete time difference equation models are not always
suitable for analyzing complex supply chain structures outside the serial supply chain, given
the high order of differential equations (one tier generally gives a 2nd-4th order system; 2
tiers even 2nd-6th order), which makes analytical analysis difficult (Holweg and Disney,
2005). Essentially, due to the complexity and mathematical intractability of multi-echelon
systems, the majority of the literature tends to focus on serial two-echelon systems (Hwarng,
2005).
Nowadays, the increasing challenges of the new generation of SCNs such as those mentioned
in Butner (2010), Christopher and Holweg (2011), and Stank et al. (2011), require more
realistic models to analyze the increasing complexity of those structures. Hence, there is a
need to assess the dynamics of SCNs characterized by more than one member in the same
echelon of the chain (Moser et al., 2011; Xuan et al., 2011; Ma et al., 2013). More
specifically, in this work we address one of most common adopted SCN structures in the real
world, i.e. the divergent or arborescent SCN (Beamon and Chen, 2001). Mineral industries
and in general consumer-oriented industries, such as cell phone manufacturers, often adopt
this typology of SCN (Hung, 2011). This structure is characterized by a tree-like structure,
where every stock point in the system receives supply from exactly one higher echelon stock
point, but can supply to one or more lower echelon stock points (Ganeshan, 1999; Hwarng et
al., 2005).
The aim of this paper is to analyze the bullwhip effect of a complex SCN. To do so, we
perform a comparative analysis between a classical serial SCN with a more complex
(divergent) SCN, modeled by means of a multi-agent based-simulation platform named
SCOPE. More specifically we firstly reproduce the four-echelon serial SCN structure (i.e. 1
Retailer, 1 Wholesaler, 1 Distributor and 1 Manufacturer) adopted by Chatfield et al. (2004)
under identical boundary conditions. Secondly, we generate a new divergent multi-echelon
SCN model (i.e. 8 Retailer, 4 Wholesaler, 2 Distributor and 1 Manufacturer) in which each
member is furnished by two downstream members. To perform the study we adopt the
framework proposed by Towill et al. (2007) for studying the bullwhip effect. In this work, the
authors identify three “observer’s perspectives” to analyze the bullwhip effect: Variance lens,
Shock lens and Filter lens. Basically, this framework suggests the typology of endogenous
input that can be adopted in bullwhip analysis in order to study different characteristics of the
SCN. More specifically we adopt two input demand patterns, i.e. the shock lens and the
variance lens. The former aims at inferring on the performance of SCNs for a stationary input
demand. The latter aims at inferring on the performance of SCNs for an unexpected and
intense change in the end customer demand. This latter approach can be viewed as a “crash
test” or a “stress test”: studying the system performance under an intense and violent
solicitation test to determine the resilience of a given SCN structure (Cannella and
Ciancimino, 2010).
The computational results reveal that there are not significant differences in term of bullwhip
effect between a divergent SCN and a serial SCN for a stationary input in customer demand.
However, a violent disturbance in customer demand causes a great different between both
SCNs: the divergent SCN is more sensitive to the higher forecast deviations in customer
demand caused by this violent disturbance, showing higher variance of orders, taking more
time to recover stability, and hence, incurring in higher costs. We can thus conclude that the
divergent structure is less robust than the serial structure.
The rest of the paper is organized as follows: Section 2 presents a literature review. Section 3
describes the methodological approach. Section 4 presents the serial SCN and the divergent
SCN. Section 5 presents the measurement system and the design of experiments. Section 6
presents the numerical results. Finally, Section 7 and Section 8 present findings, limitations,
future directions and conclusions.
2. Literature review
The bullwhip effect is one of the most widely investigated phenomena in the modern day
SCN management research (Nepal et al., 2012). The investigation on this phenomenon has
passed through diverse phases, from empirical and ad hoc studies on bullwhip causes to
mathematical approaches to infer on demand amplification solutions. Bullwhip Avoidance
Phase in the term coined by Holweg and Disney (2005) to identify the current phase of the
studies devoted to the demand amplification phenomenon. One distinctive feature of this
phase is the focus on the efficacy of bullwhip solving approaches (Cannella and Ciancimino,
2010). To accomplish this aim, increasingly complex mathematical representations of SCNs
have been developed to analyse solving approaches under several scenarios, characterised by
reverse logistic, different forecasting techniques, stochastic lead times, collaborative systems,
capacity constraints, batching, parameter configuration, pricing and so on.
