Method of Product Development Cost Estimating Based on ProA Hierarchical
Decomposition
Wen-hui Liu 1,2，Xiao-hui Zhao 2，Ya-wen Dong 2
1
School of Mechanical & Electrical,Northwest Polytechnic University, Xi’an,China
2
School of Mechanical & Electrical,Xi’an Polytechnic University，Xi’an,China
(liuwenhui1976@163.com, xhuizhao@xpu.edu.cn,dongyawen231@163.com,)
Abstract - To realize the cost estimating of product
development, a estimating method based on Activity and its
Process (ProA) hierarchical decomposition was presented
integrating with product development process modeling.
Cost attributes of ProA Input and Output Item and ProA
conversion operations were firstly studied. Cost transfer
between ProA Input and Output Item were analyzed in
detail, and rules for cost estimating of ProA were also
formulated. Finally, the method of the cost estimating was
presented, and simulation based on Matlab environments
was also conducted.
and uses Activity-Based Costing to further research the
cost attributes and cost transfer of ProA and establish a
estimating method based on ProA hierarchical
decomposition to better support cost decision-making of
the product development project.
Keywords- Activity-Based Costing, cost estimating,
hierarchical decomposition, product development
The product development process may be decomposed
into a series of sub-process and the sub-sub-process…,
each sub-process and sub-sub-process are composed of a
set of linked activities which correspond to implementation
process. There will be logical difficulty when using
formalized method to define process and activity in
decomposition course. To avoid ambiguity and solve the
difficulty, Reference [12] proposes that integrating the
process and activities as ProA and taking ProA as basic
unit of the product development process and also makes
detail study on ProA Input and Output Items, conversion
operations and ProA hierarchical decomposition. This
paper will take these concepts and the research results as
foundation of the product development cost estimating.
Using the definitions about ProA Input and Output Items
and ProA conversion operations in Reference [13], ProA
Input and Output Items and ProA conversion operations
are summarized as follows with the need of cost
estimating.
Definition 1: ProA Inputs. The things that will be
used up and transfer into output when the product
development ProA is implemented.
Definition 2: ProA Outputs. The things transform
from inputs when using certain resources to implement
ProA.
ProA Inputs set:
I. INTRODUCTION
As to product development project, cost estimating is
important for its technical and economic evaluation;
product cost optimization and control and market pricing
[1]
. Along with the increase of individuation requirements
which demand short-cycle and low-volume, the proportion
of development cost in the product life cycle cost rises
sharply [2].
At present, the researches about product cost
estimating mainly take the product as the subject matter
and roughly presume product development cost using the
product attributes [3-6]. Because multi-projects are
intercrossed concurrent, the cost estimating about the
single product development project is difficult. In order to
solve this problem, a mentality is proposed that collecting
the research and development project cost and assigning it
to the new product cost using Activity-Based Costing in
Reference [7]. Based on Reference [8] in which improved
Activity-Based Costing is used for estimating product
development cost , Reference [9] analyzes the estimating
method of activity cost driver with specific product
examples and thus brings up to the product development
cost.
However, the estimation about product development
cost is not only to obtain the product development cost.
The manifestation of cost driver, cost transfer and value
chain in the product development operation flow needs to
model the development process [10,11]. The References [12,
13] take Activity and its Process (ProA) as basic unit of the
product development modeling. That constructing product
development process based on the ProA, which avoids
ambiguity to the process and the activity, can better
support dynamic programming of product development [13].
In view of this, this paper takes the product development
process as the subject matter, quotes the concept of ProA
II. ProA OF PRODUCT DEVELOPMENT AND ITS
COST ATTRIBUTES
A. Basic Dependent Concepts
IN  in 1 , ,in i , in p 
i  1,2, , p ,
1  p  6
(1)
ProA Outputs set:
OUT  out 1 , ,out j , out q 
j  1,2, ,q ,
1  q  6
(2)
The input and output items of a ProA are usually less
than 6 [12, 13].
