Reading Assignment Report-IIPlease thoroughly go through the R.docx

Reading Assignment Report-II
Please thoroughly go through the Reading Assignment posted
under Chapter 8 on Moodle (Vanteddu et al., 2006, Research
Publication) at least twice.
Please make a summary of the research article in your own
words that is at least two pages in length, clearly identifying the
purpose, research contribution and conclusions of the research.
Provide appropriate citations of the works referred to in your
summary. Your summary must be typed. Please use
appropriate font and 1.5 line spacing.
The material posted on our course website;
Understanding the concepts;
Want to have a one-to-one demonstration of solving a given
problem;
Questions about your grade and where you stand at a given
point of time in the semester etc.
Supply chain focus dependent safety stock placement
Gangaraju Vanteddu Æ Ratna Babu Chinnam Æ
Kai Yang Æ Oleg Gushikin
Published online: 18 April 2008
� Springer Science+Business Media, LLC 2008
Abstract Increasing globalization, growing product range
diversity, and rising
consumer awareness are making markets highly competitive,

forcing supply chains
to adapt constantly to different stimuli. Growing competition
between supply chains
(as well as players within them) is also warranting a priority for
overall supply chain
performance over the goals of individual players. It is now well
established in the
literature that, among the many order winners, both overall
supply chain cost and
responsiveness (i.e., supply chain lead time) are the most
significant determinants of
supply chain competitiveness. The literature, however, mostly
focuses on supply
chain cost minimization with rather simplistic treatment of
responsiveness. By
introducing the concept of a coefficient of inverse
responsiveness (CIR), we facil-
itate efficient introduction of responsiveness related costs into
the scheme of supply
chain (SC) performance evaluation and/or optimization. Thus,
our model aids
supply chain managers in achieving better strategic fit between
individual business
unit strategies and overall supply chain requirements in terms of

cost efficiency and
responsiveness. In particular, it aids in strategic placement of
safety stocks at dif-
ferent stages in the supply chain. Our model also offers
managerial insights that help
improve our intuitions into supply chain dynamics. The model is
more suited for
G. Vanteddu � R. B. Chinnam (&) � K. Yang
Department of Industrial & Manufacturing Engineering, Wayne
State University,
4815 Fourth Street, Detroit, MI 48202, USA
e-mail: [email protected]
G. Vanteddu
K. Yang
O. Gushikin
Ford Research and Advanced Engineering, 2101 Village Road,
Dearborn, MI 48121, USA
123
Int J Flex Manuf Syst (2007) 19:463–485
DOI 10.1007/s10696-008-9050-z

strategic SC alignment, for example, when dealing with product
changeovers or
introduction of new product, rather than for operational control.
Keywords Supply chain strategy � Business strategy � Safety
stock costs �
Cost of responsiveness � Supply chain cycle time � Coefficient
of inverse
responsiveness
1 Introduction
In today’s dynamic global market environment, it has become
necessary for
organizations to focus upon all the relevant performance
metrics. Hill (1993)
advocates close attention to functional perspectives, customers’
views, and actual
orders while determining order winners and qualifiers. Among
the possible order
winners, supply chain (SC) cost and responsiveness turn out to
be more crucial than
others. Responsiveness here is the ability of the supply chain to
respond quickly to
changing customer needs, preferences, and options through
improved supply chain

cycle time (i.e., velocity), and not the higher service levels
achievable through
increased distribution of channel inventory. The optimal supply
chain strikes the
right balance between supply chain cost efficiency and
responsiveness, depending
on the nature of product(s) supplied by it.
Figure 1 divides the cost-responsiveness spectrum of the SC
into four basic
quadrants, and provides some indications of their
appropriateness. In reality, the
treatment will not be that distinct, and depending on the type of
products and
markets targeted by the SC, the focus could be anywhere on the
spectrum. In this
context, Fisher (1997) emphasizes the importance of
considering the nature of
product demand before devising the respective supply chains.
More precisely, one
needs to account for both the nature of the product as well as
uncertainty from both
demand and supply in designing the SC (Chopra and Meindl
2004). Similar
comments have been echoed in industry literature. Nazzal et al.

(2006) present a
case study for Agere Systems, focusing upon the increase of
market share and
profits by reducing lead times in the highly competitive
semiconductor manufac-
turing industry. So is the example of Revlon whose supply chain
includes more than
5,000 active finished good stock keeping units (SKUs) with
product lifecycles
spanning less than 3 years. To meet aggressive inventory
reduction targets and
achieving high customer service levels, Revlon is emphasizing
reduction of
manufacturing and supplier lead times and the associated
variability (Davis et al.
2005). Yang and Geunes (2007) emphasize that longer lead
times, in addition to
reducing customer responsiveness, increase demand forecast
error, since forecast
error generally increases as the forecast horizon increases. In
addition, longer lead
times expose the supply chain to more in-process inventories,
design changes,
degradation, accidents, changes in demand patterns, etc.

(Felgate et al. 2007), which
in turn increase the supply chain costs. In summary, striking the
right balance
between supply chain cost efficiency and responsiveness is
critical, which can be
neglected at one’s own peril. On the contrary, existing literature
overly focuses on
just one order winner: cost efficiency.
464 G. Vanteddu et al.
123
There are primarily four drivers influencing the performance of
the SC, namely,
infrastructure, inventories, transportation, and information
(Chopra and Meindl
2004). Given our assumption that the necessary network
topology is already in
place, we do not need to include infrastructure related cost
elements and
transportation related aspects explicitly in our model. These
issues, however, are
addressed in an indirect fashion in our model. For example, cost
added at a stage can

be considered to be a function of fixed costs associated with
infrastructure such as
location, buildings, machinery, etc. and transportation to the
immediate downstream
(D/S) stage. Even though we are developing the model assuming
that all the stages
are involved in manufacturing, a stage purely dealing with
transportation could be
easily accommodated. We are also assuming information
symmetry at all the stages
and leave information asymmetry related issues for future
research. Thus, we are
primarily considering the inventory cost driver in our model.
Among inventory cost elements, safety stock, maintained to
account for the
internal and external variability in the supply chain, is vital in
the sense that it
directly affects customer satisfaction and constitutes a
significant portion of the cost
of goods sold (COGS).
In summary, in terms of supply chain strategy, one can choose
to compete purely
on price (for a commodity product) or product velocity (fashion

industry, for
example) or choose a third path, a niche strategy, a hybrid of
the other two
(Cherukuri et al. 1995). Our research primarily focuses upon the
third strategy,
where there are opportunities to be exploited with respect to
both order winners.
The rest of this manuscript is organized as follows: Sect. 2
discusses relevant
literature; Sect. 3 deals with development of the overall cost
expression for the
supply chain, which accounts for supply chain (SC)
responsiveness; Sect. 4 offers
managerial insights into strategic safety stock placement in a
serial supply chain;
Sect. 5 describes how one can use the model for achieving the
strategic fit; finally,
H
ig
h
L
ow
C
os

t
Low High
Responsiveness
Poor
Strategy
Short
Lifecycle
Products
Mass
Production
Ideal
Strategy
Fig. 1 Supply chain responsiveness versus cost (source:
Vanteddu et al. 2006)
Supply chain focus dependent safety stock placement 465
123
Sect. 6 offers conclusions and limitations that should be
addressed in future
research.
2 Literature review

