This paper examines the optimal order decision in a supply chain when it faces uncertain demand and uncertain consumer returns. We build consumer returns model with decision-makers’ risk preference under mean-variance objective framework and discuss supply chain coordination problem under wholesale-price-only policy and the manufacturer’s buyback policy, respectively. We find that, with wholesale price policy, the supply chain cannot be coordinated whether the supply chain agents are risk-neutral or risk-averse. However, with buyback policy, the supply chain can be coordinated and the profit of the supply chain can be arbitrarily allocated between the manufacturer and the retailer. Through numerical examples, we illustrate the impact of stochastic consumer returns and the supply chain agents’ risk attitude on the optimal order decision.

Consumer returns policy has become an important promotion device in a market, which reassures consumers to purchase the goods. This policy can improve the market demand; meanwhile, it also has increased retailers’ or manufacturers’ processing cost and has caused their serious profits loss. Recent estimates in the consumer electronics industry suggest that the returns rate of electronic devices ranges from 11% to 20%, for a total cost of $14 billion every year in the United States alone [

In general, the management of any company who accepts consumer-returned products often finds that they have to deal with two major uncertainties: the uncertainty with the market demand for the product and the uncertainty with the quantity of the returned product. This is because these uncertainty factors seriously affect the retailer’s ordering decision and make the reallocation of profits between the manufacturer and the retailer in a supply chain. Therefore, it is important to take effective measures to coordinate the two sides. Buyback contract, which has also been called “return policy,” is an agreement between the downstream retailer and the upstream manufacturer and is used to mitigate the risk of overstocking to some extent, so that it could coordinate the supply chain under demand uncertainty.

Our research is motivated by various industry practices, such as fashion, books, and toys. At the selling season, the retailer commits to accept the returned products from consumers. At the end of the selling season, the manufacturer chooses whether to buy back the unsold units together with consumer returns from the retailer. The objective of our paper is to investigate the retailer’s order decision when both the consumer demand and consumer returns are uncertain. Specially, we introduce the following questions: how do stochastic consumer returns and decision-makers’ risk attitude affect the optimal order decisions? Can wholesale-price-only policy coordinate the supply chain with risk-averse agents? How about buyback policy?

To address these questions, we construct a newsvendor model under stochastic consumer returns. We further examine the optimal order quantity in integrated and decentralized supply chain, when the decision-makers have the risk-averse behavior under a mean-variance objective function. And we find in what conditions the supply chain can be coordinated with wholesale price policy and buyback policy, respectively. Finally, we investigate the impact of stochastic consumer returns and risk preference on the optimal decisions.

The remainder of this paper is organized as follows. In the next section, we review the related literatures. We build a newsvendor model with stochastic demand and stochastic consumer returns in Section

There are two streams of literature related to our paper. The first one is on coordination of the supply chain with consumer returns, and the second is mean-variance analysis in supply chain management. Then, we show how we position our research at the intersection of these two streams of literature.

Supply chain contracts are a good way to coordinate the relationship between supply chain members. For example, it can make the optimal decisions (price, order quantity, or sale effort level, etc.) in decentralized supply chain be conducted the same as that in centralized case, and then supply chain members can also gain more profits. Lariviere [

Considering consumer returns policy, Ferguson et al. [

On uncertain demand and returns, Wei et al. [

According to Markowitz [

Using MV analysis methods in a single-echelon supply chain, Chen and Federgruen [

On supply chain coordination under the MV framework, H.-S. Lau and A. H.-L. Lau [

The main contributions of our paper are summarized as follows. First, we investigate the optimal order decision under demand and consumer returns uncertainty. Most prior literature only investigates order decision under demand uncertainty. Second, we further to integrate the supply chain agents’ risk preference behavior into our model. Most prior literature only examines the risk-neutral case. Third, based on the first and second point, we discuss the supply chain coordination under wholesale-price-only and buyback policy, respectively. We find buyback policy is superior to wholesale price policy, and it can perfectly coordinate the supply chain. To the best of our knowledge, this paper is the first in the existing literature that studies the newsvendor problem with decision-makers’ risk attitude under stochastic demand and stochastic consumer returns.

We consider a supply chain consisting of two agents, an upstream manufacturer and a downstream newsvendor retailer, who faces demand uncertainty. In a single sale period, the manufacturer sets the wholesale price

We assume the market demand

Meanwhile, the retailer accepts consumer returns with full refund

The sales quantity is

The variance of the sales quantity is

To explain more clearly, we give the following notations.