Table 1 reports an overview of relevant contributions published during the Bullwhip
Avoidance Phase. Articles are classified according to the focus on the parameters and factors
investigated (e.g., information sharing, lead time, order policy and demand forecasting), and
the typology of SCN structure (e.g. serial and non-serial).
[Table 1 near here]
All aforementioned papers have largely contributed to better understand the causes,
economics consequences and remedies to bullwhip. Regardless the adopted methodological
approaches, the modelled SCN structure and the metrics used to evaluate the SCN
performance, the results have shown how factors such as lead time, the adoption of innovative
order policy, specific forecasting techniques and different customer demand patterns can
impact on the performance of SCN in terms of demand amplification. However, most of the
above-reported studies, in order to quantitatively assess the performance of SCN, have
exclusively adopted the classical single echelon structure or the two-stage serial SCN
(Bhattacharya and Bandyopadhyay, 2011). In other studies, in order to assess the performance
at different level of a multi-echelon system, it has been used the well-know four-echelon
“beer-game” (Sterman, 1989) model (i.e. Retailer, Wholesaler, Distributor and Manufacturer).
However, even in this case, most of those studies have adopted a classical serial SCN
assumption. Essentially, most of the scientific work in SCN dynamics concerns pure
retail/distribution chains or serial SCNs with few stages.
We note that there are only few studies based on the non-serial SCN modelling assumption
investigating the dynamics of SCNs and demand amplification phenomenon. However, most
of these papers do not report any insight on the different dynamics between a classical serial
SCN structure and a divergent SCN structure. To the best of our knowledge, the work of
Sodhi and Tang (2011) is one of the few papers that have reported some insights on the
differences between a serial SCN and a no-serial SCN in terms of their dynamic behaviour.
They report anecdotal evidence of how the bullwhip effect increases as the SCN structure
becomes more complex in an arborescent SCN due to the increase in the number of echelons,
or in the number of successors at each echelon. However, they do not provide any information
on the magnitude of this increment. This finding stimulates the need of further structured
studies on the quantification of bullwhip effect in no-serial SCNs. In our work, by adopting a
structured framework for studying the bullwhip effect, we also clarify and extend the
conclusion by Sodhi and Tang (2011). More specifically, we show how the bullwhip effect
is significantly higher for a divergent SCN compared to a serial SCN in the case of a shock in
the end customer demand. Meanwhile, the bullwhip magnitude is very similar for both SCNs
where customer demand has no shock.
3. Methodological approach
Analytic models, like linear programming, control theory, integer programming and mixed
integer programming, are among the most popular approaches for modeling SCNs. However,
a SCN is a complex adaptive system that involves dynamics, stochastic, and uncertainty (Sun
and Wu, 2005; Surana et al., 2005; Pathak et al., 2007; Wang et al., 2008; Chen, 2012).
Unfortunately, analytical models are unable to cope with these characteristics. In addition,
analytical models may prove impossible to be solved due to their complexity and nonlinearity
(Long et al., 2011). Simulation has rapidly become a significant methodological approach to
theory development in the literature focused on strategy, organizations and SCN management,
due to its ease for modeling and its capability of handling their dynamics and stochastic
behavior (Chan and Prakash, 2012; Munoz and Clements, 2008). Particularly, multi-agent-
based distributed simulation turns out to be one of the most effective tools to model and
analyze SCNs because there is a natural correspondence between SCN participants and agents
in a simulation model (see Swaminathan et al., 1998; Julka et al., 2002; Dong et al., 2006;
Chatfield et al., 2001; Govindu and Chinnam, 2010; Long et al., 2011; Chatfield et al., 2013;
and Chatfield, 2013 among others). A simulation architecture that is able to both view a
complex SCN and examine various causes and their effects at the same time would provide
new insight to the various forces and influences in a SCN (Alony and Munoz, 2007).
SCOPE is an agent-based SCN simulator described in Cañizares and Framinan (2012) for
modeling and simulating different processes taking place in SCN management, focusing in
the Order Fulfilment Process and allowing an easy model of real scale SCN. Every company
in the model can be set up with different policies and parameter values for the different
business functions. The simulator was implemented in Java and uses Swarm (a well-known
software platform for agent-based system development). It has been conceived to be open-
source and help practitioners in their research. Its modular design makes easy to add new
functions and behaviors to the agents and hence, it can be easily customized.
