Civil Engineering Reference
In-Depth Information
2
, then the expected
Assume that the mean value of
θ
is 0 and the variance is
δ
kI
a
e
r
π
(
,
)=
output of the producer service outsourcing value chain is
E
I
e
with
the hypothesis above.
Hypothesis 2.
Cost formula. The manufacturer's cost is
δ
c
I
2
2
, and the contractor's
cost is
δ
s
e
2
2
(1996), where
δ
c
and
δ
s
are the cost coefficient of manufacturer and
contractor respectively.
Hypothesis 3.
Information risk. The efforts of both sides are private information
and cannot be known by each other, while other information is public. Both the
manufacturer and contractor are risk neutral.
Hypothesis 4.
Profit distribution formula. The payment for contractor is
W
(
π
)=
kI
a
e
r
, including fixed payment and output share, where
W
F
+
βπ
=
F
+
β
(
π
)
is
the total payment for contractor,
β
is the output share (0
<
β
<
1), and
F
is fixed
payment.
Hypothesis 5.
The precondition of the producer service outsourcing occurring is
E
is the expected profit of the producer service outsourcing
value chain and
U
is contractor's expected retained profit.
(
R
)
≥
U
,where
E
(
R
)
3
Model Description
The expected profit of producer service outsourcing value chain equals to the
outcome minus the cost of both sides, that is,
)
−
δ
s
e
2
2
−
δ
c
I
2
2
−
δ
s
e
2
2
−
δ
c
I
2
2
kI
a
e
r
(
)=
π
(
,
=
E
R
E
I
e
(1)
Expected contractor and manufacturer profit respectively are
(
π
)
−
δ
s
e
2
2
−
δ
s
e
2
2
kI
a
e
r
(
)=
=
+
β
E
R
s
W
F
(2)
(
π
)
−
δ
c
I
2
−
δ
c
I
2
2
kI
a
e
r
E
(
R
c
)=
π
−
W
2
=(
1
−
β
)
−
F
(3)
The model can be described as the following optimization problem P1:
−
δ
s
e
2
2
−
δ
c
I
2
2
kI
a
e
r
(4)
−
δ
s
e
2
2
kI
a
e
r
maxF
+
β
(5)
−
δ
c
I
2
2
kI
a
e
r
max
(
1
−
β
)
−
F
(6)
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