Table of Contents
Postponement Strategies in Dynamic Environment— in terms of
Standardization
Yu-Y ing, Huang Yi-Ming Tu Ph.D Shyh-Jane, Li
Doctoral Student Associate Professor Doctoral Student
Dep. of Business Dep. of Information Dep. of Business
Administration Management Administration
National Sun Y at-Sen National Sun Y at-Sen National Sun Yat-Sen
University University University
Kaohsiung, Taiwan, R.0.C. Kaohsiung, Taiwan, R.0.C. Kaohsiung, Taiwan, R.0.C.
E-nail: artimas@ bm.nsysu.ed E-nnil:ymtu@ mis.nsysu.edu. Email: shyhjane@ bm.nsysu.e
utw tw du.tw
Abstract
This study investigates one of the emerging logistics strategies, postponement. A simple
modelis developed that captures the costs and benefits associated with the postponement
strategies for various scenarios. Moreover, this study applies the model to a postponement
approach, namely standardization that is motivated by many real examples, and discusses the
following three key questions: (1) In each scenario, where is the point of differentiation in the
production process (2) How should a firm design its processes to lower the total cost when it
is impossible to adjust or it is too costly to alter in a fast changing environment (3) If an
agile firm is able to change its mode of production to respond to aconstantly changing
environment, how should it adjust the pattem of postponement to lower the total cost
From the decision-making model applying system dynamics, the following conclusions
can be drawn First, in determining the stage at which the point of differentiation should occur,
the key variables are the investment cost per operation and the additional cost, including the
processing cost and inventory holding cost, that result from postponement. The trade-off
between those variables will determine the optimal postponement strategy. We find that when
the outside conditions are unfavorable for firms, it may not be advisable to apply the principle
of postponement. On the other hand, when the conditions are beneficial, postponement is a
better choice.
Keywords: Logistics Strategy, Postponement, System Dynamics, Flexible Decision, Cost.
Evaluation
Introduction
In the very complex and changing rapidly environment, many enterprises focus on
continuously increasing customer satisfaction requirement, shortening product life cycle and
raising flexibility, rather than only on quality and cost. In the context, simultaneously lowering
costs from mass customization and responding quickly is the main stream of logistics strategy.
Inventory management in traditional logistics strategies used the safe stock of end-product
as the way to deal with the demand fluctuation. Usually, the utility rate of resource wasn’t
efficient enough and had many problem, for example, purchased components inefficiently,
designed product unduly, exploited finns unproductive, operated logistics task costly, etc. For
recent years, logistics strategy have emphasized on delaying the timing of finishing
end- products and combing products in the distribution system so that firms can reduce waste of
materiel and supplies derived from demand uncertainty. In this context, redesigning
product/process is the popular method to delay product differentiation and that is the idea of
postponement (Cheng & Allam, 1992; Xie, 1998).
Postponement is the delay of the point of product differentiation in a production process to
the latest possible time. The value of postponement is the value of information: as production
decision time can be delayed, then more information about the customer demand will be
received and analyzed. Hence the quality of decision will be optimized. Consequently, it
improves the quality of the demand forecast as the forecasting point moves closer to
production period. It also allows flexibility in production scheduling to actual demand
resulting in a more responsive supply chain networks (Kanet, 1986; Cheng & Woo, 2001).
Postponement was first defined as a strategy to postpone changes in form and identity to
the latest possible point in marketing (Alderson, 1950), and later extended to manufacturing
and distribution sites (Zinn & Bowersox, 1988). The concept was applied to product design
and/or manufacturing process so that the decisions on time and quantity of a specific product
being produced can be delayed as late as possible. This idea is also known as delayed product
differentiation (Zinn & Bowersox, 1988; Lee & Billington, 1994; Lee & Tang, 1997; van Hoek,
1999). Bowersox & Closs (1996), and Lee& Tang (1997) used the risk-pooling concept on the
logistics postponement strategy by stocking differentiated products at the strategically central
locations that balance between inventory cost and response time. Other related concepts
include the point of differentiation, which refers to the stage in the supply chain networks in
which takes place, and the level of postponement, which refers to the relative location of the
differentiation point. Generally speaking, postponement enabled firms to reduce the inventory
level while maintaining or even increasing the customer service level.