SCOPE uses a two-layer framework for modeling the SCN. The first layer is composed of a
collection of generic agents (Enterprise Agent), each one modeling a company in the SCN
and interacting between themselves. The second layer includes a collection of nine different
functional agents, which have been selected considering the Supply Chain Planning Matrix of
Stadtler (2005). These agents are: Demand Fulfilment Agent, Demand Forecast Agent, Master
Planning Agent, Production Planning Agent, MRP (Material Resource Planning) Agent,
Scheduling Agent, Source Agent, Make Agent and Deliver Agent. Depending on the role
played by the company, the Enterprise Agent will be composed of different combinations of
these functional agents. Figure 1 shows the framework of SCOPE.
[Figure 1 near here]
Cañizares and Framinan (2012) validated SCOPE by comparing the results obtained by other
authors in the literature using different methodologies. More specifically, they followed the
same steps followed by Chatfield et al. (2004) to validate SISCO, a software built by the
authors to simulate the storage, modeling, and generation of SCNs for Integrated Supply
Chain Operations. In SISCO, the user specifies the structure and policies of a SCN using a
Graphical User Interface (GUI) based application, and then saves the SCN description in the
open eXtensible Markup Language (XML) based Supply Chain Modeling Language (SCML)
format. SISCO automatically generates the simulation model when needed by mapping the
contents of the SCML file to a library of supply-chain-oriented simulation classes. The
validation of SISCO consisted of modeling a simple serial four-stage SCN and comparing its
results (in terms of amplification of the standard deviation of orders) with the results obtained
by two well-know authors: Chen et al. (2000), employing a statistical approach, and
Dejonckheere et al. (2003), employing a control engineering approach. Table 2 shows a
comparison between SISCO and SCOPE with the experiments of Chen et al. (2000). In view
of these results, we can conclude that SCOPE can be considered a validated platform for the
subsequent computational experience.
[Table 2 near here]
4. Supply Chain Network employed as Testbed
The serial SCN modeled is that of Chatfield et al. (2004), consisting of four echelons: one
factory, one distributor, one wholesaler, and one retailer (Figure 2). The lower node places
orders to the next upper node and this node fills these orders. The customer does not fill
orders and the factory places orders with an outside supplier. A detailed description is
provided in Chatfield et al. (2004).
A divergent SCN is characterized by a tree-like structure, where every stock point in the
system receives supply from exactly one higher echelon stock point, but can supply to one or
more lower echelon stock points (Hwarng et al., 2005). The divergent SCN is modeled
following the next two guidelines:
1. In order to benchmark both SCNs and to isolate the main effects, the divergent SCN
has to be analogous to the serial SCN of Chatfield et al. (2004). Hence, the resultant
SCN should have identical values of parameters, number of stages (horizontal
complexity) and, due to the divergent topology, an increasing number of nodes per
stage (vertical complexity), maintaining the symmetry of the SCN.
2. Due to the prospective nature of this work, the resultant divergent SCN must have the
minimum complexity. To fulfill with all requirements, each node in the SCN supplies
just two nodes downstream.
The divergent SCN obtained is shown in conjunction with the serial SCN in Figure 2. The
characteristics described in Chatfield et al. (2004) for the serial SCN are adapted to the
divergent SCN as follows:
- Customers Demand. Each customer demand follows the same normal distribution
with mean , estimated by
, and variance
, estimated by
.
- Lead Time. The lead time, L, is stationary and independently and identically
distributed with mean estimated by
, and variance
estimated by
. The lead
time of interest, or “protection period,” in periodic order-up-to systems, may also
include safety lead time or other constant additions to the physical lead time,
depending on the inventory policy or other situational characteristics. According to
Chatfield et al. (2004), all nodes in the SCN use the (R, S) policy (where R is the
review period and S is the order-up-to level) with R=1, and the time period of
protection is L+R. The mean lead time is 4 time units for all nodes in the SCN (not
including the review period, R=1), and 0 for customers. These delays are gamma-
distributed, with a coefficient of variation .
- Lead-Time Demand. Let
be the demand received by node j in stage i during the
protection period L+R. Then
has mean that we estimate by
, and variance
that we estimate by
. Denoting by
the demand received by node j in stage
i at time t + k , we obtain
for an order placed at time t by the convolution:
(1)
- Inventory Policy and Forecasting. The order-up-to level,
, is the base stock that
allows the system to meet the demand during the time period L+R:
(2)
Thus, at the beginning of every period t, each node j in stage i will place an order to
raise or lower the inventory position to
. The term
is an estimation of the
standard deviation of
, and the safety factor used is (service level of
97.72%) , according to Chatfield et al. (2004). To update the
level, a node j in
stage i can access to the demand data from previous periods (used to forecast the
expected demand at time period t,
, and its variance,
), and to the lead time data
from previous periods (used to forecast the expected lead time at time period t,
),
and finally uses this information to generate forecasts of lead-time demand mean
and variance
, as indicated in (3) and (4), respectively:
(3)
(4)
To estimate (
), according to Chatfield et al. (2004), each node uses a p-period
moving averages (MA(p)) and a p-period moving variances (MV(p)) with p=15. To
estimate (
), each node uses running averages, which utilizes data available from all
previous periods.
