
Coordination of a fast fashion supply chain with profit-loss sharing contract 87
In the same case, the supply chain profit under RSC is
sc−rs−fb
= (p
rs−fb
− cx
rs−fb
)(a + a − bp
rs−fb
) − c
u
((a + a − bp
rs−fb
) − q
∗
).
(6.21)
From ∂
sc−rs−fb
/∂p
sc−rs−fb
=0, we have
p
∗
sc−rs−fb
=
v(a + a + bc
u
)
b(2v − c)
, x
∗
sc−rs−fb
=
a + a + bc
u
b(2v − c)
. (6.22)
If the supply chain can be coordinated by RSC, we have p
∗
r−rs−fb
=p
∗
sc−rs−fb
. Then we
have
w
rs−fb
= αc
a + a + c
u
b
b(2v − c)
= αcx
∗
sc−rs−fb
(6.23)
The proof in the case when −c
o
bv/(v −c) ≤a ≤c
u
bv/(v −c) and a ≤−c
o
bv/(v −c)
are apparent by using the same approach thus we omit it here.
From Proposition 6.4 we realize that the ...