Definition 3: ProA resources. The roles which
support the execution of ProA.
ProA resource set :
R  r1 , ,rk , rm 
k  1,2, ,m;1  m  6
(3)
Definition 4: ProA conversion operations. The
process of converting ProA Inputs into Outputs using
certain resources. It is expressed as:
OUT T  IN 
(4)
The conversion operation  j of ProA Output Item
uses up resources to finish the conversion from IN  to
j
out j , which actually includes a series of activities.
Assume that the enterprise has implemented the activity
cost management and sets up m activities according to
the operation flow and product characteristics. These m
activities are a1 ,as am  and their cost driver rates are
d1,ds dm 
. The product development group may
determine activity drivers’ consumption l j ,l js l jm 
1
respond to a1 ,as am  that caused by  j using
experience or probability estimation[14] according to the
enterprise’ historic data. Here, l js  0 and it indicates that
this conversion operation does not consume the activity
a m when l js  0 .
Definition 5: ProA Granularity [13].It is a value that
measure ProA activity size and the complexity of process
to describe ProA decomposition degree in the product
development process.
Along with ProA hierarchical decomposition, the
input-output relations among each sub- ProA and sub-subProA are clear gradually. The mutual quotation among
internal input and output irems build relationship between
one ProA and another ProA. So, mutual restrictions arise
about ProA execution sequence and time. And also, it will
cause cost transfer between input and output items of
up-down stream ProA. Such condition exists that multiple
ProA may take the same internal output item as their input
2 
2  and
item. As shown in Figure 1, ProA1,3
ProA2,2
2  as
simultaneously quote a internal output item in ProA1,2
their input item. So, we consider the cost of this internal
2  and
output item is also quoted and is shared by ProA1,3
2
. Thus, the cost between related internal input and
ProA 2,2
output items maintain balance in the process of ProA
hierarchical decomposition. Similarly, certain ProA output
items are both external output items and internal output
2
items. Such as the output item in ProA 2,3
, one part of the
cost is outputted, the other part flows into ProA 2,42  .As the
product development progresses, each external input items
cost and activity cost caused by convention operations are
accumulated progressively and outputted finally. So, in the
product development process, how the value on the activity
chain accumulates and transfers in the enterprise is
manifested.
D. Cost Attributes of ProA
a. Cost Attributes of Input Set
The cost attributes of input item “ ini ”is expressed as
B. ProA Hierarchical Decomposition:
Set a product development project as ProA(0)，the 2-9
sub-ProA(0) that decomposed are presented as
ProA i1 , i  R,1  i  9 , ProA i1 can be decomposed into
ProA ij2  , i, j  R,1  i, j  9 . Following the hierarchical
decomposition of ProA, its input and output items and
resources are correspondingly decomposed. Conversion
operations completed by father ProA can be separately
completed by its sub-ProA. As shown in Figure 1, ProA(0)
Input , ProA i1 Input and ProA ij1 Input Items are called
External Input Items, ProA(0) Output, ProA i1 Output and
ProA ij1 Output Items are called External Output Items.
External
input
I1
I2
I1
I2
I1
I2
I3
ProA11
2 
ProA1,1
ProA(0)
External
output
I3
1
ProA 2
2
ProA 2,1
2 
ProA1,3
2
ProA 2,2


ACini  Pini , N ini , C ini
Pini is the original cost of
(5)
ini .When ini is a external
input item, Pin is determined by the developer according to
i
the enterprise’ historic data and experience; When ini is a
internal input item, Pin is determined by the original cost of
i
the quoted internal output item.
N ini is cost distribution factor. When ini is
communal or derives from the output item of certain ProA
and also is simultaneously the input item of this ProA and
the external output item of product development process,
only part of the Pin flows into this ProA as input item cost
i
and its distribution rate is N in . In this case , the value of
O1
i
Internal
output
I3
2 
ProA1,2
O1
：
2
ProA 2,3
Internal
input
N in is 0,1 ,otherwise, the value of N in is 1. Note that if
certain ProA shares the same input item, the sum of each
ProA’s N ini is 1.
i
i
2
ProA 2,4
Fig. 1. ProA Hierarchical Decomposition
C. Cost Transfer between ProA Input and Output Items
O1
C ini is the actual input cost of the input item, the cost
that input item’s original cost Pin distributes into the
ProA.