- Reverse Logistic. With the exception of the customers, all SCN nodes are allowed to
return goods. Thus, replenishment order sizes may be negative.
- Scope of Information. Each node’s SCN knowledge-base is derived from the
incoming demand flow coming from the downstream partners and the outgoing flow
of orders being placed with the upstream partner.
- Timing of Actions. In each time period, each node (in a sequence from downstream
stages to upstream stages, and randomly for nodes in the same stage) performs the
following sequence of actions:
1. Update the order-up-to level (
) using the forecast calculated in the previous
period.
2. Place an order to raise or lower the inventory position to the
level.
3. Receive products from the upstream node.
4. Receive new orders from the downstream nodes and satisfies demand.
5. Calculate a new forecast to be used in the next period.
[Figure 2 near here]
5. Metrics and experiments design
First proposed by Chen et al. (2000), the Order Rate Variance Ratio () is the most widely
used indicator to detect the bullwhip effect (Cannella et al., 2013), measuring the internal
process efficiency and showing the performance of each node in the SCN. It is a demand-
independent measure, allowing the comparison between different SCNs. Nevertheless,
measuring the internal process efficiency at the individual level (single echelon) is insufficient
as it only accounts for the individual performance of each link in the chain separately
(Cannella et al., 2013). Therefore, a network measure has to be used as a complementary
measure of Φ. The Bullwhip Slope (BwSl) summarizes all the ratios obtained for each stage in
a single measure, allowing a complete comparison between different SCNs at the network
level (Ciancimino et al., 2012; Cannella et al., 2013). The procedure to calculate this metric is
to perform a linear regression on the values of Φ using the echelon position as independent
variable (equation 6). A high value of the slope means a fast propagation of the bullwhip
effect through the SCN, while a low value means a smooth propagation. Since BwSl is a
synthesis of Φ, there are similar costs associated to this metric (procurement, overtime and
subcontracting) but at the network level. Below, these two metrics are summarized.
- Order Rate Variance Ratio of a node i (): computed as the ratio of the order variance
in a generic node (
, estimated by
) to the order variance of the end customer
demand (
, estimated by
).
(5)
- : computed as the slope of the linear regression of the Φ curve.
(6)
Being the total number of echelons and the position of the ith echelon.
The above mentioned metrics are easy to apply to a serial SCN, but there is one important
difference when applying them to a divergent SCN, as each stage contains, in general, more
than one node. In the serial SCN, the parameter required to compute the different metrics on
each stage (i.e. the order variance) is taken from the only node in the stage. In the divergent
SCN, it is necessary to find an aggregate measure for the whole stage. To obtain this measure,
the orders of every node j in stage i () are considered at the same time and added, resulting
in an aggregate order pattern for the stage i:
, being the number of nodes in
the stage i. Following the same procedure, the aggregate end customer demand pattern can be
obtained as
, being the number of customers. Then, the aggregate variance
of each stage (
,
) can be estimated (
,
), and is:
(7)
In view of the fact that all the customer demands are assumed to be independent and that each
node places orders independently, the aggregate variance in each stage i is the sum of the
variances of orders of each node j in the stage i (
,
), estimated by (
,
), and
thus, the calculation of :
(8)
Chatfield et al. (2004) analyze the impact of stochastic lead times, information quality and
information sharing on the performance of SCNs, carrying out a factorial experiment utilizing
these three indicators. For the comparison between the serial and the divergent SCNs, we
have taken the following values of these factors from their factorial experiment: lead time
coefficient of variation ; no information sharing; quality of information utilized
for updating the S level shown in equations (3) and (4) (named IQL1 by Chatfield et al.,
2004). These factors remain fixed in our experiments.
For the bullwhip analysis, we adopt the framework proposed by Towill et al. (2007) (see
Section 1). Attending to the variance lens perspective, the demand pattern is the same as in
Chatfield et al. (2004), i.e. demands follows a distribution. Attending to the shock
lens perspective, we use a distribution, which suffer an average increment of
100% in the middle of the simulation time (not considering the warm-up period, see below),
turning into a . These demand patterns are applied to the only customer in the
serial SCN, and to every customer in the divergent SCN.
