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We integrate a retailer's return policy and a supplier's buyback policy within a modeling framework. In this setting, consumers decide whether to buy and then whether to return the product, the retailer sets the retail price, quantity, and refund price, and the supplier chooses the wholesale price and buyback price. Both the demand uncertainty and consumers' valuation uncertainty are considered; consumers realize their valuations only after purchase. We discuss four scenarios for each party in the supply chain that may offer or not offer return policy. We characterize each party's optimal decisions for all scenarios and we show that the supplier's best choice is to provide buyback policy and the retailer's optimal response is to set refund price to be the same as supplier's buyback price.

There has been a growing trend towards the consumer returns in recent years. A large portion of customer returns may be nondefective because the consumer does not like the product as much as anticipated, or the returned product does not fit the customer's need or expectation. Sciarrotta [

Suppliers whose products are subject to uncertain demand face a problem of inducing retailers to stock those products. A supplier may attempt to compensate his retailers by accepting returns of unsold goods for full or partial refunds of their purchase price. The practice of returns policy has been reported widely in both research literature and business, see Bose and Anand [

Although the approaches to dealing with customer returns and the supplier's buyback policies have been well studied, a very few research integrates customer returns policy with a buyback policy. In reality, supply chain is a network of suppliers, retailers, and customers. Some electronic firms (e.g., HP, Lenovo, Nokia) procure modules from their suppliers and sell various fashion electronic products to their customers. To keep the customer's loyalty, the firms offer return policies to their customers; on the other hand, the upstream supplier might also offer return policies to encourage the firms to order more modules to improve the service level for their customers. So consideration of return policies should not be limited within only two levels.

We consider a two-echelon supply chain with a single supplier who supplies a product to a retailer, and the retailer sells the product to the uncertain market. They both offer a return policy to their adjacent downstream firm. The consumers return unsatisfactory product back to the retailer, then the retailer will return unsold items, together with the consumer returns, back to the supplier. In order to differentiate supplier-retailer refund policy from retailer-customer return policy, we use the term “return policy” to refer to the retailer-customer agreement, and “buyback policy” to refer specifically to arrangements between the supplier and his retailers. Most research on buyback agreements only considers unsold inventory resulting from demand uncertainty being returned to the supplier. We also consider a buyback agreement that includes customer returns.

In this paper, we develop an integrated model that investigates the supplier's buyback policy and the retailer's return policy. Based on firms' operational policies, we study both the demand uncertainty and the customers' valuation uncertainty. Specially, we model the above decisions as a Stackelberg game.

The supplier, acting as the leader, offers the retailer a take-it-or-leave-it contract, specifying the wholesale price and buyback price for the returned items.

Given the supplier's decisions, the retailer chooses the order quantity, retail price, and refund price for the customers' returns under both demand uncertainty and valuation uncertainty.

Market demand uncertainty is realized. Based on the retailer's decisions, consumers make two sequential decisions. Initially, facing uncertainty in their own valuations, they decide whether to purchase the product or not. If they buy the product, after realizing their own valuation, they go on to decide whether to keep or return the product.

Unsatisfied consumers return products back to retailer for a refund, the supplier buys back all leftovers from the retailer. These leftover units include units that were unsold and units that were sold but returned.

The purpose of this paper is to shed light on the supplier's and retailer's optimal policy in the presence of customer valuation uncertainty and demand uncertainty. Considering supplier and retailer may offer or not offer return policy, we examine four combinations. For each scenario, we derive each party's optimal decisions. Finally, we figure out that it is optimal for the supplier to present buyback policy and the retailer's ideal response refund price should be as same as supplier's buyback price.

In summary, this paper contributes to the literature by:

The remainder of this paper is organized as follows. Section

The model setting we consider in this paper is a combination of three distinctive features:

A buyback contract is an arrangement where an upstream supplier agrees to provide a retailer credit for unsold product (see [

There is a stream of literatures on consumer returns. Some papers investigate how to prevent inappropriate returns from consumers with no intention of keeping their purchase (Hess et al. [

Fit risk is an important component of purchase uncertainty. For example, when purchasing clothes, buyers are not completely sure whether the new clothes fit into their daily life and the rest of their wardrobe; children may not like the musical instrument that their parents bought for them [

Only a few researchers integrate the buyback policy and consumer return policy. The supplier's buyback policy is exogenously given in Su [

Overall, our model incorporates consumers' valuation uncertainty as well as demand uncertainty. We also consider consumer returns that depend on the retailer's decision variables. This work integrates the supplier's buyback contract, retailer's pricing, refund policy, and consumer's purchase and return behavior within a unified framework.