However, to introduce the postponement strategy will lead to additional variable costs and
fixed cost from resigning products/progresses and will increase the processing cost and the
inventory holding cost per unit. For analysis the change of costs, Lee & Tang (1997) developed
a total relevant cost model which incorporates investment cost, processing cost, inventory cost
and lead time those would normally be affected by delayed product differentiation and
provided a basic measure to evaluate cost change. However, this model only considered the
costs from intemal activities enterprises and lacked the analysis of environment changes. So
we have an idea that through analyzing different scenarios to evaluate the cost changes after
introducing postponement strategies, firms could cut down operation cost and raise the
flexibility of decisions.
This paper is organized as follows. In second 2, we first review all related papers to know
what have been researched. Second 3 illustrate our model to capture the costs and benefits
associated with postponement under dynamic environment. In second 4, we consider how our
modelcan be applied to some approached motivated by real examples. This is followed by
some concluding discussions and suggestions for further research.
Literature Review
Progress in Logistics
In this section, the selection of articles represents the issues and ideas in the decades of the
1970s, 1980s and1990s. Prior to the 1960s, logistics was achieved in a series of fragmented,
uncoordinated movements and storage subfunctions. Now, logistics has an expanded role in
corporate strategy, which is to create customer value and provide firms with sustainable
competitive advantage. So, we bring together some articles (See Table 1), whichhave made a
major impact on the subject of logistics and provide an n overview of the strategic aspects of
logistics,
Table 1 Progress in logistics issues
Author Issues
La Londe, Grabner What are the altemative approaches most commonly used in the
and Robeson corporate development of integrated distribution systems? What were
/1970 the forces that led to managers’ focus on integrated distribution systems
during 1960s? What are the forces that will shape the scope and
influence of management thinking during the 1970s?
Ballou The article identified three problems areas that basis for strategic
/1977 logistical planning: inventory policy, facility location and transport
selection/routing.
LaLonde& Mason The article showed clearly that a variety of extemal and intemal factors
/1985 have changed the mix of management required to deal with what were
new problems.
Zim & Bowersox From the view of logistics cost, authors pointed out five types of
/1988 postponement: labeling packaging assembly manufactwing time
Manrodt & Davis Jr. The purpose of the article was to illustrate the historical trend towards
/1992 responsiveness and pointed out three of the foundational concepts in
service response logistics.
Cooper This paper had assessed the development of global logistics strategy
/1993 referred to the classification of Zinn & Bowersox (1988) and
considered the implication of global logistics strategies for managers.
La Londe & Masters The purpose in the article was to identify and describe what the authors
/1994 believed to be the two most important logistics strategies supply chain)
management and cycle time compression.
McGinnis & Kohn The authors felt that longitudinal research into logistics strategy would
/1997 provide insights into practice at different points in time, changes in
practice over time, and rates of change over time. The study reported in
the article began 1989 and has been replicated in 1990 and 1994.
Claycomb et al. While prior research has focused on intemal and upstream JIT, the
/1999 research examines the extent to which exchange with downstream
customers is JIT oriented.
Source be coordinated from International J ournal of Physical Distribution and Logistics
Management 23 (5), 1992
Research of postponement strategies
Postponement is one of the logistics strategies burgeoned in the late 1980s. Its core concept
is to postpone the task of differentiating a product for a specific customer until the latest
possible point in the supply network (Feitzinger & Lee, 1997). That is, all the firms in supply
chains must trade off between strategic commitment and operational flexibility (Cvsa &
Gilbert, 2002).
Although different classifications reflect respective perspectives on understanding the
postponement strategy, the purpose of postponement strategies is identical which is to raise the
effects of the whole supply chain. Related papers have arranged and presented in Table 2.
Table 2 Classification of Postponement Strategies
Author Focus Category
Zinn & Bowersox which were based on the type of labeling postponement, packaging
/1988 manufacturing operation postponement, assembly
postponed and time postponement — postponement, manufacturing
occurred during transportation postponement, and time
postponement.
Lee & Billington focused on reducing the variability form and time postponement
/1994 of production volumes so as to
reduce the cost at manufacturing
and related stages
Bowersox & Closs focused on reducing the risk of Imanufacturing postponement and
/1996 anticipatory product/market logistics postponement
commitment
Feitzinger & Lee Firms must rethink and integrate (Modular design of products,
/1997 the designs of products, the modular design of manufacturing
process used to make and deliver progresses and the design of
products, and the configuration of supply networks
their entire supply network
Lee & Tang considered the variety of design standardization of components,
/1997 changes in the production and modular design, postponement of
distribution processes operations, and re-sequencing of
operations
‘van Hoek ‘Which was drawn on the form, time and place postponement
/1999 interrelation of outsourcing and
postponement
Cheng & Woo ‘Which were based on the activities _ form, time and place postponement
/2001 taken both in the process and
product and based on time factor
Total Relevant Cost Modd
To introduce the postponement strategy will lead to additional variable costs and fixed cost
from resigning products/progresses and will increase the processing cost and the inventory
holding cost per unit .Foranalysis the change of costs, Lee & Tang (1997) developeda model
which incorporates investment cost, processing cost, inventory cost and lead time those would
nomnally be affected by delayed product differentiation.
