
12 Fashion Retail Supply Chain Management
Checking the second order derivative of π
SC
(s) with respect to s shows that it is a
strictly concave function:
dπ
SC
(s)
ds
=(r − m)b − ks,
d
2
π
SC
(s)
ds
2
=−k < 0.
As a result, the optimal service level for the fashion retail supply chain system, s
∗
SC
, can
be found by solving the respective first order condition:
dπ
SC
(s)
ds
=0 ⇒s
∗
SC
=
(r − m)b
k
.
Since in most traditional wholesaling business, the wholesale price w is larger than the
product cost m, i.e. w > m, we have Proposition 2.1:
Proposition 2.1. Under the pure wholesale pricing scheme with w > m, the optimal
service level of the fashion retail supply chain system is ...