The purpose of this paper is to coordinate the supply chain and maximize the entire supply chain’s profit. We start our analysis with the integrated supply chain. In the integrated supply chain, the whole supply chain belongs to one company; for example, the manufacturer owns his own retailer (i.e., company store).

In this paper, we consider the decision-makers’ risk preference behavior. For risk-neutral decision-makers, their aim is to decide the optimal order quantity to maximize the expected profits of the entire supply chain. For risk-averse decision-makers, their objective is to maximize the payoff of the entire supply chain under a mean-variance framework.

The profit of the entire supply chain is

The expected profit of the entire supply chain is

Since

Further, the variance of the total supply chain’s profit is

Since

Under the mean-variance framework, the payoff function of the entire supply chain is

Taking (

For the utility function

From the analysis as before, both

From Lemma

In this paper, we mainly consider both the manufacturer and the retailer are risk-averse. According to Gan et al. [

In the section, we consider the decentralized decision case under the manufacturer’s wholesale price policy. The sequence of this game is conducted as follows. The manufacturer as a leader firstly sets the wholesale price

The retailer’s profit is

The retailer’s expected profit is

Since

Comparing

The variance of the retailer’s profit is

Similar to the result of Section

Under the mean-variance framework, the retailer’s payoff function is

With wholesale-price-only policy, the manufacturer’s payoff function is

According to Lemma

For the utility function

After the manufacturer knows the retailer’s order quantity, he will adjust the wholesale price

In (

The supply chain with risk-averse agents cannot be coordinated by the wholesale price policy.

From Proposition

Cases

In addition, taking (

In this section, we consider that the manufacturer provides buyback contract for the retailer. He buys back the retailer’s unsold and returned products from consumers. The game proceeds as follows. The manufacturer sets the wholesale price

Then, the retailer’s profit is

To guarantee

The retailer’s expected profit is

Since

Comparing (

When the retailer is risk-neutral, the supply chain can be coordinated through the manufacturer’s buyback policy (

See Appendix.

Further, the variance of the retailer’s profit is

Under the mean-variance framework, the retailer’s payoff function becomes

For the utility function

The expected profit of the manufacturer is

The variance of the manufacturer’s profit is

Thus, the manufacturer’s payoff function becomes

After the manufacturer knows the retailer’s order quantity

Under the manufacturer’s buyback policy, the supply chain with risk-averse decision-makers can be coordinated, where

See Appendix.

Proposition

In addition, if

In Lemma

The optimal order quantity satisfies the following equation:

From

Let

Impact of

Impact of

Impact of

Figure

Let

From Figure

Let

From Figure

In this paper, we investigate a supply chain consisting of a manufacturer and a retailer who faces demand uncertainty and consumer returns uncertainty. We obtain the optimal order quantity when the decision-makers are risk-neutral and risk-averse, respectively. Comparing the optimal order quantity in decentralized supply chain with that in integrated case, we derive the conditions where the supply chain can be coordinated under wholesale price contract and buyback policy, respectively. Then, we demonstrate that the manufacturer’s buyback policy can coordinate the supply chain with risk-neutral and risk-averse agents, and then the profits of the supply chain may be allocated between the manufacturer and the retailer. Furthermore, the risk preference of the supply chain agent impacts on buyback price and the allocation of supply chain’s profit. The agent with a lower risk aversion takes a higher proportion of the total supply chain’s profit than the other one does. At last, through numerical examples, we illustrate that more uncertainty factors which include the degree of risk aversion, consumer returns rate, and its variance lead to less order quantity.

In this paper, we investigate how to coordinate a supply chain in case of viewing the retail price as an exogenous variable. Future work on supply chain coordination under demand and consumer returns uncertainty will be interesting through treating the retail price as a decision variable. In addition, all kinds of uncertain environment are valuable for us to explore, such as water resources management under uncertainty in Fan et al. [

Let

Then, taking

Therefore, the profit of the whole supply chain can be arbitrarily allocated between the manufacturer and the retailer.

Comparing (

Further, we require

That is,

Therefore, we have

Taking the previous

The authors acknowledge the valuable comments of the reviewers on an earlier version of this paper. Their comments have significantly improved the paper. This work is supported by Grants from the National Natural Science Foundation of China (nos. 71001025 and 71371003) and the Scientific Innovation Research of College Graduate in Jiangsu Province (no. CXLX11_0122).