
74 Fashion Retail Supply Chain Management
Proposition 5.1. Under Scenario One: The new product i with the largest ¯µ
i,(1)
leads
to the largest EP
i,R,(1)
∗
, EP
i,M,(1)
∗
and EP
i,SC,(1)
∗
for all i =1, 2, ..., n.
Proof of Proposition 5.1: From (5.4), we observe that EP
i,R,(1)
∗
=(r −w) ¯µ
i,(1)
−
(r −v)σφ
−1
r −w
r −v
. Since, (r −w) is positive and (r −v)σφ
−1
r −w
r −v
is the same
for all new products under consideration, a larger ¯µ
i,(1)
implies a larger EP
i,R,(1)
∗
. From
(5.4), we notice that EP
i,M,(1)
∗
=(w −c)
¯µ
i,(1)
+ σ
−1
r −w
r −v
. Thus, with the similar
argument for the case of EP
i,R,(1)
∗
, the new product i with the highest expected mean
demand ¯µ
i,(1) ...