Supposed that there is a manufacturing system that produces two end-product, where each
end-product requires processes performed in Nstage. The system has a buffer that stores the
5
worlin-process (WIP) inventory after each operation (Figure 1). To emphasis on the issue of
delayed product differentiation, Lee & Tang refer to operation kas the last common operation
and vary the products after k.
1 N Di
OTRO ., OTR PE ;
kH N
O operation buffer
Figure 1 Products 1 and 2 assume their identity after operation k
In Lee & Tang's model, it wants to find the optimal point of differentiation k° under certain
scenario and don’t change k* after the decision has once made. Moreover, average investment
cost, the demand of product, the processing cost per unit and the inventory holding cost per
unit are all extraneous variables that the relations between these variables and k are considered
as given conditions and then to find the minimum of total related cost.
But enterprises usually face a violently changing environment in fact and extraneous
variables above will be affected by many factors such as demand, price, exchange rate etc. that
may make the postponement unable to implement. In addition, under what scenario should
firms postpone the point of differentiation in the production process is another problem. Even
if Kis the optimal decision now, it won't be necessarily sowhen the environment (or scenario)
has changed (See Figure 2).
Optimal decision
ke0 keel k*=2
}» Lee & Tang's model
Scenario
(2) -——» A change that Lee & Tang
didn’t consider it
Figure 2 the defect of Lee & Tang’ s model
Consequently, this study is base on Lee & Tang’ s model and enlarges it by bringing into
extemal changes when we design variables. The model in this research is to evaluate when a
firm should introduce postponement strategy and when shouldn't as well as should postpone to
what stage if the firm need to implement postponement. Therefore, the model not only can
6
make firms to respond to extemal changes as soon as possible, but also can provide a decision
method with operating flexibility when firms want to apply postponement strategies.
Moreover, the study applies the model to two different postponement approaches, namely
standardization, which is motivated by many real examplesand discusses the following three
key questions: (1). In each scenario, where is the point of differentiation in the production
process (2). How should a firm design its processes to lower the total cost when itis
impossible to adjust or it is too costly to alter in the fast changing environment (3). If an
agile firm can change its mode of production to respond to the ever changing environment,
how should it adjust the pattem of postponement to lower the total cost
Modeling the Postponement Strategy
To simplify the exposition of our model, we use a simple example to build our model.
Supposed there are only two end-products in a supply chain system and the two end-products
have no common components if the system doesn't implement postponement. Notice that the
two end-products only have one different element. Moreover, the capacity in each firm is
infinite that makes a firm can change its producing mode randomly with no additional
switching cost. In the context, the supply chain system only faces one extraneous factor-
Business Cycle Indicators of Taiwan.
Our model could be expressed as:
@ N operating stage
e@ k lastcommon stage, and 0 <k <N 4
@ u, the demand of producti at the end of period t (i =1,2) where J, is nomally
distributed and Cov(u,, U.) =.90,0, . Notice that fA represents the conelation of
,and ,, where —l <p <1. Fornotational convenience, we let
0, =/Vary, Wy) =Jo7 #2p0,0, +07 . It is easy to check that o,. <o, +0, for
any fi and that o,, decreases as Adecreases.
@ —n,(k) _ the lead time of operation j when operation k is the last common
operation( j =1...N)
@ I, the average investment cost per period with operation j when operation k is the
last common operation and j <k.
p,(k) the processing cost per unit associated with operation j when operation k is
7
the last common operation. The total processing cost in operation j was determined
by product demand and expressed asp, (K)[4 +14].
@ z the “safety factor” associated with the service level for each buffer. Suppose that
a buffer faces normal demand with mean y and standard deviationo and that the
buffer replenishes its stock by following the order-up-to level inventory (Peterson &
Silver, 1979). Then the average WIP inventory is equal to nu and the average buffer
inventory is equal to 4/2 +z0,(n-) where n is the lead time of this stage. To
simplify the model, we assume the WIP inventories are valued as the same as the
output of each stage and apply the same safety factor zfor each of the buffers in the
system.