We design two sets of experiments: the stationary response set and the dynamic response set.
In the stationary response set, in order to compare the performance of the serial and the
divergent SCNs under both lenses, a global measure of Φ and BwSl are obtained for both
demand patterns. In the dynamic set, the temporal evolution of Φ is obtained under the shock
lens in order to analyze the impulse response of both SCNs in detail.
In the first set of experiments, a simulation experiment has been carried out for each SCN and
for each demand pattern. Following the simulation procedure indicated in Chatfield et al.
(2004), each experiment consists in 30 replications of 700 periods, with the first 200 periods
of each replication removed as a warm-up used to set up the system. The results obtained
from the replications are averaged for each experiment. To be able to compare the
experiments under both lenses, metrics are calculated in the same simulation period, after the
impulse time (t=450). The first set of experiments is summarized in Table 3.
[Table 3 near here]
In the second set of experiments, in order to obtain the temporal response, each SCN is
evaluated in different simulation periods. In the first observation, named T0, SCNs are
simulated until the simulation time is just before the demand impulse occurs, obtaining the
initial Φ. Then, Φ is measured in a sequence of experiments where the simulation time starts
at the demand impulse instant and the simulation time is increasing in intervals of 25 or 50
periods until the end of the original simulation time is reached (t=700), resulting in the
experiments T1-T6. As for the first set, each experiment consists in 30 replicates, and the
results obtained are averaged. This set of experiments is summarized in Table 4.
[Table 4 near here]
6. Numerical Results
6.1. Stationary response set
Under the variance lens, results obtained for Φ are very similar for both SCNs (see Figure 3),
being slightly higher for the divergent SCN at the upper stages. However, under the shock
lens there is an important difference between both SCNs, as Φ is considerably higher for the
divergent SCN (see Figure 4). The average results for Φ and BwSl, as well as the differences
between both SCNs (
) are shown in Table 5, together with
the corresponding 99%-confidence intervals.
Under the variance lens, it can be seen that the values of the measures are not statistically
different, which indicates a rather similar performance for both SCNS. At the lower stages,
the increase of Φ is below 1%, while at the upper stages the differences are slightly higher (Φ
is 5.39% higher for the divergent SCN at the distributor stage and 6.08% at the factory stage).
BwSl helps to easily compare both SCNs. The propagation of the bullwhip effect is very
similar for both SCNs, being slightly higher (6.20 %) for the divergent SCN.
[Figure 3 near here]
[Figure 4 near here]
Under the shock lens, the Φ curve is clearly stepped for the divergent SCN, with the
minimum increase at the retailer stage (1.32% over the serial SCN) and the maximum
increase at the factory stage (95.86% over the serial SCN). The bad performance of the
divergent SCN in this case is well summarized by the value of BwSl, being 94.62% higher
than in the serial SCN. Note that the differences in the indicators for both SCNs are
statistically different, thus confirming that the divergent SCN performs worse than the serial
SCN in this scenario.
[Table 5 near here]
6.2. Dynamic response set
Figure 5 shows the evolution of Φ over time for each stage after the demand impulse
(rhomboids dots for the serial SCN and square dots for the divergent SCN). The differences
for Φ observed between both SCNs in Figure 5 are plotted in Figure 6, showing the temporal
evolution of for each stage. Under an unexpected impulse in demand average:
- Both SCNs react by: 1) immediately incrementing their order variances in all stages,
and 2) decreasing their order variances over time.
- The highest increase in Φ takes place just after the demand impulse (T1). The
difference between both SCNs is maximal at this point, being higher as we move
upstream (see Figure 6).
- The shock recovery is similar for both SCNs at the lower stages (retailers and
wholesalers), whereas is near to zero after T3 (see Figure 6). However, at the
upper stages (distributors and factory), shock recovery is slower for the divergent
SCN, obtaining high values of until the end of the simulation time (T6).
[Figure 5 near here]
[Figure 6 near here]
In Figure 7, the order pattern at the factory stage is plotted against the customer order pattern
for both SCNs under the shock lens. It is easy to see the high overreaction of the divergent
SCN when the demand impulse occurs.
[Figure 7 near here]
Finally, a sensitivity analysis has been performed by systematically increasing the level of end
customer standard deviation in the shock lens part of the simulation. The results show that as
the impulse in customer demand variability increases, standard deviation of the orders placed
in the lower echelons does not increase at the same rate. For example, 47.49% increase in
customer demand standard deviation in the shock lens, resulted a 25.96% increase in the
standard deviation of the factory orders. In other words, the increase in the shock was
transmitted in lower proportions towards the upstream levels of the supply chain.
