Returns Policies and Smart Salvaging: Benefiting from a Multi-Channel World

Abstract

Up to 50% of online purchases are returned, reducing e-tailers’ profits. E-tailers employ two mitigating measures. First, returns management affects the number of returns via restocking fees and hassle cost; a restrictive policy leads to fewer returns but also depresses demand. Second, salvaging increases e-tailers’ revenue via the resale of returned items. We unite these two and analyze how to most profitably allocate returns to different salvaging channels and how this depends on and influences the returns policy, price, as well as profit. A competitive retailer must adopt a smart salvaging approach while simultaneously setting the price and restocking fee. The result is a profit-maximizing portfolio of salvage opportunities—which includes the primary market, the secondary market, and returns to the manufacturer (RTM)—as applied by highly profitable e-tailers such as Zalando. Yet in reality, most e-tailers salvage returns exclusively in the primary market; that strategy is suboptimal because it reduces profits and yields a too-strict returns policy. The alternative, smart salvaging policy reduces both price and restocking fee but still increases profit. Such a policy requires that managers respond dynamically: new competition calls for more salvaging of returns by RTM; increased market concentration calls for salvaging more in the primary and secondary markets. Products with a longer (resp., shorter) selling time are more profitably salvaged in the primary market (resp., via RTM). A firm’s investment in salvaging opportunities will not pay off unless these considerations are taken into account. We derive implications for e-tailers and recommend managerial strategies for remaining competitive.

Appendix

1.1 Model Formulation and Equilibrium Solution

1.1.1 Demand and Model Formulation

Demand in the primary market is modeled in two steps (here illustrated for the duopoly case). Step I features a Hotelling line; Step II adds a linear demand model.

Step I Two differentiated retailers are located at the opposite ends of a unit-length Hotelling line (Hotelling 1990). On that line, consumers are distributed uniformly according to their a priori product preferences Θ ∈ [0, 1]. While accounting for p, f, and product preference, they decide where to purchase by maximizing their expected utility; i.e., the likelihood of keeping the purchase (1 − α) times the utility of a perfect match (u) minus the price of product i (ε _P p _i) minus the mismatch between expectations and reality (|x _i − Θ|) minus the likelihood of returning the product (α) times the cost of a return (ε _F αf _i):

$$\displaystyle \begin{aligned} U_{i}=(1-\alpha)[u-\varepsilon _P p_{i}-\vert x_{i}-\varTheta\vert]-\varepsilon _F \alpha f_{i}\,\,\text{with}\,\, x_{i=1}=0\,\,\text{and}\,\,x_{i=2}=1. \end{aligned} $$

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There exists a marginal consumer a with Θ = x _a who is undecided between retailer 1 and 2. All consumers to the left of a (i.e., with Θ < a) purchase from 1, and all others from 2. This setting can be extended to an n-competitor circular city model (see Salop 1979). If the retailers behave symmetrically (i.e., charge the same price and restocking fee), demand is distributed equally with D _i = 1∕n.

$$\displaystyle \begin{aligned} U_{1}=U_{2}\enspace\text{for}\enspace x_{a}&=\frac{\alpha \varepsilon _F (f_1-f_2)-(\alpha -1) \left((p_1-p_2)\varepsilon _P-1\right)}{2 (\alpha -1)};\\ D_1&=x_{a}\enspace\text{and}\enspace D_2=1-x_{a}. \end{aligned} $$

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Step II Each consumer on the line is treated as a single, independent market with a negatively sloped, linear demand curve (Huang et al. 2014). Each demand depends on p _i and f _i as well as the likelihood of a return (α)—$d_{p,i}=D_{\max }-\varepsilon _{P} p_i - \varepsilon _F \alpha f_i$. Total demand for each retailer equals the share of consumers deciding to purchase there (i.e., from the Hotelling line) multiplied by the quantity purchased (i.e., from the demand curve). For retailer i, demand in the primary market unfolds as

$$\displaystyle \begin{aligned} D_i{=}\frac{\left(D_{max}{-}(\varepsilon_F \alpha f_i{+}\varepsilon_P p_i)\right) \left(\alpha \varepsilon_F (f_{i}{-}f_{i+1})-(\alpha -1) \left(\varepsilon_P (p_i-p_{i+1}){-}1\right)\right)}{2 (\alpha -1)}. \end{aligned} $$