(6)
C in  Pin  N in
i
i
i
i
The cost attributes of ProA input set is:
p
p
i 1
i 1
ACIN   Cini   Pini N ini
(7)
b. Cost Attributes of Output Set
The cost attributes of ProA output set “ out j ” is:

ACout j  Pout j , Nout j ,Cout j

(8)
Pout j is the original cost of output item, the cost value
that determined by input item cost and conversion
operations cost.
N out is external output factor. When out j is only the
j
external output item, the value of N out is 1, which indicates
j
that its cost flows out completely as part of the ProA(0)
output cost of product development project. When out j is
only the internal output item, the value of N out is 0, which
j
process of converting the inputs to output item is called the
cost contribution of input items to the output item.
Along with the unceasing decomposition of product
development process, ProA granularity and the number of
ProA input items become fewer and fewer and the input
cost is less and less. it is necessary to atomize ProA ,
neglect the correspondence between input and output items
and only care about the cost of input and output items. Set
the rules below:
Rule 1 The cost contribution of input items to output
items is consistent. That is:
As to ini  IN （ ini  IN  ini  IN  ）,the cost
j
of in i is 1 q ( q is the number of output items).
The rule leads to the expression of ProA output item
cost:
p
ACout j  C j  AC IN q  C j   Cini q
indicates that its cost flows into other ProA. When out j is
not only the external output item but the internal output
item, the value of N out is 0,1 ，which indicates the output
j
cost proportion of the external output item in this output
item’s original cost Pout .The sum of N out and N in is 1,
j
j
(14)
i 1
According to the rule, the maximum error of cost
contribution that ProA input item provides to output item is
:
 max  C in  1 qC in  1  1 q C in
i
N ini is the distribution factor of the internal input item that
quotes this output item.
Cout j is the actual external output cost of the output
j
contribution portion that in i contributes to out j in the cost
i
i
(15)
i
With ProA hierarchical decomposition, the input item
cost C in is less and less, the number of output items q also
reduces, so the error becomes smaller and smaller. To
reduce the estimating error, we should make the ProA
granularity smaller to reduce the output items when ProA
input item cost is higher. It proves that this error only
affects the cost transfer between ProA and doesn’t
influence the total cost of the product development.
Rule 2 when several ProA quote the same input item,
each ProA should share the quoted input cost according to
its cost distribution factor.
The rule can balance the incoming and outgoing of the
cost between the related ProA input and output items of
up-down stream in product development process, and
achieve cost transfer and recurrence relations between
ProA.
i
item. And,
Cout j  Pout j  Nout j
(9)
The cost attributes of ProA output set is:
(10)
ACOUT  ( APOUT , AWCOUT )
Here,
q

 APOUT   APout
(11)
j 1


q
 AWC
OUT   ACout

j 1

means
the
original
cost of ProA output set and
APOUT
AWCOUT means external output cost of output set.
j
j
c. Cost Attributes of Conversion Operations
The cost attributes of  are:
q
ACPr oA   C j
(12)
IV THE COST ESTIMATING METHOD BASED ON
ProA HIERARCHICAL DECOMPOSITION
j 1
Here,
C j is activity cost that consumed by  j .
C j  lj 1 , ,ljs , ljm d 1 , d s  d m 
T

m
 ljs
(13)
 ds
s 1
III COST ESTIMATING RULES OF ProA
Definition 6: Cost Contribution. In order to get
certain output item, all input items cost consumed in the
Based on the recurrence element rule of cost estimating
above, the process of cost estimating based on ProA
hierarchical decomposition is described in Figure 2.
a. Confirm the universe of product development ProA
and input and output items
As shown in figure 1, the process of product
development and input and output items are decomposed
hierarchically. The input and output items of the top layer
ProA(0)
are recorded as I 0   ( I01, I0 2,) and
O0   O01, O0 2, .