7. Findings and managerial implications
The results obtained in the previous section give new insights on the bullwhip effect research
topic, considering two different lenses for the comparison of two different SCN structures.
Under the variance lens, the following comments can be done:
- The bullwhip effect found in the serial and the divergent SCNs are very similar. When
the demand is predictable and the nodes can adequately adjust their inventory levels to
fulfill the demand with a high customer service level, both SCNs are quasi-
equivalents. A node at the stage i of the divergent SCN causes the same amplification
of orders that a node in the same stage i of the serial SCN, because they have the same
order-up-to and forecast policies. The orders received by each node are proportional to
the end customer demand, and hence, to the amplification of orders caused by them.
As the variance of orders in each stage is rated to the end customer demand variance,
each stage produces similar values of Φ for both SCNs.
- The small increase observed in Φ for the divergent SCN in Figure 3 is caused by
eventual excess of stock or by eventual stock-outs. Due to the uncertainties in the end
customer demand and lead times, sometimes either the demand received may be
different than the demand forecasted in the previous period, or the orders arrive earlier
or later than expected, causing this phenomenon. In these cases, where the inventory
level is far from the desired order-up-to level, a node reacts by ordering a big quantity
of products (a positive order in case of stock-out and a negative order in case of excess
of inventory). These exceptionally high orders are amplified upstream, increasing the
variance ratio mainly in the upper stages. In view of the fact that for each node there is
a certain probability that this phenomenon occurs, and that the divergent SCN has a
higher number of nodes in each stage (higher vertical complexity), it happens more
frequently in the divergent SCN, causing the little increment in the values of Φ at the
upper stages (distributor and factory). As a summary, we can conclude that the
divergent SCN has almost the same performance in terms of bullwhip effect than the
serial SCN when the end customer demand does not suffer important changes.
Using the shock lens, the following comments can be done:
- Under the shock lens both SCNs are stress tested. The end customer demand impulse
causes a massive stock-out situation at the retailer stage, which is then propagated and
amplified along the SCN, causing stock-outs in all the stages of the SCNs. While the
factory in the serial SCN has to manage the instability caused by the stock-out of one
retailer, the same factory in the divergent SCN has to manage it with the stock-outs of
eight retailers. The disproportional orders of the factory and distributors in the
divergent SCN can be observed in Figure 7, and are the cause of: the excess of
variance observed in Figure 4, the high peaks of variances, and the slow recovery
observed in Figure 5.
- The divergent SCN has a bad performance as compared to the serial SCN under
important unpredicted changes in demand tendencies. We can thus conclude that
divergent SCNs are less robust than serial SCNs.
It is worth mentioning the relevance of the framework for the analysis of the bullwhip effect
proposed by Towill et al. (2007). The authors stated that “the detection of bullwhip effect
depends on which lens is used”, and they proposed three different lenses for bullwhip analysis
(variance, shock and filter lens). Our experiments have shown different behaviors depending
on the lens used: while for the classical variance lens analysis (stationary stochastic demand
input) the bullwhip effect is similar for both SCNs, the shock lens analysis (step demand
input) reveals that the divergent SCN performs worse than the serial SCN.
With respect to the managerial implications of the study, to face up with the less robustness of
divergent SCNs, managers may find useful to consider the following:
- Under a shock in end customer demand, the bullwhip effect increases when the SCN
structure becomes more complex as the number of echelons increases, or as the
number of successors at each echelon increases. Thus, to mitigate this incremental
bullwhip effect, a firm could consider simplifying the SCN structure by reducing the
number of echelons or by reducing the number of successors (Sodhi and Tang, 2011).
This is particularly important for SCNs characterized by high variations in the end
customer demand. On the contrary, traditional arborescent SCNs operaing in markets
characterized by a stable consumer demand are less prone to the detrimental
consequences of the demand amplification phenomenon.
- An adequate forecast method adjusted to the end customer demand would prevent the
firm from eventual excess of stock or from stock-outs. Therefore, it is important to
make an effort to implement techniques in order to better understand the end customer
demand tendencies (i.e. surveys) and to anticipate important changes.
- The implementation of well-known techniques for reducing the bullwhip effect (i.e.
information sharing) is highly desirable. These techniques may help managers to have
a better control of the bullwhip effect in case of important changes in the end customer
demand that cannot be anticipated by the above techniques. However, it has yet to be
proved how these techniques (usually tested in serial SCNs) perform in non-serial
SCNs.
