
Customer service management in fashion retail supply chains 17
supplier. Then the fashion retailer’s profit under the consignment contract is equal
to (1 −λ)(r −m)(a +bs
∗
SC
) −
1
2
ks
∗
SC
2
, and the supplier’s profit is λ(r −m)(a +bs
∗
SC
).
To make the fashion retailer’s profit under the consignment contract larger than the
uncoordinated case, i.e., π
retail
(s
∗
retail
(w
0
)), in this example, we need:
(1 − λ)(r − m)(a + bs
∗
SC
) −
1
2
ks
∗
SC
2
> 472
⇒(1 − λ)(10 − 4)(100 + 30 × 1.8) − 50 × 1.8
2
> 472
⇒(1 − λ)(924) > 472 + 162
⇒(1 − λ)(924) > 472 + 162
⇒λ<31.3853%.
For the supplier to also benefit from this coordination, we need the supplier’s profit
under the coordinated