Decompose ProA hierarchically and
confirm the universe of ProA and its
input and output items
Initialize the cost parameters
Search from ProA(k) to find ProA
whose input item cost attributes are
obtained completely
confirm the cost attributes of
 input item and input set
ProA x,ky,

confirm the cost attributes of
ProAx,ky, convertion operations
Color ProAx,ky, output item and
output set by submodel 3
N
j
Y
Fig. 2 The process of cost estimating based on ProA hierarchical
decomposition
As the decomposition of ProA(0) and its input and output
items, the next layer ProA(1) is obtained and
ProA(1)=(ProA1(1), ProA2(1),…, ProAn(1)).The sets of
ProA(1)
input
and
output
items
are
and
I 1  ( I11, I1 2,, I21, I2 2,)
we
can
(1)
sequentially decompose ProA to obtain different layers
of ProA and its input and output items. Until ProA is no
longer decomposed ,the bottom layer of ProA set is
recorded as ProA(n) and its input and output items sets are
I n  and O n 
The universe of product development ProA is recorded
as U ProA then U ProA =(ProA(0), ProA(1),…, ProA(k)). The
universe of ProA input and output items are recorded as
U I  I 0  , I 1 , I n   and U O  O 0  , O 1 ,O n   .As to
ProA  U ProA , ProA input set IN  U I , ProA output
set OUT  U O , ProA input item ini  U I and ProA output
item out j  U O .
b. Initialize the cost parameters
Firstly, using experience and probability estimation
to estimate the activities required by each ProA conversion
operation and the consumed quantity l j ,l js l jm  of
activity drivers according to enterprise’s historical data, so
as to confirm the cost of ProA conversion operation
 j .Then, give the cost value of all external input items,
1
cost distribution factor N in of each ProA input item and
i
external output factor N out of each output item in the
j
process of hierarchical decomposition.
1
developer ,confirm cost attributes of output item . Then the
cost attributes of ProA x,ky,  output set are obtained by
Confirm product development cost
and the cost of each output item
.Similarly,
j
to the estimated activity drivers quantity l j ,l js l jm 
and activity drivers rates d1 ,d s dm  required by
conversion operations. So, the cost attributes of ProA 1,k
conversion operations are obtained by Equation (12).
④ By Cost Estimating Rules, according to external
output factor N out of output item determined by the
All cost attributes of ProA
output set in ProA(k) are
confirmed
O1  (O11, O12,, O21, O22,)
c. Confirm the cost attributes of ProA input and
output items in term of Cost Estimating Rules
①Suppose the process of product development is
decomposed to layer k , searching from ProA(k) to find
ProA x,ky,  whose input item cost attributes are obtained
completely.
②confirm the cost attributes of ProA x,ky,  input set by
Equation (9).
③get the cost C of each conversion operation due
Equation (11) and cost estimating rules.
⑤ ProA x,ky,  output items are usually the input items of
downstream ProA or output items of the whole product
development process, based on this, we can confirm the
cost attributes of input items of downstream ProA.
⑥ Judge that whether the cost attributes of ProA
output set in ProA (k) are all confirmed, or return to ①.
d. Product development cost
When the cost of output set in ProA (k) is all
confirmed, searching from ProA (k) to find all the ProA
output items then sum the external output cost, that is the
sum of ProA output set in ProA (k) and this sum value is
the product development cost. Now, we get not only the
product development cost but the cost of each output item.
V SIMULATION EXAMPLE
In order to carry out other assembly tasks, we need to
test the flexibility of the one-way valve after one-way
valve group of the car oil pump are assembled in oil barrel.
The design of the testing part is the core of one-way valve
tester. As shown in Figure 3, on the basis of design target,
the development process model of one-way valve testing
part is builded based on ProA hierarchical decomposition.
