Mathematical Problems in Engineering

Volume 2018 (2018), Article ID 2560153, 9 pages

https://doi.org/10.1155/2018/2560153

## A Marketing Strategy in a Closed-Loop Supply Chain with Loss-Averse Consumers

^{1}School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Jiangsu, China^{2}School of Mathematics and Information Science, Yantai University, Yantai, China

Correspondence should be addressed to Bi-feng Liao; moc.361@1101oailty

Received 10 May 2017; Accepted 7 November 2017; Published 10 January 2018

Academic Editor: Ibrahim Zeid

Copyright © 2018 Bi-feng Liao and Bang-yi Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The importance of remanufacturing system has been extensively investigated in recent years. Taking into account the consumer valuation uncertainty and the demand uncertainty, this paper addresses the issue of closed-loop supply chain with remanufacturing by game theory. We consider two types of consumers in the market: loss-neutral consumers and loss-averse consumers. The loss-neutral consumers are completely rational. The loss-averse consumers, on the other hand, are with losses being more painful than equal-sized gains being pleasant. When multichannel structure can be chosen, the manufacturer has three pricing strategies in direct market: keeping the price high with a small discount, no customers choose the online store; keeping the price high with a moderate discount, only the loss-neutral customers choose the online store; keeping the price low with a big discount, all customers choose the online store. Consumers make up their decisive selections through comparing the price and channel attributes. We introduce utility function for analyzing the market demand and then identify the optimal pricing and channel strategy to maximize the manufacturer’s profit. Finally, the rationality and validities of the proposed model are illustrated by numerical examples, and sensitivity analyses of the parameters are also presented.

#### 1. Introduction

Nowadays, the importance of the environmental performance and sustainable development is being recognized. In order to reduce environmental pollution and enhance the resource utilization, we push forward the stable development of closed-loop supply chain systems with production remanufacturing. Remanufacturing recovers value from used products to bring the product to like-new condition. Examples from industry show that the quality of remanufactured products is as good as or better than that of the new products; hence they can be sold in the same market. In this paper, we assume that there is no distinction between a new and a remanufactured product.

Our paper relates to several streams of literature; we review them one by one in the following.

The research on the reverse logistics management issues for remanufactured products has received a considerable amount of attention in the past few years. We refer to Fleischmann et al. [1] and Guide Jr. et al. [2] for complete reviews. Most of these research papers use game theory to model remanufacturing decisions [3–6], inventory control [7–9], and collection structures [10–13].

With the rapid development of Internet, a large number of firms have established avenues for selling direct to consumers (e.g., IBM, Nike, Kodak, and Dell). A manufacturer has the right to choose whatever distribution channels he desires and usually takes dual channel as a tool to create more demand. Consumers purchase products based on price and channel preference. Many works regard the Internet channel as the second distribution channel. Liu and Xiong [14] demonstrate the channel model where the new products are sold through the retailer, while the remanufactured products are sold through the direct channel. And then they obtain the price strategy. Wang et al. [15] model the channel structure for marketing the remanufactured products. They find that the subsidy can incentivize the remanufacturing activity in the sense of social welfare and environmental protection, while the manufacturer’s optimal choice may be inefficient. Yan et al. [16] consider the model in which the manufacturer sells new products through the retailer while marketing remanufactured products through the online channel or a third party. The findings show that the manufacturer has less incentive to adopt the online channel because the profit may be worse than subcontracting to the third party. Wang et al. [17] deal with the channel structures for marketing the new and remanufactured products. They compare the three channel strategies and obtain the optimal distribution channel structure for new and remanufactured products. The results show that the dual channel may do harm to the retailer but benefit the consumers. Gao et al. [18] present a dual channel closed-loop supply chain model and analyze the effect of the consumer acceptance of Internet channel on pricing decisions. Giri et al. [19] study the closed-loop supply chain with dual channel and obtain analytically the pricing decisions under five different settings.

As the manufacturer is unlikely to predict all relevant factors, the demand usually does not match what is expected. Most papers studying the closed-loop supply chain in the operations management literature focus on demand uncertainty. Ahiska and Kurtul [20] consider such a system where product returns and demands are stochastic. They show that, in general, the demand risk reduces the system profits and always negatively impacts the manufacturer. Sun et al. [21] present a price-sensitive stochastic demand model based on the loss-averse retailer. With uncertain levels in the amount of raw material supplies and consumer market demands, Zeballons et al. [22] propose a multiperiod, multiproduct, and 10-layer network model. The effects of uncertain demand and supply on the network are analyzed. Li et al. [23] consider the remanufacturing and pricing decisions when both the remanufacturing yield and the demand for remanufactured products are random. They explore two typical decision strategies as first remanufacturing and then pricing and first pricing and then remanufacturing. And they obtain the remanufacturing quantity and selling price for each strategy.

On the other hand, most marketing researchers mainly focus on consumer valuation uncertainty when buying from the direct channel (e.g., [24–26]).