@ h,(k) the inventory holding cost for holding one unit of inventory at bufferj for one
period when operation k is the last common operation. Moreover, the total inventory
holding cost includes WIP inventory and the buffer inventory. The total WIP
inventory is h,(k) Bh (uy +) because it must concem the lead timen, (k) in
assembling processes. The total buffer inventory is h,(k) AL /2+2 fa, (k) +18,
es _ different business cycle indicators. We base on the monitoring indicators from
Council for Economic Planning and Development Executive Y uan, Taiwan, R.O.C.
which scores the business cycle indicators as blue, yellow-blue, green, yellow- red
and red. Let the demand of products, the investment cost, the processing cost per unit
and the inventory holding cost for one unit be variables that changed linearly when
the scenario has changed, and can be denoted as_,(s) , I(9), P, (k,s), h(ks).
Notice that according to the economics, if the economic circumstance becomes
boom, the demand of products will increase that will make p,(k,s) andh,(k,s) rise
and the availability of money will be loosed which will make I, (s) drop.
Considering the uncertainty of y;(s) I,(s) p,(ks)andh,(k,s), let Z(k,s) be the total
relevant cost per period when operation kis the last common operation under scenario s and be
expressed as:
Z(k,s) =
k N N
> 1,(s) 2, p(k S)[11(s) H42(9)] 23 b (Kk s)Fh, (W\(u,(9) +H2(9) A
J J J
k 31
y hk,s) aa aus +0, fH GB.)
= Ou,(s) +4, (s) O
a 5) rn 40,) a9 a:
Tn equation (1), we could see that demands, investment cost, processing cost per unitand
inventory holding cost per unit have changed with the changes of scenario so that produce
different total relevant cost Z(k, s) . With the optimal solutionk” that makes Z(k, s) minimized,
firms could determine postpone to what stage under what scenario.
When extemal environment changes rapidly or is unable to predict, how a firm with an
unchanged production structure should design its product/process to make the total cost
minimized? To solve this problem, we suppose that each scenario s is with the probability
Pr ob(s) . If a firm determined to let kbe the last common operation no matter what the
scenario is, the expectation of total relevant cost, V(k) , is
vib & Prob(s 4k 9 (3.2)
From (3.2), we shall find k pin Vis) , Le, when k=0, k =1...andk =N -1, we
“{
should choose a specific stage that will make the expectation of total relevant cost minimized
under any scenario as the last common stage and this stage is called as_k which is the static
decision in the dynamic environment. So, V(K) =min V(k) =V and V is the expectation of
total cost under the static decision.
If a firm can adjust its production mode without limits, how should it change that will make
the total cost least? We have known what is the optimalk’ under each different scenario
from (3.1). Now, let W denote the expectation of total cost when each k is the optimal one
(k’) in each scenario and show as:
W= Prob(s)Z(k, 9 (3.3)
SE-5}
A this time, W is the expectation of total cost under the dynamic decision and means that
choosing the k‘ corresponding to each scenario to product will make the total relevant cost
9
minimized Further, W <V, which will prove if a firm can adjust its production structure
followed by the change of environment, it has the cost reduce to least.
Then, this study will use a real case applied the standardization design which is one of the
postponement approaches to compareZ.(k +1,s) —Z(k,s) and find the optimal postponement
strategies under distinctscenarios.
Applications: standardization design
In this section we shall discuss if a firm should introduce postponement strategies under
different scenarios and the firm should postpone to what stage. For the purpose, we use
equation (3.1) as an original model to analyze a generally used product/process redesign
approach, namely component part standardization, which is motivated by real examples in Lee
& Tang's research (1997).
‘The System Dynamics model of standardization
Component part standardization is a widely accepted strategy in improving manufacturing
performance while maintaining the required level of product variety to satisfy the customer
needs. The term component standardization refers to the situation in which several components
are replaced by a single component that can perform the functions of all of them (Perera et al. ,
1999). Use of the standardized components in several products or in the same product reduces
many costs such as inventory costs, R&D costs and material cost.
However, the development cost of a standardized component may be greater than that of
each individual unique component since the standardized component needs to be designed to
satisfy the requirements of all the unique components. Thus, when making a decision on
component part standardization, the firm should consider all the applicable costs throughout
the product life cycle.