Gallego and Zipkin (1999) develop and analyze several heuristic
methods to study
the problem of stock positioning in serial production-
transportation systems and
offer a number of interesting insights into the nature of the
optimal solution. A
stochastic service model as advocated by Graves and Willems
(2003) addresses the
issue of strategic placement of safety stocks across a multi-
echelon SC in the
presence of demand uncertainty. As with Graves and Willems
(2003), the primary
emphasis of our research is to provide decision support for SC
design, rather than
SC operation, and the intent is not to find inventory control
policies as is the case
with much of the multi-echelon inventory literature. Another
common feature is that
the local decisions (decentralized control as opposed to central
control) are made at
each stage based on local information. It is worth noting at this
point, as supported
by Graves and Willems (2003), that a SC subjected to
decentralized control is not

equivalent to a SC being locally optimized. In an optimization
context, the model
attempts to find the optimal parameter values, under the
assumption of decentralized
control, that minimize the total SC cost. The primary purpose of
their model is to
develop a multi-echelon model, and the relevant optimization
algorithm is
specifically designed for optimizing the placement of safety
stocks in a real-world
SC. Unlike Graves and Willems (2003), where inventory is the
only lever to counter
demand and supply variability, our model has two levers,
namely, echelon inventory
and responsiveness (cycle time).
The supply chain configuration problem, a special case of the
supply chain design
problem, consists of the set of decisions that are made after the
network design that
act to configure each stage in the network by taking into
account certain relevant
parameters; see Graves and Willems (2003), who argue that the
central question is
to determine what suppliers, parts, processes, transportation

modes (called options)
to select at each stage in the supply chain. Our model is similar
in spirit to their
optimization model (Graves and Willems 2003). The primary
similarity is that both
models balance the increase in cost of goods sold (COGS)
against the decrease in
inventory related cost, though the two models differ
significantly with regard to the
methodology adopted and serve different end purposes.
For a stochastic service model (Graves and Willems 2003;
Simchi-Levi and Zhao
2005; Lee and Billington 1993; Ettl et al. 2000), which we have
adopted in our model,
we assume that the increase in cost at a stage depends on the
opportunities that exist for
resource flexibility and model it as a continuous function of a
novel dimensionless
parameter called the coefficient of inverse responsiveness
(CIR), with a focus on: (a)
developing managerial insights with regard to strategic safety
stock placement in a
serial supply chain and (b) achieving strategic fit between the
supply chain strategy and

the individual business strategies for a given set of parameter
values.
Assuming an installation, continuous time base stock policy for
supply chains
with tree network structures, another interesting paper that is
based on the stochastic
123
service model concept is that by Simchi-Levi and Zhao (2005)
in which they derive
recursive equations for the back order delay (because of stock
out) at all stages in
the supply chain, and, based on those recursive equations,
dependencies of the back
order delays across different stages of the network are
characterized and useful
insights with respect to the safety stock positioning are
developed in various supply
chain topologies. The two other papers that use a stochastic
service approach that
are relevant to our research are those by Lee and Billington
(1993) and Ettl et al.

(2000). We share the ample production capacity assumption
with Simchi-Levi and
Zhao (2005) and Graves and Willems (2003). For capacitated
models using a
modified base stock policy, the reader can refer to Glasserman
and Tayur (1995,
1996) and Kapuscinski and Tayur (1999). Simchi-Levi and Zhao
(2005) enhance the
work of Gallego and Zipkin (1999) and provide stronger results.
They also point out
through their computational study of the Bulldozer supply chain
problem (Graves
and Willems 2003) the perils of ignoring lead time
uncertainties, which is accounted
for in our model. In addition, Simchi-Levi and Zhao (2005)
present a nice summary
of the literature for installation policies that are used in various
network topologies:
multistage serial systems (Simpson 1958; Hanssmann 1959; Lee
and Zipkin
1992) and distribution systems (Axsäter 1993; Graves 1985; Lee
and Moinzadeh
1987a, b).

Given the size and complexity of supply chains such as those
found in the
computer, electronics, and auto industries, a common problem
for asset managers is
not knowing how to quantify the trade-off between service
levels and the investment
in inventory required to support those service levels (Ettl et al.
2000). This problem
is compounded by the response related performance measures.
Similar to Ettl et al.
(2000) model, our model is also intended to be a strategic model
not caring much
about the operational details.
Eppen and Martin (1988) present a very nice critique of the
standard procedure
using a (Q,r) model for setting safety stocks in the presence of
stochastic lead time
and demand. Chopra et al. (2004) build on the work of Eppen
and Martin (1988) but
their focus is on the flaws in the managerial prescriptions
implied by the normal
approximation. In particular they infer the following by using
the exact demand
during the lead time instead of the normal approximation: For
cycle service levels

above 50% but below a threshold, reducing lead time variability
increases the
reorder point and safety stock, whereas reducing the lead time
decreases the reorder
point and safety stock. Our research addresses the issue of
reducing lead time
variability indirectly as a result of reducing the lead time
because of the flexibility
options available at a stage.
For a thorough comparison of installation and echelon stock
policies for
multilevel inventory control, the reader is referred to Axsäter
and Rosling (1993),
who primarily consider serial and assembly systems and prove
that for (Q,r) rules
echelon stock policies are, in general, superior to installation
stock policies.
Advocating the necessity of models that include both cost and
responsiveness,
Moon and Choi (1998) suggest extending the lead time
reduction concept to
different inventory models to justify the investment to reduce
the lead times. Choi
(1994) used an expediting cost function to reduce the variance