As shown in Table 1, the activities and activity drivers
in product development are setted according to the
characteristics of business process and activity driver rates
are calculated in term of resources consumed by activities
in nearly one year.
As shown in Table 2, the product development group
and experts initialize the input and output items and
conversion operations of the 12 ProA in the third layer of
the hierarchical decomposition in Figure 3.
According to this estimating method, the simulation
model in Matlab environments for polychromatic sets
recurrence element model is builded. The cost of product
development process is estimated by the simulation model
and the simulation result is shown is Table 3.
Considering the case above, the cost estimating
method of product development based on ProA
hierarchical decomposition can be analyzed as follows:
The estimating method is flexible. As the hierarchical
decomposition continues, the estimating accuracy is
promoted gradually.
Based on this estimating method, the enterprise can
know the cost of the product development and each output
Design assignment
Oil barrel assembly drawing
Funds
Design assignment
Design assignment
Oil barrel assembly
drawing
Design assignment
Oil barrel assembly
drawing
Preliminary
scheme
Funds
Schematic design
Oil barrel assembly drawing
ProA1(1)
item, the organization can know well about how the value
on the product development activity chain accumulates and
transfers in the enterprise, and also the method can well
support the cost analysis of operation process and the
improvement of business process.
The estimating method is based on the processoriented cost analysis and is useful for the cost estimating
of the product life cycle and cost analysis of business
process, thereby supporting the function cost analysis of
the business process.
Development of oneway valve tester
ProA(0)
Tester
Detailed design and Components
and parts
trial-produce
ProA2(1)
Test the assembly
Tester
ProA3(1)
Preliminary
Measuring head and protector
Measuring head design
scheme
and trial-produce
Funds Fixture design and
Fixtures
Funds
(2 )
ProA2,1
trial-produce
Funds Gas circuit design and
Gas circuit
ProA2,2(2)
trial-produce
components
ProA2,3(2)
Schematic design
ProA1 ,1(2)
Drawings and
technical
Schematic Preliminary Measuring documents
scheme head design
design
ProA1,1,1(3)
ProA 2,1,1(3)
Drawings
and technical
Customized
Measuring head documents measuring head
protector design
protector
ProA2,1,2(3)
Funds
Tooling requirements and routing
ProA 2,2,1(3)
Drawings and
technical
documents
Funds
Fixture
material
purchase
ProA2,2,2(3)
Measuring head protector
ProA2,1,3(3)
Measuring
head material
purchase Material Measuring
head
Funds
manufacture
ProA2,1,4(3)
ProA2,1,5(3)
Tooling requirements and routing
Fixture design
Test the assembly
Measuring head
Gas
Gas circuit
circuit