This example is from a computer manufacturer that produce two type of printers: black ink
(mono) and multicolor ink (color) printers. Due to the functionality of these two products, the
demands for the two products in each period are negatively correlated. The manufacturing
process of the two printers consists of three major steps: printed circuit board assembly (PCA),
final assembly and test (FA &T) and final customization (Customization). At each step,
different components are used for different end-products. Hence, we can view the
manufacturing to printers as two distinct processes and notate as N =3andk=0 when none
of the processes is standardized (See Figure 3).
10
Mono PCA Mono FA&T Mono Customization
—iigtintic=
WIP M1 WIP M2 wip M3 Mono Printer
Color PCA Color FA&T Color Customization
WIP C1
WIP C2 WIP C3. Color Printer
Figure 3 No delayed product differentiation (k =0 )
In this case, to delay product differentiation could be achieved by either standardizing the
PCA stage (k =1), or standardizing both the PCA and the FA &T stages (k =2) showed as
Figure 4.
MC FAST Mono Customization
wip M3 Mono Printer
Color FA&T Color Customization
wip MCL : MO
wie c2 wip c3 Color Printer
a: when k =1
Mono Customization
MC PCA MC FA&T ( ) ( )
© WIP M3 Mono Printer
wiP MCL WIP MC2 DED
WIP C3 Color Printer
b:when k =2
Figure 4. With delayed product differentiation
Standardizing the PCA stage requires the standardization of a key component, known as
the head driver board, for both the mono and the color printer. Due to technical difficulties, the
11
investment cost (1,(s) ) for the “common” head driver boards are relatively high. Next,
standardizing the FA &T stage requires also the standardization of a key component at the stage,
namely, the print mechanism interface. This is a relatively simple task and the investment cost
(1,(s) ) is relative low. Because the company manufactures the print mechanism interface
inhouse, there is actually a strong incentive to standardize the component so as to exploit the
benefits of economies of scale. In addition, the lead time ist affected neither when the PCA
stage is standardized nor when the FA &T stage is.
In this case, I,(s)0 1,(s) >0, n,(k) =n,, Vj , and the processing cost can be expressed
as:
p(ks) =p, forall jandalls when k =0 (4.1)
Furthemore,
p(ks) =p, +0,(s) if j<k and k>1 (4.2)
p(ks)=p, if j>k ad k=l (4.3)
The term a, =0 shows the additional material and processing costs when operation i is
standardized. Because the common head driver board is much more difficult to develop and
process, a(S) >d,(s) =0. Then, the unit inventory holding cost can be specified as:
hk, s) =h, forall j and all s when k =0 (4.4)
Besides,
hk,s) =h, EB (s) +..+Bi(9)F for jsk and k21 (4.5)
hk,s) =h, HR(s)+..+B(9] for j>k and k>1 (4.6)
Welet B;(s) 20 represent the “additional value added” at stage i when it is standardized. In
12
this case, the value of the common head driver board is high so that B,(s)H 0. On the other
side, because it doesrit require significant effort to standardize the print mechanism interface,
B,(s) +0. Notice that hh, captures the cumulative value added at each operation i so itis
reasonable to assume that h, is nondecreasing in i.