of suppliers’ lead
times.
123
As opposed to network design models that focus on the trade-off
between the
fixed costs of locating facilities and variable transportation
costs between facilities
and customers, Sourirajan et al. (2007) present a model for
single-product
distribution network design problem with lead times and service
level requirements,
which enables them to capture the trade-off between lead times
and inventory risk
pooling benefits. The objective is to locate distribution centers
(DCs) in the network
such that the sum of the location and inventory (pipeline and
safety stocks) is
minimized. Our CIR concept is similar in spirit to the
replenishment lead time
calculation at a DC (Sourirajan et al. 2007), which depends
upon the volume of flow

through the DC.
One very interesting (Q,r) model with stochastic lead times that
could serve as a
building block in supply chain management was proposed by
Bookbinder and
Cakanyildirim (1999) as opposed to the constant lead time
assumption in many
other studies. This paper introduces a term called an expediting
factor for the lead
time, which is similar in spirit to the dimensionless quantity
proposed in our model,
CIR. Ryu and Lee (2003) consider dual sourcing models with
stochastic lead times
in which lead times are reduced at a cost that can be viewed as
an investment. They
make use of the concept of expediting factors proposed by
Bookbinder and
Cakanyildirim (1999) in their model. They analyze (Q,r) models
with and without
lead time reduction and compare the expected total cost per unit
time for the two
models.
Even though we did not consider product mix flexibility related
issues in our

model, the reader can refer to Upton (1997) to explore the
relationship between
process range flexibility and structure, infrastructure and
managerial policy at the
plant level. We assume information symmetry at all the stages
in our model. The
effect of information sharing for the time series structure of the
demand on safety
stocks is addressed in Gaur et al. (2005).
3 Model development
This section mostly develops the total cost expression, made up
of safety stock costs
and responsiveness related costs, for a serial supply chain.
3.1 Expression for safety stock costs
We follow the building block model (Graves and Willems 2003)
with installation
base stock policies and a common underlying review period for
all stages. A
typical base stock policy works as follows. When the inventory
position (i.e., on-
hand plus on-order minus back orders) at stage i falls below
some specified base
stock level Bi, the stage places a replenishment order, thereby
keeping the

inventory position constant. Simchi-Levi and Zhao (2005)
attribute the popularity
of the base stock policy to the fact that it is simple, easily
implementable, and has
been proven to be optimal or close to optimal in many cases.
For example, in
serial supply chains with zero setup costs and without capacity
constraints,
because the installation base stock policy is equivalent to an
echelon base stock
123
policy under certain initial conditions (Axsäter and Rosling
1993), it is indeed
optimal in these cases (Clark and Scarf 1960). In serial systems,
even a modified
base stock policy with capacity constraints is still close to
optimal (Speck and van
der Wall 1991; van Houtum et al. 1996).
In an installation policy, each facility only needs the inputs
from the immediate
upstream (U/S) and downstream (D/S) facilities and makes

ordering decisions based
on its local order and inventory status (Simchi-Levi and Zhao
2005) as opposed to
an echelon base stock policy, which is a centralized control
scheme that allows for a
central decision maker to coordinate and control the actions at
all stages in the SC
(Graves and Willems 2003).
Even though our model assumes all stages to be manufacturing
stages, without
loss of generality, a stage could be modeled as a DC as well. A
pure transportation
function can also be modeled with the building block concept,
wherein the transport
time is the lead time with pipeline inventories.
Orders are placed at discrete time intervals and each stage is
considered as a
building block (Graves 1988) that generates a stochastic lead
time. A building block
is typically a processor plus a stock keeping facility. Depending
on the scope and
granularity of the analysis being performed, the stage could
represent anything from

a single step in manufacturing or distribution process to a
collection of such steps to
an entire assembly and test operation (Graves and Willems
2003). Demand is
assumed to be stationary and uncorrelated across
nonoverlapping intervals and there
are no capacity constraints.
Our model is designed as a decentralized supply chain (Graves
and Willems
2003; Lee and Billington 1993) to mimic reality more closely,
with each stage
following a local base stock policy. Supporting the same view,
Lee and Billington
(1993) state that organizational barriers and restricted
information flows between
stages may result in complete centralized control of material
flow in a supply chain
not being feasible or desirable.
The primary distinction between centralized and decentralized
supply chain is
put in the following succinct form by Lee and Billington (1993)
‘‘Centralized
control means that decisions on how much and when to produce
are made centrally,

based on material and demand status of the entire system.
Decentralized control, on
the other hand, refers to cases where each individual unit in the
supply chain makes
decisions based on local information’’.
Assuming that each building block operates independently using
a simple
installation policy, one can first characterize various building
blocks such as serial,
assembly, distribution, etc. and then identify the links among
these building blocks
(Simchi-Levi and Zhao 2005). We have chosen series system for
simplicity of
analysis and primarily to develop certain insights that are
insensitive to the specific
supply chain topology. Also, other networks such as assembly
system can be
reduced to an equivalent series system (Rosling 1989). Most of
the features are
similar to the features of a serial system presented in Gallego
and Zipkin (1999)
with some modifications.
There are several stages or stocking points arranged in series.

The first stage
receives supplies from an external source. Demand occurs only
at the last stage.
Demands that cannot be fulfilled are immediately backlogged.
There is one product,
123
or more precisely, one per stage. To move units to one stage
from its predecessor,
the goods must pass through a supply system representing
production or
warehousing activities. There is an inventory holding cost at
each stage and our
model does not consider back-order penalty cost, which could
easily be included.
The horizon is finite, all data are stationary, and the objective is
to evaluate the
performance and optimize depending upon the supply chain
focus on the cost–
responsiveness spectrum. Information is centralized but control
is decentralized.
As in Gallego and Zipkin (1999), the numbering of the stages

follows the flow of
goods; stage 1 is the first, and demand occurs at the last stage.
The external source,
which supplies stage 1, has ample stock and it responds
immediately to orders
(Fig. 2).
We have assumed that the service level targets required at each
of the players
are exogenous, i.e., they are dictated by the immediate D/S
player or the final
customer. Following Graves and Willems’ (2003) treatment of
stochastic service
model in supply chains, let U(k1), …, U(kn) be the service
levels for
corresponding safety factors k1, …, kn where U(ki) represents
the cumulative
distribution function for a standard normal variable. kj is the
multiplying factor for
the variability term for stage j, which along with the average in
process inventory
would give the expected base stock to achieve a given service
level. Let the
processing time at stage j be a random variable sj (measured in
time periods) with
mean Lj and variance r2j :
The stochastic service model (Graves and Willems 2003;
Simchi-Levi and Zhao

