Design outsourcing in the fashion supply chain: OEM versus ODM

Abstract

Design innovation is the engine of fashion. Many fashion firms outsource design innovation to their suppliers. Design outsourcing is on the rise in the fashion supply chain, but research in this area lags behind industry practice. In this paper, we examine how design outsourcing affects the supply chain, and we compare supply chain performance under an Original Equipment Manufacturer (OEM) strategy versus an Original Design Manufacturer (ODM) strategy. We evaluate a market size outsourcing model where design enhancement influences market size, and a success probability outsourcing model where design enhancement influences the success probability of innovation. We find that when the supplier trades with the retailer via a wholesale price contract under the ODM strategy, the supplier has no incentive to invest in innovation. In the market size outsourcing model, the design innovation in the centralized supply chain is higher than that under the OEM strategy. However, in the success probability outsourcing model, the success probability of innovation under the OEM strategy is higher than that in the centralized supply chain. Furthermore, we find that a profit sharing contract can achieve supply chain coordination under both OEM and ODM strategies; whereas, revenue sharing and buyback contracts cannot.

Appendix

All proofs

Proof of Proposition 1

• For (i), differentiating the profit function of retailer with respect to H and p, we find if 2β>e ², π _R (H, p) is jointly concave in both H and p. When ∂π _R (p, H)/∂p=0 and ∂π _R (p, H)/∂H=0, we yield p ^* _OE (w)=[(1−e)βL−w(e−β)]/(2β−e ²) and H ^* _OE (w)=[(1−e)eL−w(2−e)]/(2β−e ²). Substituting H ^* _OE (w) and p ^* _OE (w) into the profit function of supplier and differentiating it with respect to w, we assume H−p>0, thus when (1−e)(e−β)L>(β+2(1−e))k, w ^* _OE is obtained. For (ii), differentiating the profit function of retailer with respect to p, we can show that π _R (p) is concave in p and p ^* _OD (H, w)=[eH+(1−e)L+w]/2. Substituting p ^* _OD (H, w) into π _S (H, w) and differentiating it with respect to w, we can obtain the unique optimal solution of the wholesale price, that is, Substituting into π _S (H, w) and differentiating it with respect to H, we can obtain that which is negative when β>(2−e)²/4. It implies that the lower bound of H is optimal, ie, H ^* _OD =L. Consequently, w ^* _OD =(L+k)/2 and p ^* _OD =(3L+k)/4 when L>k. Here, the condition L>k guarantees H−p>0.(Q.E.D.) □

Proof of Proposition 2

• For (i), differentiating the profit function of retailer with respect to e and p, we can find that if 2α>(H−L)²are met, π _R (e, p) is jointly concave in both e and p. When ∂π _R (p, e)/∂p=0 and ∂π _R (p, e)/∂e=0, we yield e ^* _OE (w)=(H−L)(L+w)/[2α−(H−L)²] and p ^* _OE (w)=a(L+w)/[2α−(H−L)²]. Substituting e ^* _OE (w) and p ^* _OE (w) into the profit function of supplier and then differentiating it with respect to w, since H−p>0, namely when (2H−L−k)α>(H−L)² H, w ^* _OE is obtained. For (ii), differentiating the profit function of retailer with respect to p, we can show that π _R (p) is concave in p and p ^* _OD (e, w)=[eH+(1−e)L+w]/2. Substituting p ^* _OD (e, w) into π _S (e, w) and taking the first derivative with respect to e, we obtain that ∂π _S (e, w)/∂e=−(w−k)(H−L)/2−∂e<0, implying that the lower bound of e is optimal, ie, e ^* _OD =0. Substituting e ^* _OD into π _S (e, w) and taking the first and second derivatives with respect to w, we can obtain that π _S (e ^* _OD , w) is concave in w, and w*=(2H−L+k)/2. Consequently, we have p ^* _OD =(2H+L+k)/4 when 2H>L+k. Here, the condition 2H>L+k guarantees H−p>0. Note that π _R (p ^* _OD )=(L−p)−w(H−p) when e ^* _OD =0. Then in order to guarantee π _R (p* _OD )>0, we obtain that L ²+2Lk+12HL−12H ²−4Hk−k ²>0.(Q.E.D.) □