Our paper contributes to the literature related to prospect theory. The behavioral characteristic is of practice relevance and has a significant impact on the consumer’s decision and the manufacturer’s profit. A principle of behavioral economics is that many consumers are loss-averse. Loss-averse expression means the consumers whose perceived benefit of any gain is outweighed by the perceived cost of an equivalent loss [27]. As consumer valuation uncertainty plays a decisive role when they purchase a product, the loss-averse consumer has received a considerable amount of attention in recent years.

To the best of our knowledge, Sibly [28] incorporates the effect of consumer disposition toward a company in the model and draws the conclusion that the equilibrium price is rigid in the face of demand and cost shocks when the consumers are loss-averse. Heidhues and Koszegi [29] establish a model with loss-averse consumers. They embed these consumers in a market with a monopolistic seller for analyzing the demand and investigating the pricing strategy. Several definitions of loss-averse expression are put forward by Abdellaoui et al. [30]. They find the strong evidence of loss aversion at both the individual and the aggregate level. Under prospect theory, Won [31] presents a theoretical investigation on pioneering advantage based on the loss-averse effect. To develop effective market entry strategies, he suggests that companies should carefully analyze the loss-averse consumers and perceived uncertainty of their products. Kim and Lee [32] examine the profit maximizing firm behavior in the context of loss-averse consumers. They analyze the implications of loss aversion on the practice of product differentiation and price discrimination. Rosato [33] considers the problems of profit maximizing pricing and product-availability sales when the retailer sells two substitute products to loss-averse customers. He points out that the limited-availability strategy can manipulate customers into an ex ante purchase.

In this paper, firstly consumers are classified into two segments: loss-neutral (N) and loss-averse (L). Secondly the consumer valuation for direct channel and indirect channel is introduced and the consumer surplus is analyzed for different settings. Finally, the consumer choice is presented according to the consumer utility functions.

Our paper reveals that the standard deviation of consumer valuation, the loss-averse index, the acceptation of the direct channel, and the collection amount of the used products have a much larger effect on the manufacturer’s profit, while the correlation of the two types of consumers does not have a significant effect on the profit. We also observe that the demand variability and the loss-averse degree become especially important for the manufacturer who needs to determine whether or not to introduce the direct channel.

The rest of the paper is organized as follows. Section 2 describes the model. By analyzing the consumer utility functions, we determine the consumer purchasing behavior and characterize the equilibria in Section 3. In Section 4, we compare the three strategies and conduct the sensitivity analysis. Finally in Sections 5 and 6, we present the computational results and offer brief conclusion, respectively.

#### 2. Model Setting

Two marketing channels are considered in this paper: the traditional retailer channel (physical store) and the Internet channel (online store).

When a product first appeared on the market, it is hard for consumers to value it because of the lack of using information. If the products are available on the online store, it provides a virtual description with only the text graphics or symbols in the website. In this case, the consumers’ valuation is even uncertain. Let random variable represent consumer valuation with a density function . To make further analysis easier, we assume follows a uniform distribution, which has a mean and a standard deviation . In order to extract the consumer surplus and not to drive the consumer away, a reasonable price should fall in the range .

Consumer surplus is different depending on the consumer choice. We analyze it case by case.

If the consumer purchases a product in the physical store, the random variable is realized as . For both type of consumers, utility equals surplus.

Since the consumer cannot obtain the use of smell, touch, and taste from the direct market, the consumer surplus may be negative. The utility for type consumers equals surplus, while for type consumers the utility functions are as follows.where indicates how averse a consumer is to loss, and the larger shows that the consumer is more loss-averse.

Let denote a consumer purchasing from the physical store and represent the online store. The stochastic market demands of type and consumers denote by and , respectively. They are jointly distributed as a bivariate normal distribution with expected values and , standard deviations and , and correlation coefficient .

Throughout the paper, we will use the following notations. Let denote the production of new products by manufacturer to meet the* R*-Channel, denote the build-to-order production in the -Channel, and denote consumer value discount for the -Channel, and we characterize the return rate of the end of used products from the customers by . Symbol denotes the unit cost of manufacturing a new product, denotes the unit cost of manufacturing an end of used product into a new one, and thus the average unit cost of manufacturing can be computed as , where is the unit cost saving from reuse. is the retail price through the physical store. When the direct channel is introduced, a consumer pays the discount price for the product; that is, is the retail price through the Internet channel. The total cost of collection can be written as a function of the returned rate of the end of used products and is given by , where is the total returned number from the customers. All of them can be remanufactured into new products.

For convenience, we use the notation as the expected utility of a type consumer when buying in channel , where and .

The expected utility functions are as follows:

#### 3. Analysis and Results

As a benchmark scenario, we start our analysis that focuses on the impact of the loss-averse segment. Our goal is to identify the conditions under which the introduction of online store is profitable.

Proposition 1. *(1) If , both type and customers choose the R-Channel; that is, no customers choose the -Channel.*

*(2) If and , only the type customers choose the -Channel.*

*(3) If , all customers choose the -Channel.*

Based on Proposition 1, we analyze the manufacturer’s expected profit in the following three scenarios.

*Case 1 (both type and customers choose the R-Channel (only R-Channel)). *The demand via the

*R*-Channel is . The random variable has a normal distribution with the mean and standard deviation as follows:The expected profit of the manufacturer isTo maximize the manufacturer’s expected profit, it is well known that the optimal production is where ; and are the density and cumulative function of the standard normal distribution, respectively.