By substituting (4.1)-(4.6) into (3.1), we can evaluate the totalrelevant costs Z(0,s),
Z(1,s) and Z(2,s):
Z(0,s) =(9 + B +p)[H.(9 +,(9]
+hn +h +hnlly(9+n,(s]
4h +h +h) L,(S) ils s) (4.7)
+20, +0,) Fh. fo +41 +h,,fn, 4 +h,fn, +14
ZA, 8) =1 (9) (pn +a(s) +p +R u(s+u(s]
“ats §)n +h +A(s9)n Hh +B(s)n][H(9) +4(9)]
+{(h +8(9) Hh, +8(s) Hh, +B(9 9) HAAS) (48)
+0, fh +8(9) Hp
+10, +0,) Ab +R(9) fn + +(h +B(9)4/n, +1f
Z(2, 3) =1,(3) +L,(3) H(p +a4() +(p, +0,(8) +p, [U4 (9 +H,(9)]
4{(h +8(5))n +(h +8 (9 +B(5))n +h +B(9 +B(5)n [409 +H,(9]
A{(h +B(9) Hh +8(9 +B(3) +h +89 +8(9HEFKS iggy
+20, fh, +A(s),/0 1 +h +A(s) +B,(5)/n, 1G
440 +0.) Ih +B(9 +B(9)/m 41g
To go on, let us compare (4.7)-(4.8). First, Z(1, s) —Z(0, s) can be shown that:
13
Z(1, 8) -Z(0,s) =
1,(s) +0,(s)[H,(s) +H2(9]+B,(s)(q, +1, +.) [Hi( 9 +H,(9)]
#88(9 KOFI) (4.10)
+2.fn +) [h, +B,(8))o, —h(o, +0,)]
+2z8,(s)(0, +0, fn, 41) +(,fn, +4
The first five terms on the right-hand side represent the incremental cost incurred when we
standardize the PCA stage. The sixth term corresponds to the potential savings due to
reduction of inventory at the buffer located immediately after the first stage. However, the fifth
tem [(h +B,)0,.— 8,0, +0,)] may be positive when , is large enough and makes the
incremental costs clearly outweigh the potential savings. Hence, we have Z(1) >Z(0). It
means that when the standardization of parts is costly, it may not pay to delay product
differentiation. In addition, since Z(1) >Z(0), the optimal k° =0 or 2, i.e. we can eliminate
the probability of standardizing the first stage and should either standardize both PCA and
FAGT stages or none. However, when Z(1) >Z(0) , we need to compareZ(1) and Z(2) to
determine the optimal point of differentiation.
Z(2,s) -Z(L,s) =
3
L(s) +a,(9[H(9) +H,(9)]+B,(9)> 0, [1,(9 +4,(s)]
ra
(411)
428,(9 HOFER) 4, fn, +1)[B,(s\(0, +0,)]
+2(fn, +1) [(b, + B,(s) +B,(s))o. “(h +8,(5))(@, +0,)]
In (4.11), although the first five terms are positive, the sixth term seems to be negative
since I, isnot larye enough, a, >a, =0 and B, >B, ~0.Therefore, Z(2) <Z(1) that
means firms should make PCA and FA &T standardized simultaneously. Then, we shall exam
that if it needs to postpone the point of differentiation.
14
Z(2,s) -Z(0,s) =
1(s) +1,(9 +o, (s) +0,(9 [H( 9 +H,(9]
3 3
+8,(s) ny[un(s) +H2(9]+B,(5)). 0, [4,(3) +u,(s)]
J= I=
(4.12)
+[3B,(s) +28, (9S EIS +2( Jf, #1)[(B,(s) 48, (8)(0, +0,)]
42( fn, #1)[(h, +8,(s))o,, —h(o, +0,)]
+2(,fn, +1)[h,+ B,(s)+B,(s)o,, —h(o, +0,)]
In (4.12), only the last two terms [(h, +B,(s))o,, —h(o, +0,)]
[(h, +B,(9 +B,(9)0,, —h(o, 40,)] may be negative. So, whether Z(2,s) -Z(0,s) is
positive or negative, the key point is the tree variables: I; ,2, and B, . But these variables will
change depended on the variation of scenarios and the optimal k’ must be determined by
different situations.
Through the analysis above, we can know that comparing different Z(k) respectively under
different scenarios can acquire k’ that make the total relevant minimized.
4.2. The numerical analysis
For the purpose of defining different scenarios and finding the optimal kK under
different scenarios, we base on the monitoring indicators from Council for Economic Planning
and Development Executive Y uan, Taiwan, R.O.C., whichscores the business cycle indicators
as five scenarios and let ,(s), I;(s), p,(k,s) and h,(k,s) change linearly as the scenario
changed. In addition, the following set of case parameters are employed where (Emst &
Kamrad, 2000)
B p=-0.99>6, =O, =20 Oo, =2.8
= p=p=p,=2 dollas wit
= h=h =h =2 dollars wit
= n=n =n =3 minutes uit
= z=0.9
By applying (4.7)-(4.9) to the above case parameters the following table of summarized
15
results is obtained:
Table 3 Optimal standardization under different scenarios
s sl s2 $3 s4 so
H, =H, 80 90 100 110 120
A=B=R 2 2 2 2 2
a, =a, 0.07 0.06 0.05 0.04 0.03
h 3 3 3 3 3
h, =h, 2 2 2 2 2
B, 0.07 0.06 0.05 0.04 0.03
B, 0.035 0.03 0.025 0.02 0.015
I, 240 220 200 180 160
I, 70 60 50 40 30
0, =0, 20 20 20 20 20
On 28 2.8 2.8 28 28
Z(0, s) 5384 5994 6604 7241 7824
Z(1,s) 5562 6146 6725 7300 7870
Z(2, 8) 5558 6130 6695 7253 7805
(Compare
withZ(k,s) | 40) <2) <Al) | 20) <2) <A) | 2) <2) <A) |<) <) | )<2 <A)
k 0 0 0 0 2
Based on the Table 3, we can know how the Z(k) changes when a firm delays the last
common stage to different phases under distinct scenarios and can obtain the optimal k’
where the Z(k) is least. Hence, each scenario will generate its own cost structure and has
different k’.