2005; Lee and Billington 1993; Ettl et al. 2000) assumes that
the delivery or service
time between stages varies based on the material availability at
that stage and that
each stage in the supply chain maintains a base stock that is
sufficient to meet its
service level target (Graves and Willems 2003). If Di is the
random delay at the
preceding stage i, then the replenishment cycle time at stage j
equals
cj ¼ sj þ Di: ð1Þ
We have adopted the procedure for calculating this delay due to
the stock out at the
preceding stage as presented in Graves and Willems (2003) and
Ettl et al.(2000)
with a modification that takes into account the fact that there is
only one player at
the preceding stage. Thus, we are assuming that the expected
value of this delay is
simply equivalent to the probability of stock out at the
preceding stage pi times its
average processing time.
Therefore, expected replenishment cycle time at stage j is given
by

E cj
� �
¼ Lj þ piLi; ð2Þ
where
pi ¼ 1� UðkiÞ ð3Þ
Assuming that the demand is N(l,r2 ), where l is the mean
demand during one time
period and r2 is the demand variance during one time period, to
satisfy average
demand l, given the average replenishment cycle time from (2),
the average cycle
stock is given by
123
l� Lj þ 1� UðkiÞð ÞLi
� �
: ð4Þ
Assuming the independence of processing times at a stage and
between the stages,
we realize that
r2Di ¼ r
2
i ð1� UðkiÞÞ ð5Þ

r2cj ¼ r
2
j þ r2i ð1� UðkiÞÞ: ð6Þ
When the demands are uncorrelated between time periods, then
the mean and
variance of the demand during replenishment period for stage j
denoted by the
continuous random variable WJ are obtained as follows by
slightly modifying the
equations to account for the portion of the lead time variability
transferred from the
preceding stage (see, for example, Eppen and Martin 1988 and
Feller 1960).
lWj ¼ lE½cj�
r2Wj ¼ r
2E½cj� þ r2cjl
2:
ð7Þ
Now, we introduce another parameter cj, termed the coefficient
of inverse respon-
siveness (CIR), defined as the ratio of the average demand to
the rate of production
(throughput) pj:
cj ¼ l=pj: ð8Þ
Assuming that there is enough capacity at all the stages to
satisfy a given demand, cj

B 1 at all times. When cj = 1, the expected replenishment cycle
time is given by (2).
We also assume that there is some upper bound above which the
rate of production
cannot be increased further. The CIR at a stage is similar to the
expediting factor
proposed by Bookbinder and Cakanyildirim (1999). They define
the expediting
factor s as the constant of proportionality between the random
variables ~T (the
expedited lead time) and T(ordinary lead time). For expedited
orders (s 1),
shorter than average lead time can be obtained at a cost.
Similarly, longer mean lead
time results in a rebate for the customer when (s[ 1). By
considering a model with
three decision variables (Q,r,s), they show that the expected
cost per unit time is
jointly convex in the decision variables and obtain the global
best solution.
Keeping the average cycle stock constant (given in (4)), from
Little’s law, at
expedited rates of production (cj 1), average replenishment
cycle time for player j,
when operating at a CIR level cj will be equivalent to
E cj
� �
¼ ðLj þ ð1� UðkiÞÞLiÞcj; ð9Þ

r2cj ¼ ðr
2
j þ r2i ð1� UðkiÞÞÞcj: ð10Þ
As cj decreases, the average replenishment cycle time for player
j decreases, which
means that player j is becoming more responsive. Because of
this inverse
relationship between cj and the responsiveness at stage j, cj is
termed the coefficient
of inverse responsiveness at stage j.
In light of Eqs. 9 and 10, we assume that demand during
replenishment period WJ
for stage j is normally distributed as follows:
123
lWj ¼ lE cj
� �
rWj ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffi
r2E cj
� �
þ ðr2cjÞl
2
q : ð11Þ

This equation considers both the demand variability and the
replenishment cycle
time variability. Replenishment cycle time variability is made
up of two
components:
1. The processing time variability at stage j.
2. The portion of the processing time variability at stage i that
is transferred to
stage j.
We assume that base stock at stage j is given by Bj ¼ lE cj
� �
þ kjrWj ; where kj is
the safety factor to achieve the service level target U(kj) for
that stage.
After accounting for the average demand over the replenishment
period, expected
on-hand inventory is given by
E Ij
� �
¼ kjrWj : ð12Þ
By augmenting the above expression with the following term,
which is the expected
number of back orders (Graves and Willems 2003; Ettl et al.
2000),
E BO½ � ¼ rWj

Z1
z¼kj
ðz� kjÞ/ðzÞdz ð13Þ
we realize the following expression for the expected safety
stock at stage j:
E SSj
� �
¼ rWj kj þ
Z1
z¼kj
ðz� kjÞ/ðzÞdz
0
[email protected]
1
CA: ð14Þ
At stage j, let Cj be the nominal cumulative cost of the product
realized when cj = 1,
and let hj be the holding cost rate per period. The per-unit
holding cost of safety
stock at stage j per period equals Cj hj. The total safety stock
holding cost at stage j
per period is given by:
CSSCj ¼ CjhjE SSj
� �

: ð15Þ
Total safety stock holding cost for the supply chain per period
is given by:
CSSC ¼
Xn
j¼1
CSSCj : ð16Þ
3.2 Expression for responsiveness related costs
When players (1, …, n) operate with their respective CIRs,
being (c1 , …, cn), stage j
incurs two types of responsiveness related costs, as described
below.
123
3.2.1 Direct responsiveness related costs
The difference in nominal cumulative costs of the product at
two consecutive stages
j and i (i.e., Cj - Ci) will increase by a value that is assumed to
be a function of (1 -
cj). This is the cost that stage j will pay for operating at a
higher processing speed
that lowers the average replenishment cycle time at stage j.