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1.1.2 Equilibrium Solution

Resulting in a symmetric equilibrium, n retailers choose p _i and f _i to maximize π _i. All retailers face the same cost and revenue functions as well α at 50% as in line with Zalando (Seeberger et al. 2017). Assuming ε _S = 1 and ε _F = ε _P = ε and deriving a general solution we solve the retailers’ maximization problem (2) and (8).

$$\displaystyle \begin{aligned} \mathcal{L}(p_{i},f_{i},\lambda)=\pi_i^{**}(p_{i},f_{i})+\lambda_1(D_{\max}\varepsilon^{-1}-p_i-\alpha f_i)+\lambda_2(p_i-f_i). \end{aligned} $$

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$$\displaystyle \begin{aligned} \begin{aligned} & \mathrm{(A)} && \frac{\partial \mathcal{L}}{\partial p_i} && = \frac{\partial \pi_i^{**}}{\partial p_i} -\lambda_1+\lambda_2 && \leq0 \textit{,} \\ & \mathrm{(B)} && \frac{\partial \mathcal{L}}{\partial f_i} && = \frac{\partial \pi_i^{**}}{\partial f_i} -\alpha \lambda_1-\lambda_2 && \leq0 \textit{,} \\ & \mathrm{(C)} && \frac{\partial \mathcal{L}}{\partial \lambda_1} && = D_{\max}\varepsilon^{-1}-p_i-\alpha f_i && \geq0 \textit{,} \\ & \mathrm{(D)} && \frac{\partial \mathcal{L}}{\partial \lambda_2} && = p_i-f_i && \geq0 \textit{,} \\ & \mathrm{(I)} && p_i\frac{\partial\mathcal{L}}{\partial p_{i}} && = p_i \frac{\partial \pi_i^{**}}{\partial p_i} -p_i \lambda_1+p_i \lambda_2 && =0 \textit{,} \\ & \mathrm{(II)} && f_{i}\frac{\partial\mathcal{L}}{\partial f_{i}} && = f_i\frac{\partial \pi_i^{**}}{\partial f_i} -f_i\alpha \lambda_1-f_i\lambda_2 && =0 \textit{,} \\ & \mathrm{(III)} && \lambda_1 \frac{\partial\mathcal{L}}{\partial \lambda_1} && = \lambda_1 \left(D_{\max}\varepsilon^{-1}-p_i-\alpha f_i\right) && =0 \textit{,} \\ & \mathrm{(IV)} && \lambda_2 \frac{\partial\mathcal{L}}{\partial \lambda_2} && = \lambda_2 \left(p_i-f_i\right) && =0 \textit{,} \\ & \mathrm{(N)} && && f_i,p_i, \lambda_1, \lambda_2 && \geq0 \textit{.} \\ \end{aligned} \end{aligned}$$

Price and Restocking Fee Reviewing the FOC for a maximum $\frac {\partial \pi _i}{\partial p_i} \overset {!}{=} 0$ yields one solution for $p_i^*$. With assumptions made in Table 7, $p_i^*$ fulfills the SOC for a maximum $\frac {\partial ^2\pi _i}{\partial p_i^2}<0$. For $f_i^*$, there are five possible solutions to the FOC. The optimal f _i as a function of q _S,i and q _P,i are the two solutions when solving the first derivative of π _i with respect to f _i for f _i; which one represents the optimum f _i depends on q _S,i and q _P,i. Here, the first derivative of π _i (w.r.t. f _i at $f_i=f_i^*$) is equal to zero whereas the second derivative is strictly negative and thus fulfilling the SOC for a maximum for $f_i=f_i^*$ and $p_i=p_i^*$. Note that the term for $f_i^*$ is highly complex. We therefore do not show the closed form within this chapter.

Salvaging E-tailers set the salvaging allocation while accounting for $f_i^{*}$ and $p_i^{*}$. Even though a closed-form solution (satisfying both the FOC and SOC for a maximum) can be obtained for the optimization problem (see Eq. (9)), it is highly complicated. As the general form is not needed in this chapter, we do not show it.

$$\displaystyle \begin{aligned} \mathcal{L}(q_{P,i},q_{S,i},q_{R,i},\lambda) =\pi_i^{*}(q_{P,i},q_{S,i},q_{R,i})+\lambda(1-q_{P,i}-q_{S,i}-q_{R,i}). \end{aligned} $$