Corollary 2 (the optimal production increases with the return rate and correlation coefficient ). *By substituting and rearranging we yield *

*Case 2 (only the type customers choose the -Channel (both channels)). *When the manufacturer offers a price discount such that the type consumers buy in -Channel, while the consumers buy in* R*-Channel, then, the demands during the two channel structures are and , respectively.

Since random variables and follow a bivariate normal distribution, and also have a bivariate normal distribution. The means that standard deviations and correlation coefficient are as follows:Note that the direct market has the features that consumers submit the orders and they will not receive the product immediately. The manufacturer may provide distribution services a few days later. Thus the delivery time of goods to customers provides a certain buffer time for manufacturer. To reduce the risks, the build-to-order production is more effective for manufacturer in such market circumstance. In this model, the manufacturer lowers the loss of overstock and shortage to zero, while in the physical shop the consumption will lead to the result that purchasing of products does not originate from advertisement anymore but from the product itself. The proper stocking level can ensure that the customer shopping experience is easy and fun. At the end of the selling season, the manufacturer inevitably faces the losses of unmarketable goods or sales.

Then, the expected profit can be expressed as follows:The optimal production and expected profit are In order to attract consumers to turn to -Channel, we know that the price cannot be larger than from Proposition 1. The manufacturer’s objective is to maximize his profit, so he provide the price .

We transform the profit from the -Channel as follows: Therefore, we have the following profit expression:

*Case 3 (all customers choose the -Channel (only -Channel)). *Because the price of the product is different, the demand channel is also very different. When the manufacturer offers a very low price in the -Channel, both type and type consumers buy through -Channel. Hence, the demand is .

During the selling period, the manufacturer’s production of the goods just fits in with the needs of the society.

Then the expected profit isThe optimal profit can be expressed as follows:According to Proposition 1, the price in the -Channel should satisfy . In order to maximize the expected profit, the manufacturer offers a price to satisfy

Corollary 3 (the optimal price of -Channel in Case 3 is always smaller than in Case 2). *To attract both type and consumers to buy in -Channel, the manufacturer has to provide a deeper price discount. It is intuitive since the type consumers require a lower price than type consumers as the motivation to buy in -Channel.*

*Remark 4. *With an increase in the acceptance of the -Channel, the possibility of the type of loss-averse consumers buying from -Channel will increase. But, on the contrary, as the consumers become more loss-averse, the purchase action of consumers will greatly decrease. The manufacturer should attract more consumers to buy products from -Channel by decreasing the price.

#### 4. Sensibility Analysis

By comparing the optimal profits from the above three cases, the manufacturer can make the channel decisions. We show the effects of loss-averse and other parameters on consumers’ equilibrium strategies and the manufacturer’s pricing decisions.

Let denote the profit difference between the Cases 2 and 1; that is, . From the optimal profit expressions, we have where .

Proposition 5. * has the following features.**(1) is a concave function of . When , the -Channel hurts the manufacturer in profit.**(2) increases with . When is more than a certain threshold, the -Channel favors the manufacturer in profit. A higher willingness to pay for -Channel favors -Channel more than R-Channel.*

*(3) increases in .*

*Proof. *(1) To prove that the expression is a concave function of , we take the second derivative of with respect to . Denote and . Part increases in and is always nonnegative.

It is easily to see that increases in if and decreases in if .

When and , that is, , we infer , and . Therefore we have . It shows that the -Channel hurts the manufacturer in profit.

When and , the first part is positive, and the second part is greater than zero for any , so the manufacturer benefits from the -Channel.

From the above analysis, we know that changes from negative to positive. So there exists a threshold such that .

Furthermore, when , the manufacture should not open the -Channel and only sell in the* R*-Channel. When , the -Channel favors the manufacturer in profit. The manufacturer should set a discount to attract the price-sensitive consumers to purchase over the -Channel.

Differentiating with respect to and , we can get the other two conclusions in Proposition 5.

After some algebra, and are obtained as the following expressions:

Proposition 6. *(1) increases in and .**(2) decreases in .*

*Proof. *

Proposition 7. *(1) increases in and .**(2) decreases in and .**Through differentiating with respect to , , , and , we can easily get the proposition.**The manufacturer can compare Cases 2 and 3 by checking the sign of . If , Case 2 is dominated by Case 3, and the manufacturer chooses strategy 3. Otherwise, Case 2 should be followed.*

In view of the complex expressions and , we handle them by numerical analysis.

#### 5. Numerical Experiments

In this section, we examine how the manufacturer’s profit changes with the various parameter values such as consumer loss-averse degree, correlation, the collection rate, the deviation of consumer valuation, and the willingness to pay for -Channel.

The parameter values used in the numerical tests are as follows: = $100, = $60, = $20, = $5, = $10, , , and . Also initially, , , , , and . The curve with squares in Figures 1–5 represents the profit from the -Channel. The curve with asterisks represents the profit from the* R*-Channel. The third curve illustrates the profit from both channels.