8. Conclusions
The literature review has revealed a lack of research on the bullwhip effect topic when the
structure of the SCN is different than a serial SCN. However, real SCNs rarely adopt a
traditional serial structure, often following a more complex topology. The present work is a
first attempt to cover this research gap by analyzing the bullwhip effect in a divergent SCN
and by comparing its performance with those of a serial SCN already analyzed in the
literature by several authors. This analysis has been carried out using the variance lens and the
shock lens proposed by Towill et al., (2007). The bullwhip effect has been observed both
from a static and a dynamic perspective, being measured at the node level by the Order Rate
Variance Ratio (which has been adapted to the divergent SCN), and at the network level by
the Bullwhip Slope.
The main result obtained show that divergent SCNs are more sensitive to unexpected violent
changes in demand signal than serial SCNs. Two situations have been considered:
- Variance lens, i.e. stationary demand signal. In this case the performance of both
SCNs is very similar, being just a little worse for divergent SCNs.
- Shock lens, i.e. demand signal suffers an unexpected violent change. In this case the
performance of the divergent SCN is much worse than that of the serial SCN, showing
higher variance of orders and taking more time for recovery, incurring in higher costs.
Bhattacharya and Bandyopadhyay (2011) indicated that there are operational and behavioral
causes of the bullwhip effect, and that the root of all the causes is the lack of coordination
among the SCN members. Our paper shows that there are also structural factors that amplify
the bullwhip effect caused by those operational and behavioral factors.
Our study is of an exploratory nature since this topic that has not been previously addressed.
Therefore we have tried to not add excessive complexity that may obscure the interpretation
of the results. This comes at the price of a number of limitations that have been identified and
that constitute future research lines. Some of these are:
- The present work is limited by fixed operational factors (order-up-to policy,
forecasting, etc.) and by the SCN structure itself. As underlined by Dejonckheere et al.
(2004), more or less bullwhip could be obtained by selecting other vectors of
parameters. A deeper analysis must be done to better understand this type of SCNs,
considering different operational factors and structural factors (horizontal and vertical
complexity).
- The less robust structure of the divergent SCN might be compensated by a good
information system, in order to share end customer demand (information sharing) and
current inventory levels (synchronized supply, see Cannella and Ciancimino, 2010;
Ciancimino et al., 2012), allowing a faster and proportional response to violent
changes in the end customer demand. Such information system can be adapted to
divergent SCNs and its efficiency tested.
- It has been shown that, in addition to the number of stages, other structural factors
may influence the bullwhip effect. An identification of these factors and a
quantification of their effects could be done.
Acknowledgments
We wish to thank the anonymous referees for insightful comments on earlier versions of the
paper. This research was funded by a grant from the Junta de Andalucía (Spain), grant P08-
TEP-03630, and the Spanish Ministry of Science and Innovation, under the project “SCORE”
with reference DPI2010-15573/DPI.
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Figure 1: Multi-Agent Framework of SCOPE.
Factory
Distributor
2
Distributor
1
Wholesaler
1
Wholesaler
2
Wholesaler
3
Wholesaler
4
Retailer 2
Retailer 7
Retailer 6
Retailer 5
Retailer 4
Retailer 3
Retailer 1
Retailer 8
Customer 2
Customer 7
Customer 6
Customer 5
Customer 4
Customer 3
Customer 1
Customer 8
Stage 1 Stage 2 Stage 3 Stage 4
Factory Distributor Wholesaler Retailer Customer
External
Provider
External
Provider
Figure 2. Serial vs Divergent SCNs.
Figure 3. Φ under the Variance Lens.
Figure 4. Φ under the Shock Lens.
0
10
20
30
40
50
60
70
Customers Retailers Wholesalers Distributors Factory
ΦSerial SCN
Divergent SCN
0
20
40
60
80
100
120
140
160
Customers Retailers Wholesalers Distributors Factory
ΦSerial SCN
Divergent SCN
Order Rate Variance Ratio
Figure 5. Evolution of Φ over time under the Shock Lens.
Figure 6. Divergent SCN Φ increments over the serial SCN.
0
200
400
600
800
1000
T0 T1 T2 T3 T4 T5 T6
Factory
0
50
100
150
200
250
T0 T1 T2 T3 T4 T5 T6
Distributors
0
10
20
30
40
T0 T1 T2 T3 T4 T5 T6
Wholesalers
0
1
2
3
4
5
6
T0 T1 T2 T3 T4 T5 T6
Retailers
0
100
200
300
400
500
600
700
T1 T2 T3 T4 T5 T6
(%)
Factory
Distributors
Wholesalers
Retailers
Figure 7. Factory vs end customer demand order patterns under the shock lens.