Proof of Proposition 3

• For (i), differentiating the profit function of supply chain with respect to H and p, we find that if 2β>e ², π _SC (H, p) is jointly concave in H and p. We assume H−p>0, namely when (1−e)(e−β)L>(β+2(1−e))k, let ∂π _SC (p, e)/∂p=0 and ∂π _SC (p, e)/∂e=0, p ^* _SC and H ^* _SC are obtained. For (ii), similarly, differentiating the profit function of supply chain with respect to e and p, we find that if 2β>e ², π _SC (e, p) is jointly concave in e and p. Since H−p>0, we have when (1−e)(e−β)L>(β+2(1−e))k, e ^* _SC and p* _SC are obtained.(Q.E.D.) □

Proof of Proposition 4

• (i), for H, since H ^* _SC −H ^* _OE =[(2−e)(w ^* _OE −k)]/(2β−e ²)>0, we have H ^* _SC >H ^* _OE . Since H ^* _OE is the optimal solution for , we have H ^* _OE >L=H ^* _OD . Thus, H ^* _SC >H ^* _OE >H ^* _OD .

  For w, w ^* _OE −w ^* _OD =−[(1−e)L+(2−e)βL]/(2β+4(1−e))<0.

  For p, p ^* _SC −p ^* _OE =[(e−β)(w ^* _OE −k)]/(2β−e ²)>0=>p ^* _SC >p ^* _OE .

  

  When A=((5e ²−4eβ−2β+2e−4)βL+2(3e+β)(e−β)(1−e)L)/((2−e)(β+2(1−e))e)⩾k, p ^* _OE ⩾p ^* _OD , otherwise, p ^* _OE <p ^* _OD . If B=(3Le ²−2(2e+1)βL)/((2e−2β+2e−e ²))⩾k, p ^* _SC ⩾p ^* _OD , otherwise, p ^* _SC <p ^* _OD .

  Therefore, when A⩾k, p ^* _SC >p ^* _OE ⩾p ^* _OD ; if B⩾k and A<k, p ^* _SC ⩾p ^* _OD >p ^* _OE ; if A<k and B<k, p ^* _OD >p ^* _SC >p ^* _OE

  For (ii), w ^* _OE −w ^* _OD =−((H−L)² H)/(2α)<0, so w ^* _OE <w ^* _OD .

  For e, e ^* _SC −e ^* _OE =−(w ^* _OE −k)(H−L)/[2α−(H−L)²]<0 and e ^* _SC>e ^* _OD =0, then e ^* _OE >e ^* _SC >e ^* _OD .

  For p, p ^* _SC −p ^* _OE =[H(H−L)²−(2H−L−k)α]/[2(2α−(H−L)²)]<0. The inequality holds by the condition (2H−L−k)α>(H−L)² H in Propositions 2 and 3.

  p ^* _SC −p ^* _OD =(−2(2H−L−k)α+(2H+L+k)(H−L)²)/(4[2α−(H−L)²]) , if (2H+L+k)(H−L)²>2(2H−L−k)α, p ^* _SC ⩾p ^* _OD , otherwise, p ^* _SC <p ^* _OD .

  And p ^* _OE −p ^* _OD =((L+k)(H−L)²)/(4(2α−(H−L)²)>0, thus, if (2H+L+k)(H−L)²>2(2H−L−k)α, then p ^* _OE >p ^* _SC ⩾p ^* _OD , otherwise, p ^* _OE >p ^* _OD >p ^* _SC .(Q.E.D.) □

Proof of Proposition 5

• For RS, we consider these four models one by one. For (i), first taking the first and second derivatives of π _R (p, H) with respect to p and H, we can have when 2β>λe ² (and this condition holds because of 2β>e ²), π _R (p, H) is jointly concave in both p and H, then we can obtain p ^* _OE (w)=(λβ(1−e)L+(β−λe)w)/λ(2β−λe ²) and H ^* _OE (w)=(λe(1−e)L+(e−2)w)/(2β−λe ²).

If (H ^* _SC , p ^* _SC )=(H ^* _OE , p ^* _OE ) for some feasible solutions of λ and w, then we can say that the supply chain can achieve the coordination. By solving the equations (H ^* _SC , p ^* _SC )= (H ^* _OE , p ^* _OE ), we obtain that λ=1 and w=k, under which supplier obtains zero profit. Thus, revenue sharing contract cannot achieve the coordination for the OEM strategy with market size outsourcing model. For (ii), (iii) and (iv), similar approach is adopted.

For (ii), we have p ^* _OD (w)=(2β(1−e)L+(w−k)(2−e)e)/(2(2β−(1−λ)e ²))+(w)/(2λ) and H ^* _OD (w)=((1−λ)(1−e)eL+(w−k)(2−e))/(2β−(1−λ)e ²). By solving the equations (H ^* _OD , p ^* _OD )=(H ^* _OE , p ^* _OE ), we obtain that λ=w=0, under which retailer obtains zero profit. Thus, revenue sharing contract cannot achieve the coordination for the ODM strategy with market size outsourcing model.