The increase in cost is typically due to increase in investment in
the so-called 5M
resources (i.e., manpower, machine, methods, material, and
measurement). We are
addressing the issue of cycle time reduction due to the
opportunities for flexibility
available at a stage which can be harnessed at a cost. This
should not be confused
with cycle time reductions due to better operational efficiencies
such as efficient
removal of wastes from the processes such as downtime, setup
time, etc, which we
will consider in the extension of this framework. Flexibility
related costs will
increase/decrease depending on how flexible these 5M resources
are at a stage.
Direct response related costs at stage j per period are given by
DRCj ¼ ½f ð1� cjÞ�ðCj � CiÞl: ð17Þ
Even though we do not advocate any specific function type for
modeling f(1 - cj),
the cost of volume flexibility function (COF), we strongly
recommend that it be
derived from the historical data. For example, for a specific
average demand, from

the past data one could fit a regression model between (1 - cj)
and the incremental
cost at a stage. Moon and Choi (1998) advocate the use of a
piecewise linear
crashing cost function that is widely used in project
management in which the
duration of some activities can be reduced by assigning more
resources to the
activities. They used a piecewise linear crashing cost function
in their model. Ben-
Daya and Raouf (1994) could be a useful reference when
considering using other
types of crashing cost functions.
Bookbinder and Cakanyildirim (1999) assume the expediting
cost per unit
(because of technological investments or hiring extra workers
etc.) time w(s) to be a
decreasing convex function of the expediting factor with w(1) =
0 (additional cost
when CIR = 1 is zero in our model as well). As opposed to our
model, they allow
w(s) to take negative values for s[ 1, meaning that for longer
lead times they
assume that the manufacturer gives the buyer some rebate per
unit time.
Proceeding from the research of Bookbinder and Cakanyildirim
(1999), Ryu and

Lee (2003) chose their expediting cost functions w1 (s1) and
w2(s2) to be decreasing
convex functions of the expediting factors s1 and s2. They
considered w1 (s1) = c1
(-1 + 1/s1) and w2(s2) = c2 (-1 + 1/s2), where c1 and c2 are
positive coefficients.
Our cost function, for example Eq. 17, looks similar in spirit to
these cost functions.
Yang and Geunes (2007) expect the cost of reducing
procurement time, because
of supplier’s investment in production processes or
technologies, to increase at a
nondecreasing rate with the amount of lead time reduction and
therefore employ a
convex function for lead time reduction. They consider a
piecewise linear, convex
and decreasing form (as the production lead time increases) for
the unit procurement
cost function but note that their analysis of this function applies
to general piecewise
linear functions and convexity is therefore not required,
although they expect this
function to be convex in practical context. For our numerical
analysis, we consider a

123
simple increasing convex function, although the results would
not be different for
any nondecreasing function.
3.2.2 Indirect responsiveness related costs
In addition to the above mentioned direct responsiveness related
costs, the stage
will experience an increase in safety stock costs when it
operates at cj, for the
reasons mentioned in Sect. 3.2.1. As a result, the difference in
nominal
cumulative costs of the product at stages j and i will increase by
a value, which
is a function of (1 - cj). Therefore, indirect responsiveness
related cost at stage j
is given by:
IRCj ¼ ½f ð1� cjÞ�ðCj � CiÞhjE SSj
� �
: ð18Þ
Therefore, the total responsiveness related cost at stage j is
given by
TRCj ¼ DRCj þ IRCj: ð19Þ
Hence, total safety stock costs in the presence of increase in

costs at stage j that
account for increase in the responsiveness per period is given
by
CTSCj ¼ CSSCj þ TRCj: ð20Þ
Hence, the total safety stock related cost for the whole supply
chain per period is
given by
CTSC ¼
Xn
j¼1
CTSCj : ð21Þ
4 Managerial insights for strategic safety stock placement
In this section, we attempt to study the safety stock placement
problem primarily
with respect to the key parameters such as replenishment cycle
times, replenishment
cycle time variability, cost of responsiveness etc. as we travel
from U/S to D/S and
offer some interesting insights.
4.1 Position of the bottleneck player
We consider a hypothetical serial supply chain with five stages
to study the impact
of the position on the bottleneck player on supply chain

performance. The different
parameters for this serial supply chain are illustrated in Table 1.
For the purpose of our discussion, we consider the player with
no flexibility
whatsoever with respect to its processing time as the bottleneck
player. The effect of
changing the position of the bottleneck player on the SC safety
inventory costs is
depicted below. We have considered three cases, wherein the
processing time
variability progressively increases (IV in Fig. 3), decreases (DV
in Fig. 3), and
remains constant (EV in Fig. 3) as we move from the most U/S
stage to the most D/
S stage. For the increasing and decreasing cases, we kept the
total processing
123
variability constant and progressively increased/decreased the
process variability as
we move from U/S to D/S in a symmetric fashion. When a
particular stage is a

bottleneck, the CIR for that particular stage would be unity and
for all other stages
the CIR is considered to be 0.9. Response related costs are not
considered in the
analysis as our primary intention is to show the effect of
reducing the lead time on
the safety stocks as the bottleneck player moves from U/S to
D/S. By considering
the incremental total supply chain safety stock costs with
respect to a benchmark
case, wherein all the players are operating at a CIR equivalent
to 0.9 and the
processing variability is the same at all the stages (as with the
EV case in the chart),
one can clearly see that the incremental total supply chain
safety stock costs
progressively increase as the bottleneck player moves from U/S
to D/S for all three
cases.
Key managerial insight #1: Safety stock cost depends on the
placement of the
bottleneck player in a serial supply chain and it is desirable for
the bottleneck
player to be located towards the U/S rather than the D/S.

4.2 Safety stock costs versus responsiveness costs
We illustrate the impact of CIR on the different cost curves in
Fig. 4, using the cost
expressions developed earlier.
We know that, for any stage, safety stock related costs decrease
(Eq. 15) and
response related costs increase (Eqs. 17 and 18) with decrease
in cycle time, or in
Table 1 Parameters of the five-
stage serial SC adopted for
numerical analysis
Stage/player
1 2 3 4 5
Nominal cumulative cost Cj 80 112 175 327 863
Average demand l 100 100 100 100 100
Demand variability r2 400 400 400 400 400
Mean processing time
(periods) Lj
1 1 1 1 1
Processing variability ðl2r2j Þ
(in number of units

of product)
50 50 50 50 50
CIR cj 1 1 1 1 1
Safety coefficient kj 1.28 1.28 1.28 1.28 1.28
Average back order coefficient 0.1 0.1 0.1 0.1 0.1
Probability of stockout pj 0.1 0.1 0.1 0.1 0.1
Inventory holding cost hj 0.017 0.017 0.017 0.017 0.017
Service level U(kj) 0.9 0.9 0.9 0.9 0.9
External
supplier Customer
Supply
Demand
h i j lk
Fig. 2 Schematic description of a serial supply chain
123
other words, with decrease in CIR. Hence, without loss of
generality, we can say