According to the data from Council for Economic Planning and Development Executive
Yuan, the total scores of monitoring indicators from Jan 1968to Feb 2002 in R.O.C. could
display as the red is 18%, the yellow-red is 22%, the green is 33%, the yellow-green is 15%
and the blue is 12% (refer to appendix A). To get the probability distribution and the results in
Table3 into V(k) = Probh(3 4k g , then, V(0) =6725.84, V(1) =6831.593 and
sKrss}
(2) =6796.633 . Consequently, when the extemal environment changes rapidly or is
unpredictable that a firm car! t adjust its production mode immediately, choosing k =0 will
let the firm respond to the extemal change with the lowest expectation of total cost
(V =V(0) =6725.84) and k =0 is the static decision in the dynamic environment.
16
On the side, if a firm can arrange its production mode without limit, it should
choosek =0 when s=s,.s, and choose k=2when s=s.. To get the result into (3.3) and tie
in the probability of each scenario happens, we can obtain W =6722.459 that is the
expectation of total cost under the dynamic decision in the dynamic environment. Due to
W<vV, we can argue that a firm can lower its cost least if it can alter following the extemal
changes. Notice that the difference between Wand V isn’t quite large in this study. Besides the
design problem of our model, the reason may be the additional switching cost from changing
production mode. If a manufacturer considers the switching cost, it may be not willing to
adjust its mode immediately when the environment changes just now. Because the basic
assumption in this research doesn’t consider the switching cost, we don’t exam the event.
In this section, we have used a simple case exam our model in section 3. For the problem of
how to determine k’ in different scenarios, postponing to what stage is decided by the trade-off
among I;, a, andB;. If the cost of standardization is quite high and take account of
additional processing costs, firms aren’t necessarily willing to standardize until the business
cycle booms and the demand of products expand that make 1, anda. , lower to certain level.
Besides, if operation j standardizes and the saving of inventory cost is larger that the expanse
of investment cost and processing cost, firms will be more willing to standardization design.
5.Conclustion
We have presented a dynamic model to evaluate the costs associated with different
scenarios in which the product differentiation is delayed through standardizing component part.
Such postponement may incur some investment costs and additional processing costs, but
lower inventory costs. Moreover, these cost factors will change following the extemal
environment In terms of the static decision in the dynamic environment wherever a firm isn’t
able to alterits production mode, choosing V(k) =minV( k) =min Prob(s)Z(k, s) =V
ss}
can make a firm to respond to various scenarios with the lowest expectation of total costs. In
tems of the dynamic decision in the dynamic environment whenever a firm can adjust its
mode, choosing the k’ of each scenario and getting them into W = 2, Prob(s)Z(k, 9
sis}
can make the total costs minimized.
Generally speaking, postponement is a kind of strategy or principle. When enterprises
17
introduce it, there are many kinds of variation. Although our model is only applied in
standardization design, it could be used in different kinds of postponement strategy to find
some common principles.
In our further studies, we shall apply our model to more kinds of postponement strategy to
help enterprises determine the problem of designing a product/process. We also shall apply this
research to different products or different industries because the focus of cost factors may be
different in each industries. Moreover, we plan to add other cost factors to expand our model.
In the current model, we don’t think about the switching cost which may be a very important
factor to influence manufactures’ decisions.