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$$\displaystyle \begin{aligned} \begin{aligned} & \mathrm{(A)} && \frac{\partial\mathcal{L}}{\partial q_{P,i}} &&= \frac{\partial\pi_i^*}{\partial q_{P,i}}-\lambda q_{P,i} && \leq0 \textit{,} \\ & \mathrm{(B)} && \frac{\partial\mathcal{L}}{\partial q_{S,i}} &&= \frac{\partial\pi_i^*}{\partial q_{S,i}}-\lambda q_{S,i} && \leq0 \textit{,} \\ & \mathrm{(C)} && \frac{\partial\mathcal{L}}{\partial q_{R,i}} &&= \frac{\partial\pi_i^*}{\partial q_{R,i}}-\lambda q_{R,i} && \leq0 \textit{,} \\ & \mathrm{(D)} && \frac{\partial\mathcal{L}}{\partial \lambda} &&= 1-q_{P,i}-q_{S,i}-q_{R,i} && =0 \textit{,} \\ & \mathrm{(I)} && q_{P,i}\frac{\partial\mathcal{L}}{\partial q_{P,i}} &&= q_{P,i}\frac{\partial\pi_i^*}{\partial q_{P,i}}-\lambda q_{P,i}^2 && =0 \textit{,} \\ & \mathrm{(II)} && q_{S,i}\frac{\partial\mathcal{L}}{\partial q_{S,i}} &&= q_{S,i}\frac{\partial\pi_i^*}{\partial q_{S,i}}-\lambda q_{S,i}^2 && =0 \textit{,} \\ & \mathrm{(III)} && q_{R,i}\frac{\partial\mathcal{L}}{\partial q_{R,i}} &&= q_{R,i}\frac{\partial\pi_i^*}{\partial q_{R,i}}-\lambda q_{R,i}^2 && =0 \textit{,} \\ & \mathrm{(N)} && && q_{P,i},q_{S,i},q_{R,i},\lambda && \geq0 \textit{.} \\ \end{aligned} \end{aligned}$$

1.1.3 Numerical Proof of Conjectures

We outline in the following the proofs for Conjectures 1–5. Without loss of generalizability, we supply proofs that hold for all admissible parameter values (see Table 7). Note that for simplicity within this chapter, we show mainly numerical simulations (analytic proof for all conjectures is available upon request).

Conjecture 1 Given the properties of the first derivative of π _i with respect to f _i at f _i = 0, we can show that $f_i^*=0$ is not optimal. Since $f_i^*=0$ would be a boundary solution to the optimization problem, this could only be true if $\frac {\partial \pi _i}{\partial f_i}$ at f _i = 0 is ≤ 0. While this can also be shown analytically, a simple numerical simulation outlines the same. In detail, we vary a, b, γ, ρ, and c from their minimum to their maximum with a 10⁻² step size and vary n from 1 to 10⁶ competitors. When c < 0.5, the first derivative of π _i with respect to f _i at f _i = 0 always exceeds zero. Consequently, increasing f _i at f _i = 0 increases π _i. Thus f _i = 0 cannot be profit maximizing (except for c ≥ 0.5).

Conjecture 2 A single-source salvaging portfolio with q _P,i = 1 is a boundary solution to the optimization problem; q _P,i = 1 can only be optimal if the first derivative of π with respect to salvaging in the primary market is larger than the derivatives with respect to the other channels; otherwise, switching to another channel would boost profit—$q_{P,i}^* = 1$ if $\frac {\partial \pi _i}{q_{P,i}} > \frac {\partial \pi _i}{q_{S,i}}$ and $\frac {\partial \pi _i}{q_{P,i}} > \frac {\partial \pi _i}{q_{R,i}}$. For robustness, we review these conditions in a setting which is most favoring toward salvaging in the primary market: duopoly competition (i.e., n = 2) and no refurbishment cost advantage in the secondary market (i.e., a = b = 0). For the above statement to be true, both $\frac {\partial \pi _i}{q_{P,i}} - \frac {\partial \pi _i}{q_{S,i}}$ and $\frac {\partial \pi _i}{q_{P,i}} - \frac {\partial \pi _i}{q_{R,i}}$ must be positive. Otherwise q _P,i = 1 would not be an equilibrium solution. Considering all admissible parameter values, the terms are only positive (i.e., $q_{P,i}^*=1$) if γ > γ _crit, ρ ≤ ρ _crit, and c ≥ c _crit. As the exact critical values are not subject to this chapter and the results represent lengthy statements, they are omitted for brevity.