Consider a supply chain consisting of one supplier (he), one retailer (she), and end consumers. The upstream supplier initiates the process by offering a wholesale price

Similar to Che [

As in Su [

Similarly, we can give the supplier's profit function as:

Considering each party in the supply chain system may offer or not offer return policy, we discuss four combinations in this section. There are neither the supplier nor the retailer offers a return policy (i.e.,

We introduce a dummy variable that takes the values 0 or 1 to indicate the absence or presence of return policy. We will use subscripts and superscripts to facilitate the expression of the model variables. The superscripts

In this scenario, the returns are not accepted in both the supplier and retailer, which means

Observe that when consumer returns are not accepted, the highest price consumers are willing to pay is

Anticipating this, the upstream supplier chooses his optimal wholesale price to maximize

If

All the proofs are provided in the appendix.

In this case, the returns are only accepted in the retailer, which means

The retailer's optimal price

If the supplier does not offer buyback policy, he just find optimal wholesale price to maximize his profit:

If

Remember that the retailer's optimal refund price in this scenario is zero, so when the upstream supplier does not buyback returns, the retailer's optimal response is to choose not to provide return policy to customer either. Notice the other decisions are all the same as the correspondence in scenario 1, so scenario 2 is degenerate into the simply scenario 1.

From the analysis of scenario 1 and scenario 2, we find that if the upstream supplier do not provide buyback policy to the retailer, then the retailer's optimal response is do not allow return behavior of the downstream customer either.

In this case, the returns are only allowed in the supplier, which means

Observing the retailer's optimal response will be (

For any fixed

Combine (

Now we plug

In this case, a supplier sells the product at unit price

For given wholesale price

The optimization problem has a structure similar to that of the centralized problem in Proposition

The retailer's optimal price

Knowing that the retailer chooses

Plugging

For any fixed

After substituting

In Section

Recall the analysis of scenario 1 in Section

From (

From Proposition

From Propositions

From Proposition

However, we cannot analytically make a comparison between

From the above analysis, we can draw the following conclusions: whether the retailer offers return policy to consumers or not, the upstream supplier's optimal policy is always offer buyback policy to the retailer. This is because the supplier has an incentive to enlarge the market by offering buyback policy. In addition, if the retailer does not present return policy, the supplier can profit from the most generous buyback price; if the retailer presents return policy, the supplier can gain profit from the buyback policy, the specific buyback price depends on the system parameters. For the retailer, supplier's buyback policy may hurt her profit. As she is the follower in the supply chain, her optimal response to supplier's buyback price is to implement the same return price.

We provide a guideline for the supplier offering a buyback policy for unsold inventory and customer returns as how to contract a buyback price with the retailer and also guide the retailer how to decide the return policy for the end consumers.

In this paper, we examine return policies in a two-echelon supply chain that comprises an upstream supplier, a downstream retailer, and end consumers. In this environment, the upstream supplier decides his wholesale price and buyback price for returned items; the downstream retailer then chooses her order quantity, retail price, and refund price for customers' returns. The end consumers face uncertainty in their valuation for products. With returns polices, the consumer can then decide whether to keep or return the product. Using this model, we put forth the following results.

If the upstream supplier does not provide buyback policy, the retailer's optimal response is not to provide return policy either; otherwise, the retailer's optimal refund price would be the same as that of the buyback price.

The supplier will adopt buyback policy, as he can always gain more profit than absence of buyback price. Retailer would expect the supplier not to adopt buyback policy, because she may gain a lower profit by facing the buyback policy.

As supplier is the leader of this Stackelberg game, so in the two-echelon system, the supplier will present buyback policy, then the retailer will offer the same amount return policy. The analysis of the specific amount relies on all environmental parameters.

We believe this research will provide new insights for the return policies in a two echelon supply chain. This research can be enriched in several directions. In practice, many retailers permit consumer returns up to a certain time limit, to understand how the duration of returns policy take effect may be necessary. It would be interesting to investigate a related but different context, in which consumers return the product directly to the supplier rather than to the retailer. It is difficult to generate closed-form solutions for general demand distributions; this needs to be investigated in further research.

From (

The first step in maximizing (

The proof here is totally the same as that of Proposition

From (

We define

We can rewrite (

Above all,

We can rewrite (

The analysis here is strikingly similar to that of Proposition

To show

From (

If we fix

The authors wish to express their sincerest thanks to the editors and anonymous referees for their constructive comments and suggestions on the earlier versions of the paper. W. Hu thanks J. Li who is the corresponding author and they both gratefully acknowledge the support of the National Natural Science Foundation of China (NSFC) nos. 71202162, 71171088, 70901029, 71131004, and 71071134 and the Fundamental Research Funds for the Central Universities nos. 65011451, HUST: CXY12M013.