18
Appendix A: Total Scores of Monitoring Indicators in
1968-2002
ear\Mont] 1 2 3 [ 4 Ses eso aon aria
1968 | 37 [| 39 [| 41 [ 42 | 43 [ 447 44 [ 45 | 42 [ 38 | 37 [ 32
1969 | 31 [| 31 | 31 | 31 | 31 | 33] 34 [ 34] 35 [ 34] 34 | 35
1970 | 36 | 34 |] 34 [ 34/7 35 [ 35 7 36 [ 36 | 37 [ 36 | 35 | 35
1971 | 34 | 35 [ 34 | 33 | 32 | 34] 34 | 34 | 36 | 37 [ 38 | 40
1972 | 39 | 38 | 38 [ 36 | 36 | 36] 37 [ 39 | 40 [ 40 | 40 | 43
1973 | 44 [| 45 | 44 | 46 | 47 | 50] 52 | 52 | 52 [ 53 | 54 | 54
1974 | 55 [| 50 |] 45 [ 36 | 32 | 28] 27 [ 24 | 21 [ 20] 19 | 19
1975 | 17 | 16 | 15 [ 17 | 20 | 23] 31 [ 36 | 38 [ 40 | 46 | 44
1976 | 41 | 40 [ 40 | 38 | 33 [| 35 [ 35 | 32 | 34] 28 [ 29 | 24
1977_| 17 | 20 | 20 | 25 | 27 | 27] 31 [ 29 | 37 [ 37 | 37 | 35
1978 | 43 | 33 | 45 | 45 | 51 | 49 | 53 [ 53 | 53 | 47 | 50 | 44
1979 | 38 | 49 | 43 [ 37 | 32 | 36] 30 | 28 | 32 [ 31 | 26 | 26
1980 | 38 | 35 | 28 | 29 | 29 | 26] 33 [ 29 | 28 | 32 | 31 | 30
1981 | 30 | 24 [ 29 | 31 | 27 [| 25 [ 25 | 24 | 19 | 18 [ 17] 21
1982 | 19 | 20 {| 20 / 19 | 17 | 17] 17 | 19 | 18 | 17 | 19 | 17
1983 | 16 | 19 | 18 | 29 | 31 | 38] 37 [ 39 | 38 [ 36 | 42 | 35
1984 | 42 | 39 | 37 | 34 | 37 | 30] 30 [| 27 | 25 | 28 | 21 | 21
1985 | 16 [| 19 | 14] 14] 14] 127 12 [ 13] 14 [ 15 |] 15 | 22
1986 | 21 | 19 | 33 | 28 | 29 | 37] 34 [| 39 | 36 | 36 | 38 | 37
1987 | 36 [| 40 | 32 [ 41 | 39 | 38] 34 [ 36 | 37 [ 31 | 35 | 32
1988 | 29 [| 33 | 28 [ 27 | 31 [ 30 [ 30 [ 31 | 28 [ 29 | 33 | 32
1989 | 36 | 34 |] 40 | 39 | 34 | 30] 32 [ 27 | 24 [ 25 | 24 | 25
1990 | 23 [ 27 [| 21 [ 20 | 17 [ 14] 17 [ 17 | 18 [ 21 [ 20 | 15
1991 | 20 [| 19 | 19 | 20 | 23 | 24 | 29 [ 27 | 27 [ 30 | 30 | 28
1992 | 29 | 29 [ 28 | 28 | 24 [ 25 [ 25 | 25 [ 22 [ 25 [ 21 | 24
1993 | 19 | 23 | 24 | 20 | 20 | 17] 21 [ 22 | 23 [ 24] 21 [ 27
1994 | 33 [ 29 | 25 [ 30 | 30 | 32 [ 30 [ 33 | 34 [ 36 | 39 [ 31
1995 | 30 | 34 |] 30 [ 29 | 28 | 25 [ 23 [ 21 | 22 [ 15 | 13 | 16
1996 [| 18 [| 18 | 13 [ 21 | 15 [| 177 19 [ 20 | 24 [ 22 | 26 | 28
1997 | 26 | 24 [ 31 | 24 | 24 | 28] 30 | 26 | 31 [ 26 [ 28 | 29
1998 | 23 [| 27] 25 [| 20] 19 | 20] 16 [ 22 | 18 [ 16 | 19 | 14
1999 | 18 | 17 | 16 | 20 | 22 | 25] 24 | 23 | 19 [ 26 | 26 | 28
2000 | 32 | 30 [ 29 | 28 | 29 | 27 7 26 | 28 | 28 [| 23 [ 17] 16
2001 | 10 | 10 [ 10 | 9 | 9 [ 9 9 | 11[ 9 9 | 10 | 15
2002 [15 | 15
1 There are twelve indexes in 1968-1983 years and nine indexes from 1984 to 2002.
2. Above 38 points is red, 32-37 points is yellow-red, 23-31 points is green, 18-22 points is yellow-blue and
bellow 17 points is blue.
19
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