-600
-100
400
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
Serial SCN
Factory
Customer
-1500
500
2500
4500
6500
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
Divergent SCN
Factory
Customers
Table 1. An overview of relevant contributions published during the Bullwhip Avoidance Phase.
Chen et al. (2000)
Cachon and Fisher (2000)
Dejonckheere et al. (2002)
Disney and Towill (2003a)
Disney and Towill (2003b)
Dejonckheere et al. (2003)
Chatfield et al (2004)
Dejonckheere (2004)
Disney et al. (2004a)
Disney et al. (2004b)
Machuca and Barajas (2004)
Shang et al. (2004)
Warburton (2004)
Zhang (2004)
Chandra and Grabis (2005)
Gonçalves et al. (2005)
Ingalls et al. (2005)
Byrne and Heavey (2006)
Disney et al. (2006)
Hosoda and Disney (2006a)
Hosoda and Disney (2006b)
Kim et al. (2006)
Lalwani (2006)
Villegas and Smith (2006)
Ouyang and Daganzo (2006)
Zhou and Disney (2006)
Boute et al. (2007)
Chen, Disney (2007)
Disney et al. (2008)
Hosoda et al.(2008)
Jakšič and Rusjan (2008)
Information sharing
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Lead Time
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Order Policy
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Forecast
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Non-Serial
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Kim, Springer (2008)
Aggelogiannaki et al.(2008)
Caloiero et al. (2008)
Kelepouris et al. (2008)
Wright and Yuan (2008)
Agrawal et al. (2009)
Chen and Lee (2009)
Cannella and Ciancimino (2010)
Chaharsooghi and Heydari (2010)
Yuan et al. (2010)
Bottani and Montanari (2010)
Ouyang (2010)
Sari (2010)
Hussain and Drake (2011)
Ali and Boylan (2011)
Dass and Fox (2011)
Barlas and Gunduz (2011)
Cannella et al. (2011)
Yang et al. (2011)
Sodhi and Tang. (2011)
Kristianto et al. (2012)
Adenso-Diaz et al. (2012)
Hussain et al. (2012)
Cannella et al. (2012)
Nepal et al.(2012)
Chen et al. (2012)
Ciancimino et al. (2012)
Su and Geunes (2012)
Chatfield and Pritchard (2013)
Cho and Lee (2013)
Garcia Salcedo et al. (2013)
Li and Liu (2013)
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Table 2: Validation of SCOPE
Echelon
Chen et al. (2000)
Chatfield et al. (2004)
SISCO
Cañizares and Framinan (2012)
SCOPE
Retailer
1.89
1.90
1.90
Wholesaler
3.57
3.59
3.53
Distributor
6.74
6.70
6.66
Factory
12.73
12.84
12.58
Table 3. Stationary response set of experiments.
Bullwhip Effect Lens
Demand Pattern
Structure of the SCN
Metrics
Variance Lens
[0-700]
Serial SCN
Φ
BwSl
[450-700]
Divergent SCN
Shock Lens
[0-449]
[450-700]
Serial SCN
Divergent SCN
Table 4. Dynamic response set of experiments.
Bullwhip Effect Lens
Demand Pattern
Simulation Periods
Structure of the SCN
Metrics
Shock Lens
[0-449]
[450-700]
T0: [200-449]
Serial/Divergent
Φ
T1: [450-475]
Serial/Divergent
T2: [450-500]
Serial/Divergent
T3: [450-550]
Serial/Divergent
T4: [450-600]
Serial/Divergent
T5: [450-650]
Serial/Divergent
T6: [450-700]
Serial/Divergent
Time
Market demand
Time
Market demand
Time
Market demand
Table 5. Numeric results for Φ and BwSl.
Lens
SCN
structure
Φ
BwSl
Retailer
Wholesaler
Distributor
Factory
Variance Lens
Serial
2.2530.0308
6.3290.1766
19.1530.7367
57.7662.6669
13.0430.603
Divergent
2.2580.0289
6.3310.1695
20.1867626
61.2762.6517
13.8520.603
0.222
0.032
5.393
6.076
6.203
Shock Lens
Serial
2.6550.0126
7.7320.1203
23.4530.4962
69.5391.7386
15.7900.394
Divergent
2.6900.0119
8.9230.1188
39.5950.8211
136.1962.8934
30.7300.654
1.318
15.404
68.827
95.856
94.617
Time
Market demand
Time
Market demand