that the total cost function, which is a combination of safety
stock and response
related costs, tends to be convex, the optimum CIR shifting
either towards or away
from unity depending on whether responsiveness cost
component or safety stock
cost component is dominating. A very interesting result relevant
to the nature of the
total costs is due to Bookbinder and Cakanyildirim (1999), who
show that the
expected cost per unit time is jointly convex in the decision
variables (Q,r,s), s
being the expediting factor for a (Q,r) inventory system with
expedited orders and
random lead times.
4.3 Effect of cycle times and processing time variability on total
stage cost
Figure 5 illustrates the effect of increasing processing time
variability at a particular
stage on the total cost while keeping the other parameters
constant. For the sake of
numerical analysis, we have considered the parameter values for
stage 3. PV in the
chart stands for processing time variability and DV stands for
demand variability.

Increasing process variability tends to increase both the safety
stock related costs
and responsiveness related costs at different rates, primarily
depending on the
nominal cumulative cost Cj, the cost of volume flexibility
function f(1 - cj), and the
cost added at a stage (Cj - Ci). In the presence of increasing
processing time
variability, therefore, optimum CIR either moves away from or
towards unity,
-10
0
10
20
30
40
1 2 3 4 5
Supply Chain Bottleneck StageI
nc
re
as
e
in

T
ot
al
S
af
et
y
St
oc
k
C
os
t (
%
)
IV EV DV
Fig. 3 Incremental SC safety stock costs versus position of the
bottleneck player
0
100
200
300

0.55 0.7
CIR
C
os
t
SS cost
Response Cost
Total Cost
10.85
Fig. 4 CIR versus stage costs
123
depending on whether safety stock cost component/or the
responsiveness cost
component is dominating. With increasing variability, the
degree of departure of the
optimum CIR value either way depends on the three factors
mentioned above for a
particular stage. To explain, to counter the excessive
variability, a typical supply

chain manager tries to reduce the cycle time (by reducing CIR),
which would
minimize the SS related costs. However, that action does not
necessarily lead to
reduction of the overall costs. For example, if the cost added at
a particular stage is
very high then the decrease in safety stock costs by cycle time
reduction might not
be able to offset the increase in cycle time reduction
(responsiveness) costs. In such
a scenario, moving CIR counterintuitively towards unity (i.e.,
increasing the cycle
time), which means in the direction that increases safety stock
costs, could be a
better measure to reduce overall costs.
Key managerial insight #2: As the processing time variability
increases for a
stage, the optimum value of CIR moves away from unity if
safety stock cost
component dominates the responsiveness cost component and
towards unity if the
responsiveness cost component dominates the safety stock cost
component.
In Fig. 5, optimum CIR is progressively moving away from
unity as the PV/
DV ratio increases, because we have considered the safety stock

costs component
to be larger than the responsiveness cost component for our
numerical analysis.
The trend will be reversed if the response related costs
dominate the safety stock
related costs. In Fig. 5, for the case of PV/DV = 0.25, the
optimum CIR value is
0.919, for which the respective safety stock and responsiveness
cost components
are $91.65 and $1.749 per period, respectively. For the case of
PV/DV = 2,
wherein the process variability increases eightfold compared to
PV/DV = 0.25, the
corresponding safety stock and responsiveness cost components
are $138.6 and
$1.75, respectively. In this case, not only is the safety stock
component larger but
also the effect of increasing process variability is much greater
on safety stock
component compared with responsiveness cost component.
Hence, the optimum
CIR value for the PV/DV = 2 case will move in the direction
that will mitigate the
effect of increasing safety stock costs and to a point where the

cost advantage in
terms of safety stock cost reduction by reducing the CIR is
equalized by the
corresponding increase in responsiveness costs. The optimum
value for the PV/
DV = 2 case occurs at a CIR value of 0.909 (moving away from
unity), with
50
150
250
350
0.55 0.7 0.85
CIR
T
ot
al
C
os
t
PV/DV:0.25 PV/DV:0.5
PV/DV:0.75 PV/DV:1
PV/DV:1.5 PV/DV:2

1
Fig. 5 CIR versus total stage costs
123
corresponding safety stock and responsiveness cost components
of $137.86 and
$2.48, respectively.
We extend the above analysis by performing a simple sensitivity
analysis by
considering the changes in mean processing time and nominal
cost added at stage 3,
while keeping other parameters constant. Table 2 presents the
case with the mean
processing time and nominal cost added both being halved.
Table 3 presents the
case with mean processing time and nominal cost added both
being doubled.
For the sake of simplicity, we have just considered the cases
PV/DV = 0.25 and
PV/DV = 2. For both of these cases, the optimum CIR for
PV/DV = 2 occurs at a

slightly lower value than that for PV/DV = 0.25 for the reasons
mentioned in the
preceding paragraph. The changes made in the parameter values
are not able to
make the responsiveness related costs increase at a faster rate
than the decrease in
safety stock related costs (with decreasing CIR), hence, the
optimum CIR is still
moving away from unity, primarily due to the parameter values
we have assumed
for our numerical analysis. We show in Sect. 4.4 that changes in
the cost of
flexibility function (COF), that is f(1 - cj), in our model cause
the responsiveness
related costs to increase at a faster rate than the decrease in
safety stock related costs
(with decreasing CIR), making the optimum CIR move towards
unity. In a practical
context, it all depends on the actual values of the parameters,
which make either of
the cost components dominating.
The optimum value of the CIR for a stage will primarily depend
upon the
cumulative cost of the product, which in turn will depend upon
the position of the

stage in the supply chain, the cost added, and the nature of cost
of volume flexibility
function. Using the cycle time reduction as a lever may or may
not be cost effective
depending on, for example, whether a windscreen wiper is being
assembled or an
engine is being assembled at a stage. For the same cost of
volume flexibility function,
it might be a good idea to reduce the cycle time if a windscreen
wiper is being
assembled as opposed to an engine. Irrespective of the
component that is being
assembled, this effect will be more pronounced D/S when
compared to U/S because
the cumulative cost of the product will progressively increase as
we move D/S.
Key managerial insight #3: To reduce the safety stock costs,
reducing the cycle
time is a better lever at downstream stages when compared to
upstream stages for a
given responsiveness cost, all other parameters being held
constant.
Key managerial insight #4: All other parameters being constant,
for a given
cycle time reduction, the cost of flexibility function has to be
milder for a stage with

