Quick Response Fashion Supply Chains in the Big Data Era

Abstract

The quick response strategy has been widely adopted in the fashion industry. With a shortened lead time, quick response allows fashion supply chain members to conduct forecast information updating which helps to reduce demand uncertainty. In the big data era, forecast information updating is even more effective as more data points can be collected easily to improve forecasting. In this paper, after reviewing the related literature, we explore how the quick response strategy with n observations can improve the whole fashion supply chain’s performance. We study how the number of observations affects the expected values of quick response for the fashion supply chain, the fashion retailer, and the fashion manufacturer. Then, we analytically how the robust win–win coordination can be achieved in the quick response fashion supply chain using the commonly seen wholesale pricing markdown contract. Insights are generated.

A.1 Appendix: All Proofs

Proof of Lemma 2.1.

(a) By directly comparing between the cases of QR and SR, the demand uncertainty under QR (with n-observation based information updating) is always smaller than the demand uncertainty under SR. By differentiation, we can find that d ₁(n) is decreasing in n, which implies the demand uncertainty reduction ((d ₀ + δ) − (d ₁(n) + δ)) is increasing in n. (b) When n → ∞, $\underset{n\to \infty }{ \lim }{d}_1(n)=\frac{d_0\delta }{nd_0+\delta }=0$ and hence the demand uncertainty under QR (d ₁(n) + δ) becomes δ. (Q.E.D.)

Proof of Lemma 3.1.

(a) First of all, from (14.8), we have EVQR _SC (n)=$\left(\sqrt{d_0+\delta }-\sqrt{d_1(n)+\delta}\right){T}_{SC}\left({s}_{SC}\right)$. From (14.3), we have:

$$ {T}_{SC}\left({s}_{SC}\right)=\left(p-v\right){\Phi}^{-1}\left({s}_{SC}\right)+\left(r-v\right)\Psi \left[{\Phi}^{-1}\left({s}_{SC}\right)\right]\\ =\left(p-v\right){\Phi}^{-1}\left({s}_{SC}\right)+\left(p-v\right)\Psi \Big[{\Phi}^{-1}\left({s}_{SC}\right)\Big]+\left(r-p\right)\Psi \left[{\Phi}^{-1}\left({s}_{SC}\right)\right]. $$

(14.30)

At Time 0, since the expected product leftover by the end of the season can be expressed as $\sqrt{d_0+\delta}\left\{{\Phi}^{-1}\left({s}_{SC}\right)+\Psi \left[{\Phi}^{-1}\left({s}_{SC}\right)\right]\right\}$, which must be non-zero in the model we considered in this paper, we thus have:

$$ \left[{\Phi}^{-1}\left({s}_{SC}\right)+\Psi \left[{\Phi}^{-1}\left({s}_{SC}\right)\right]\right]\ge 0. $$

(14.31)

Put (14.31) into (14.30) implies that T _SC (s _SC ) > 0. Since $\left(\sqrt{d_0{+}\delta }{-}\sqrt{d_1(n){+}\delta}\right)>0$, from (14.31), we have: EVQR _SC (n)=$\left(\sqrt{d_0+\delta }-\sqrt{d_1(n)+\delta}\right){T}_{SC}\left({s}_{SC}\right)>0$.

(b) Differentiate EVQR _SC (n)=$\left(\sqrt{d_0+\delta }-\sqrt{d_1(n)+\delta}\right){T}_{SC}\left({s}_{SC}\right)$ with respect to n reveals that dEVQR _SC (n)/dn > 0.

(c) When n → ∞, from Lemma 2.1, we have: d ₁(n) = 0, and hence EVQR _SC (n → ∞)=$\left(\sqrt{d_0+\delta }-\sqrt{\delta}\right){T}_{SC}\left({s}_{SC}\right)$. (Q.E.D.)

Proof of Lemma 4.1.

Similar to the Proof of Lemma 3.1. (Q.E.D.)

Proof of Lemma 4.2.

Notice that Φ⁻¹(s _R ) < 0 if and only if s _R  < 0.5 and Φ⁻¹(s _R ) ≥ 0 if and only if s _R  ≥ 0.5. Then, Lemma 4.2 can be proven by following the same approach as in the proofs of Lemmas 3.1 and 4.1. (Q.E.D.)

Proof of Lemma 4.3.

When c > p, by direct observations from the analytical expressions, we have:q _0 , R∗<q _{0 , SC∗} and q _1 , R∗|μ ₁(n)<q _{1 , SC∗}|μ ₁(n). (Q.E.D.)

Proof of Lemma 5.1.

(a) By equating ${q}_{1,R\ast}^{\Omega}\Big|{\mu}_1(n)$ and q _{1 , SC∗}|μ ₁(n), we know that ${q}_{1,R\ast}^{\Omega}\Big|{\mu}_1(n)=$ q _{1 , SC∗}|μ ₁(n) if and only if $\widehat{m}=m\ast$. (b) Checking the first order derivative reveals that ${EVQR}_R^{\Omega}\left(n|\widehat{m}=m\ast \right)$ is a decreasing function of $\widehat{c}$, and ${EVQR}_S^{\Omega}\left(n|\widehat{m}=m\ast \right)$ is an increasing function of $\widehat{c}$. (Q.E.D.)

Proof of Lemma 5.2.

Directly implied by using Lemma 5.1. (Q.E.D.)