Conjecture 3 Via a brute-force approach we calculate the restocking fee, price, and the optimal salvaging portfolio for all admissible combinations of exogenous parameters. We vary a, b, γ, ρ, and c from their minimum to their maximum with a 10⁻² step size and vary n from 1 to 10⁶ competitors. While also showing the above claims to hold, this shows for n ≥ 1 and for any possible combination of variables (that allow a portfolio with all three salvaging channels), that $q_{P,i,n}^*-q_{P,i,n+1}^*\in \mathbb {R}^{-}$, $q_{S,i,n}^*-q_{S,i,n+1}^*\in \mathbb {R}^{+}$, and $q_{R,i,n}^*-q_{R,i,n+1}^*\in \mathbb {R}^{-}$.

Conjecture 4 Equation (4) shows that in the primary and secondary markets, scale and learning effects accumulate (i.e., $\sum _{j=1}^{t}q_{P/S,i,j}$ increases in t as q _P∕S,i,j ≥ 0); no other components are affected by T. This lowers the retailer’s cost (per the minus before $\sum _{j=1}^{t}$) and these channels become more attractive in T. Contrary, impediments accumulate in the RTM market and increase cost (per the plus before $\sum _{j=1}^{t}$). Thus RTM becomes more costly. The optimal salvage allocation depends on the achievable margin, which is directly related to salvaging costs. Therefore, RTM becomes less advantageous while the other channels become more attractive. Then, the salvaging portfolio will be shifted away from RTM. Via a numerical simulation (see proof of Conjecture 3) we show that this intuition holds for all parameter values that allow a portfolio with all three salvaging channels. Here, for T between 2 and 10⁴, $q_{P,i,T}^*-q_{P,i,T+1}^*\in \mathbb {R}^{-}$, $q_{S,i,T}^*-q_{S,i,T+1}^*\in \mathbb {R}^{-}$, and $q_{R,i,T}^*-q_{R,i,T+1}^*\in \mathbb {R}^{+}$.

Conjecture 5 Business outcomes improve when acting dynamically (see Eq. (10) for constraints) in response to a changing environment. We use a numerical simulation (see methodology used for proof of Conjecture 3) to compare the least dynamic (B) against the static case (A). The profit effect is described by $\sum \pi _{\mathrm {B}}-\sum \pi _{\mathrm {A}}\in \mathbb {R}^{+}_{0}$. The simulation shows that $\varnothing p_{\mathrm {B}}-\varnothing p_{\mathrm {A}}\in \mathbb {R}^{-}_{0}$ and $\varnothing f_{\mathrm {B}}-\varnothing f_{\mathrm {A}}\in \mathbb {R}^{-}_{0}$ for all admissible parameter values. Note that a dynamic retailer can replicate the decisions of a static one. Thus the former’s profit cannot be worse. Moreover, the dynamic retailer can adjust to new environments and achieve a superior salvage margin. Hence returns become less harmful. Therefore, $\pi _i^*$ increases, $f_i^*$ decreases, and $p_i^*$ decreases.

$$\displaystyle \begin{aligned} \begin{small} \begin{gathered} \max_{\substack{p_{i,t},f_{i,t}, \\ q_{P,i,t},q_{S,i,t},q_{R,i,t}}} \sum^T_{t=1}\pi_{i,t}\quad \mathrm{s.t.}\enspace \begin{cases} \text{A:} & q_{P,i,t}+q_{S,i,t}+q_{R,i,t}=1, q_{P,i,1}=\cdots=q_{P,i,T}, q_{S,i,1}\\ & =\cdots=q_{S,i,T}, q_{R,i,1}=\cdots=q_{R,i,T}, f_{i,1}=\cdots=f_{i,T},\\ &p_{i,1}=\cdots=p_{i,T}; \\ \text{B:} & q_{P,i,t}+q_{S,i,t}+q_{R,i,t}=1, q_{P,i,1}=\cdots=q_{P,i,T},\\ & q_{S,i,1}=\cdots=q_{S,i,T},\, q_{R,i,1}=\cdots=q_{R,i,T}; \\ \text{C:} & q_{P,i,t}+q_{S,i,t}+q_{R,i,t}=1; \\ \text{D:} & \sum_{i,t}^{T}[(q_{P,i,t}+q_{S,i,t}+q_{R,i,t})R_{i,t}]=\sum_{i,t}^{T}R_{i,t}. \end{cases} \end{gathered} \end{small} \end{aligned} $$

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