high cost addition when compared to a stage with low cost
addition, to justify
savings in safety stock costs.
Table 2 Sensitivity analysis 1
CIR PV/DV = 0.25 PV/DV = 2
1 69.869 103.747
0.9 68.432 100.405
0.8995 68.441 100.404
0.899 68.450 100.403
0.895 68.533 100.407
123
The insight from Ryu and Lee (2003) ‘‘that in order to attain
greater savings from
the symmetric cost scheme for the two suppliers, the investment
cost for the supplier
with the more unreliable lead time should be smaller’’ looks
similar in essence to
our key managerial insight 2, albeit in a different context. One
of the key insights
offered, that downstream lead times have a greater impact on

system performance
than upstream ones (Gallego and Zipkin 1999), is also similar in
spirit to our
research.
4.4 Effect of cost of volume flexibility on total stage cost
Figure 6 illustrates the effect of cost of volume flexibility at a
particular stage on the
total cost while keeping the other parameters constant. For the
sake of numerical
analysis, we have once again considered the parameter values
for stage 3. COF in
the chart stands for cost of volume flexibility function
mildness/steepness, when
compared to a randomly chosen increasing convex function
(COF: 1).
In Fig. 6, as expected, optimum CIR is progressively moving
towards unity as the
COF increases. As opposed to processing time variability,
which affects both the
safety stock cost component and the responsiveness cost
components, cost of
flexibility affects only the responsiveness cost component.
Intuitively speaking,

given that the stage is not operating at optimal CIR, increasing
the cost of flexibility
makes a typical supply chain manager operate close to nominal
cycle times (CIR
close to unity), but going back to the example given earlier, if a
windscreen wiper is
being assembled, particularly at a D/S stage, it is quite likely
that there will be
significant savings in safety stock costs by reducing the cycle
time (moving the CIR
away from unity), overtaking the extra cost of responsiveness
because of a steeper
flexibility function. The opposite will be true, for example, if
an engine is being
assembled at a stage.
Table 3 Sensitivity analysis 2
CIR PV/DV = 0.25 PV/DV = 2
1 132.232 202.513
0.95 129.834 198.290
0.93 129.952 197.664
0.92 129.952 197.664
0

500
1000
1500
2000
2500
0.55 0.7 0.85
CIR
T
ot
al
C
os
t
COF:0.01 COF:0.1
COF:0.33 COF:1
COF:2 COF:5
COF:10
1
Fig. 6 CIR versus total stage costs
123

Key managerial insight #5: Given that a stage is not operating at
optimal CIR, as
cost of volume flexibility function becomes steeper, the
optimum value of CIR moves
towards unity if the responsiveness costs segment dominates the
safety stock cost
segment, and vice versa.
Key managerial insight #6: All other parameters being constant,
for the same
cost addition at a stage, cost of flexibility function has to be
milder at U/S than D/S
for a given amount of savings in safety stock costs.
While our model assumes information symmetry, it is still
applicable, including
the managerial insights, in supply chains with information
asymmetry. For
example, in the presence of bullwhip effect attributable to
information asymmetry
or other related issues, demand variability will progressively
increase as we move
towards the upstream stages. It is still advisable that mitigating
measures are put
in place to reduce the causative factors of the bullwhip effect.
In the absence of
any mitigating measures, one could also consider the actual
variability at different

stages and still use the model. The effect will be to accentuate
both the safety
stock component and the responsiveness cost component as we
proceed upstream.
If the increase in the cost of responsiveness at a stage is
significantly larger
compared to the reduction in safety stock costs for unit
processing time reduction,
the optimum CIR will move towards unity. The opposite trend
will be witnessed
in the opposite case. The change in the optimum CIR value at
downstream stages
may also be significant because of larger cumulative costs and
typically large
amounts of cost addition, in spite of the effect of bullwhip
effect being smaller
compared to upstream stages.
5 Model usability for achieving strategic fit
The model can be used primarily as a building block in any kind
of supply chain
network both to evaluate the performance of individual stages
with respect to the
key order winners, cost, and responsiveness, and to optimize the

supply chain
depending upon the focus within the cost-responsiveness
spectrum. The results can
be used to evaluate the gap between the individual business
strategies of different
stages and the supply chain strategy, so that appropriate actions
can be taken to
achieve the strategic fit. Once the supply chain design is
completed and the network
is in place, the model will be particularly useful for making
strategic decisions with
regard to the safety stock placement while considering a
changeover or introducing
a new product.
5.1 Performance evaluation
Total safety stock related cost (safety stock cost and
responsiveness cost)
expression for all the stages (using Eq. 20) can be easily
evaluated given the
different parameter values and one can obtain the costs
separately for safety stock
holding and cycle time reduction (if so desired by a stage) and
the expected cycle

times assuming that all the stages operate without any
coordination with respect to
the overall supply chain strategy (that is, there is no central
decision maker). This
123
will allow stages to evaluate their performance with regard to
the key order
winners of cost and responsiveness and facilitates their
comparison to the internal
performance benchmarks. For example, a particular stage may
realize that better
operations management practices that involve the reduction of
waste (lean
practices) that had been planned for are ineffectual. Hence, they
may want to
know what went wrong and implement appropriate corrective
and preventive
actions such that cost and cycle time reductions can be achieved
without any
major investments.
5.2 Optimization

Now, assuming that there is a central decision making
mechanism, which acts to
coordinate the whole supply chain, the overall safety stock
related cost expression
for the supply chain (Eq. 21) can be optimized, say for the
optimal CIR values at all
the stages given the constraints on target supply chain cycle
time, individual stages’
rates of production, service levels, inventories, cost of
inventory holding, etc. The
optimal costs (safety stock inventory and responsiveness) can
be compared with the
costs obtained assuming the absence of the central decision
maker (as for
performance evaluation explained in Sect. 5.1) to initiate
necessary actions.
We also offer a simple optimization example based on the
parameter values
presented in Table 1 that lend support to the managerial insights
developed in Sects.
4.3 and 4.4.
Figure 7 depicts the optimal CIR values under different
scenarios considered in