For (iii), we have p ^* _OE (w)=((λL+w)α)/(λ(2α−λ(H−L)²)) and e ^* _OE (w)=(λL+w)(H−L)/(2α−λ(H−L)²). By solving the equations (e ^* _SC , e ^* _SC )=(e ^* _OE , p ^* _OE ), we obtain that λ=1 and w=k, under which supplier obtains zero profit. Thus, the revenue sharing contract cannot achieve the coordination for an OEM strategy with a success probability outsourcing model.

For (iv), we have p ^* _OD (w)=((H−L)²(λk−w)+2α(λL+w))/(2λ(2α−(1−λ)(H−L)²) and e ^* _OD (w)=((H−L)((1−λ)L+k+w)/(2α−(1−λ)(H−L)²). By solving the equations (e ^* _SC , e ^* _SC )=(e ^* _OE , p ^* _OE ), we obtain that λ=w=0, in which the retailer obtains zero profit.

Thus, the revenue sharing contract cannot achieve the coordination for an ODM strategy with a success probability outsourcing model. For BB, we also consider these four models one by one. For (i), first taking the first and second derivatives of π _R (p, H) with respect to p and H, we can have when 2β>e ², π _R (p, H) is jointly concave in both p and H, then we can obtain H ^* _OE (w)=((1−e)eL−(2−e)w+2(1−e)b)/(2β−λe ²) and p ^* _OE (w)=((1−e)eb+β(1−e)L+(β−e)w)/(2β−e ²). If (H ^* _SC , p ^* _SC )=(H ^* _OE , p ^* _OE ) for some feasible solutions of b and w, then we can say that the supply chain can achieve the coordination. By solving the equations (H ^* _SC , p ^* _SC )=(H ^* _OE , p ^* _OE ), we obtain that b=0 and w=k, under which supplier obtains zero profit. Thus, buyback contract cannot achieve the coordination for the OEM strategy with market size outsourcing model. For (ii), (iii) and (iv), similar approach is adopted.

For (ii), we have H ^* _OD (w)=(2(w−k)(2−e)−2(1−e)b)/(2β) and p ^* _OD (w)=((w−k)(2−e)e−2(1−e)eb+2(1−e)βL+2βw)/(4β). By solving the equations (H ^* _OD , p ^* _OD )=(H ^* _OE , p ^* _OE ), we obtain that w ^* _OD =k and b ^* _OD =(βk(2−e)−(1−e)βeL)/((2β−e ²)(1−e))<0. Substituting w ^* _OD and b ^* _OD into supplier’s profit function, π _S ^OD*=−β(H−L)((2β−e)L+k(2−e)/(2(2β−e ²))<0, supply chain fails to coordinate for the ODM strategy with market size outsourcing model.

For (iii), we have e ^* _OE (w)=((L+w)(H−L)−2(H−L)b)/(2α−(H−L)²) and p ^* _OE (w)=(α(L+w)−(H−L)² b)/(2α−(H−L)²). By solving the equations (e ^* _SC , e ^* _SC )=(e ^* _OE , p ^* _OE ), we obtain that b=0 and w=k, under which supplier obtains zero profit. Thus, buyback contract cannot achieve the coordination for the OEM strategy with success probability outsourcing model.

For (iv), we have p ^* _OD (w)=(2(H−L)² b−(w−k)(H−L)²+2α(L+w))/(4α) and e ^* _OD (w)=(2(H−L)b−(w−k)(H−L))/(2α). By solving the equations (e ^* _SC , e ^* _SC )=(e ^* _OE , p ^* _OE ), we obtain that w ^* _OD =k and b ^* _OD =(α(L+k))/(2α−(H−L)²).Substituting w ^* _OD and b ^* _OD into supplier’s profit function, π _S ^OD*<0 Thus, buyback contract cannot achieve the coordination for the ODM strategy with success probability outsourcing model.

For PS, this is similar to Proposition 3, for (i) and (iii), first taking the first and second derivatives of retailer’s profit function, the results are same as Proposition 3; for (ii) and (iv), first taking the first taking the first and second derivatives of retailer’s profit function with respect to p and then taking the first and second derivatives of supplier’s profit function with respect to H or e, the results are same as Proposition 3. (H ^* _OD , p ^* _OD ) or (H ^* _OE , p ^* _OE ) are independent of φ. Thus supply chain can be coordinated.(Q.E.D.) □