components
Gas circuit scheme Customized
gas
circuit
design
Funds
ProA 2,3,1(3)
ProA2,3,2(3)
Fixture
manufacture
Material
Test the
assembly
ProA 3,1,1(3)
Fixture
ProA2,2,3(3)
Figure 3 The development process model of testing part based on ProA hierarchical decomposition
TABLE I
THE SET-UP OF ACTIVITIES AND ACTIVITY DRIVERS IN THE PROCESS OF PRODUCT DEVELOPMENT
Activity codes
Activity names
Activity drivers
Activity driver rates(Yuan/
Activity unit）
a1
Discussion
Task time
20
a2
Documentation
Task time
20
a3
Drawing design
Number of drawing
100
a4
Checking the drawing
Number of drawing
30
a5
Process design
Task time
20
a6
Process audit
Task time
20
a7
Tooling preparation
Task time
15
a8
Material purchase
Material quantity
5
a9
Basic trial-producing
Task time
18
a10
NC trial-producing
Task time
250
a11
Assembling
Task time
20
a12
Testing
Task time
40
TABLE II
INITIALIZATION OF THE COST PARAMETERS
ProA
Codes
Input items
Input items
Cost
External input
Output
Output items and their conversion operations
Activities consumed by output items
Tester
ProA3,1,1(2)
External
Tester
distribution
factors
item cost
items
conversion operations
output
factors
O1,1,1
Ф1,1,1=(10,4,1,1,0,0,0,0,0,0,0,0)
0
I2,2,2-2=150
NULL
NULL
I2,3,2-2=5800
O2,1,1-1
O2,1,1-2
O2,1,2
O2,1,3
O2,1,4
O2,1,5
O2,2,1-1
O2,2,1-2
O2,2,2
O2,2,3
O2,3,1
O2,3,2
Ф2,1,1-1=(8,4,12,12,0,0,0,0,0,0,0,0)
Ф2,1,1-2=(0,0,0,0,36,16,0,0,0,0,0,0)
Ф2,1,2=(3,4,1,1,0,0,0,0,0,0,0,0)
Ф2,1,3=(0,0,0,0,0,0,0,3,0,0,0,0)
Ф2,1,4=(0,0,0,0,0,0,0,9,0,0,0,0)
Ф2,1,5=(0,0,0,0,0,0,35,0,35,0,0,0)
Ф2,2,1-1=(6,4,6,6,0,0,0,0,0,0,0,0)
Ф2,2,1-2=(0,0,0,0,16,8,0,0,0,0,0,0)
Ф2,2,2=(0,0,0,0,0,0,0,6,0,0,0,0)
Ф2,2,3=(0,0,0,0,0,0,15,0,15,0,0,0)
Ф2,3,1=(2,2,1,1,0,0,0,0,0,0,0,0)
Ф2,3,2=(0,0,0,0,0,0,0,11,0,0,0,0)
0
0
0
0
0
0
0
0
0
0
0
0
NULL
O3,1,1
Ф3,1,1=(0,0,0,0,0,0,0,0,0,0,2,2)
1
ProA1,1,1(3)
I1,1,1-1，I1,1,1-2
1,1
I1,1,1-1 =0,
I1,1,1-2=0
ProA2,1,1(3)
I2,1,1
1/3
NULL
ProA2,1,2(3)
ProA2,1,3(3)
ProA2,1,4(3)
ProA2,1,5(3)
I2,1,2
I2,1,3-1,I2,1,3-2
I2,1,4-1，I2,1,4-2
I2,1,5-1，I2,1,5-2
1/3
1，1
1/3,1
1/3,1
NULL
I2,1,3-2=150
I2,1,4-2=150
NULL
I2,2,1
1/3
ProA2,2,1(3)
ProA2,2,2(3)
ProA2,2,3(3)
ProA2,3,1(3)
ProA2,3,2(3)
ProA3,3,1(3)
1/2,1
I2,2,2-1，I2,2,2-2
1/2,1
I2,2,3-1，I2,2,3-2
I2,3,1
1/3
1,1
I2,3,2-1，I2,3,2-2
I3,1,1-1，I3,1,1-2，
1，1，1，1
I3,1,1-3，I3,1,1-4
NULL
TABLE III
SIMULATION RESULT
Output
Items
Output
Items Cost
（￥）
External
Output Factors
of Output Items
ProA2,1,2(3)
O1,1,1
O2,1,1-1
O2,1,1-2
O2,1,2
410
1868.34
1108.33
1204.16
0
0
0
0
ProA2,1,3(3)
O2,1,3
1369.16
0
ProA2,1,4(3)
O2,1,4
1129.16
0
ProA2,1,5(3)
ProA2,2,2(3)
O2,1,5
O2,2,1-1
O2,2,1-2
O2,2,2
3392.49
548.34
1048.34
1228.34
0
0
0
0
ProA2,2,3(3)
O2,2,3
2271.68
0
ProA2,3,1(3)
O2,3,1
346.67
0
ProA2,3,2(3)
O2,3,2
6201.67
0
ProA3,3,1(3)
Product
Development
Cost
O3,1,1
13355
1
ProA Codes
ProA1,1,1(3)
ProA2,1,1(3)
ProA2,2,1(3)
13355
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