Sects. 4.3 and 4.4. The only constraint considered was 0 B cj B
1.
The total cost function was optimized under different scenarios.
SC: Standard cost of flexibility function for all stages and other
parameter values
as per Table 1.
DC: Decreasing cost of flexibility function (i.e., the function
becomes milder
compared to the SC case as we move from U/S to D/S); stage
3’s cost of flexibility
function remaining the same as in the SC case. Other parameters
for all the other
stages remain as in the SC case.
IV: Progressively increasing process variability as we move
from U/S to D/S. For
stage 3, process variability remains the same as in the SC case.
Other parameters for
all the other stages remain as in the SC case.
0.86
0.88
0.9
0.92

0.94
0.96
0.98
1
1 2 3 4 5
Player
C
IR
SC
DC
IV
DV
Fig. 7 Player versus optimal CIR
123
DV: Progressively decreasing process variability as we move
from U/S to D/S.
For stage 3, process variability remains the same as in the SC
case. Other parameters

for all the other stages remain as in the SC case.
The results, as can be seen from Fig. 7, clearly reinforce the
insights developed in
the earlier sections. The shift in the optimum CIR value at stage
5 shows strong
variability owing to the fact that cost added constitutes a
significant portion of the
cumulative cost at that stage, thereby increasing the cost of
responsiveness
significantly for the same cost of flexibility function when
compared to other stages.
The same is the case with stage 4, although on a reduced scale.
Since stage 3 is the
transition stage under different scenarios retaining the same
parameter values as
compared to the SC case, there is no perceptible change in the
optimum CIR value.
5.3 Achieving strategic fit
If the overall costs at a stage are increasing as a result of
optimization to achieve the
strategic supply chain objectives, when compared to the costs in
the absence of a
central decision maker, i.e., by following its independent

business strategy, then, by
devising a scheme for the sharing of the additional profits for
the whole supply chain
in an equitable fashion, say, through changing the contract
structure, discounts or
other incentives, efforts could be made to coordinate the
individual business
strategies with the supply chain strategy to achieve the strategic
fit.
One way of doing this is by considering the supply chain
objectives at different
levels, say, strategic, tactical, and operational levels, and
performing a gap analysis
Strategic Objective:Customer Satisfaction
Tactical Objective:Total customer Cycle time
Performance evaluation for a hypothetical supply chain:
Cost
Estimate(Cip) $25,000 $100,000 $50,000 $0 $25,000 $0
Sum(Cip) $200,000
Time Required in
months (Tip) 2 12 3 0 3 0 Max (Tip) 12
Tier-3
Supplier
Tier-2
Supplier

Tier-1
Supplier Mfg Unit D.C
Retail
Unit
5
4
3
2
1
Cost Estimate(Cjp) $5,000 $15,000 $0 $0 $6,000 $0 Sum(Cjp)
$26,000
Time Required in
months (Tjp) 1 4 0 0 1 0 Max (Tjp) 4
5
4
3
2
1
Cost
Estimate(Ckp) $5,000 $15,000 $2,000 $10,000 $6,000 $0
Sum(Ckp) $38,000
Time Required in
months (Tkp) 2 2 1 1 1 0 Max (Tkp) 2

5
4
3
2 Overall cost=
1 Sum(Sum(Cip)+
…+Sum(Ckp)) $264,000
Max(T) : Max(max(Tip),max(Tjp),max(Tkp)) 12
NC product
level
Throughput
rate
Information
symmetry
level
P
E
R
F
O
R
M
A

N
C
E
M
E
T
R
IC
S
Fig. 8 Performance comparison for different players in a supply
chain (adopted from Vanteddu et al.
2006)
123
between the individual business strategies and the supply chain
strategy in terms of
costs and responsiveness. Vanteddu et al. (2006) offers a simple
Excel based model
to achieve strategic fit assuming that quantitative data is
available to make use of the
tool, as illustrated in Fig. 8.

By simply modifying the performance metrics by placing
emphasis on cost
efficiency and responsiveness, one can use the above model to
achieve the strategic
fit. Actual costs related to cost and responsiveness can be
obtained by using the
model proposed in this paper.
6 Conclusions
In this paper, in addition to offering several managerial insights
with regard to
strategic safety stock placement in a supply chain, an attempt
has been made to
address the problem of achieving compatibility between the
supply chain strategy
and the individual stage’s business strategy by primarily
considering safety stocks
and responsiveness related costs. We introduce a new parameter
called the
coefficient of inverse responsiveness (CIR) to model response
related costs at a
stage, which also enhances the scalability of the model. The
developed cost function
for the building block could be easily extended for any type of
supply chain

network. By knowing the values of the parameters of the model,
one can know the
safety stock costs and responsiveness related costs at each stage
and compare them
to an ideal supply chain strategy in terms of cost and
responsiveness to make
informed decisions. The key managerial insights developed are
generic in nature
and applicable to any supply chain irrespective of its placement
on the cost-
responsiveness spectrum and topology.
To make the model more tractable we had to make certain
simplifying
assumptions and following are some of the limitations related to
those assumptions.
For example, we did not factor the bullwhip effect into our
model. It would be an
interesting extension to our research if the bullwhip effect and
other information
asymmetry related issues were factored into the model. We have
not incorporated
order sizes into our model because the model is supposed to be
largely a strategic

model. Research could be extended by incorporating this aspect
into the model to
see how it affects the managerial insights that we offered.
Relaxing the assumptions
on the stationary nature of the demand and stage base stock
policy with periodic
review will make the model more realistic and robust to real-
world situations.
Introducing contracts that affect the flexibility at a stage with
financial ramifications
will also be a very fertile area to pursue that will make our
model mimic reality
more closely. Another such area is the consideration of other
types of network
topologies, particularly assembly and distribution; we are
planning to consider
extension of the framework in this direction. It would also make
more sense to
consider capacity constraints at certain stages. Product mix
related flexibility is also
a crucial factor which is not addressed in our model. Addition
of this feature would
truly make the research more in tune with reality, especially in
mass customization

settings. Finally, we really would like to see this model used in
some real-world
application so that insights presented in our model could be
validated.
123
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Supply chain focus dependent safety stock
placementAbstractIntroductionLiterature reviewModel
developmentExpression for safety stock costsExpression for
responsiveness related costsDirect responsiveness related
costsIndirect responsiveness related costsManagerial insights
for strategic safety stock placementPosition of the bottleneck
playerSafety stock costs versus responsiveness costsEffect of
cycle times and processing time variability on total stage
costEffect of cost of volume flexibility on total stage costModel
usability for achieving strategic fitPerformance
evaluationOptimizationAchieving strategic
fitConclusionsReferences
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