Introduction

Recent years, problems of environmental pollution and resource scarcity have attracted more and more attentions. Governments and enterprises are within their research to make different efforts on these aspects. In practice, governments formulate proper carbon tax policies to restrain the production of products with high pollution and encourage the production of green products [1, 2]. A higher carbon tax rate is proved to be beneficial from an environmental point of view [3]. As is well known, promoting the development of closed-loop supply chains is an effective approach to enhance the yield of green products.

With the raising of consumers’ environmental awareness, the green segment is becoming increasingly important to firms [4]. In Europe, 83% of consumers pay attention to the impact of products over environment [5]. Upwards of 60% of respondents are willing to pay such a premium for green products, on average, the premium that consumers are willing to pay is 16.8% [6]. Following these viewpoints, this study thinks that the emission saving of the remanufactured product attracts extra consumers.

Different from traditional supply chains, closed-loop supply chains focus on recycling and remanufacturing so as to lower the waste of resource, which is regarded as an environmentally friendly and profitable pattern [7]. In many cases, the remanufactured product has the same performance as the new product [8], and we also hold this opinion in this study. Apparently, how to recycle the core component plays a critical rule in the remanufacturing process.

This study considers a manufacturer who produces and sells new products and remanufactured products strategically. Consumers’ different preferences are taken into consideration. For some traditional consumers, they prefer new products rather than remanufactured products. For other consumers who concern carbon emission, the emission saving will attract their attentions. An emission saving is generated when producing a remanufactured product. We aim to examine both single-product market and mixed-product market so as to obtain the optimal strategy under a certain circumstance.

Remanufacturing is a recovery process that transforms a used product into a “like-new” product [9]. In practice, many factors are involved when considering the product remanufacturing, such as carbon tax, production strategy, recycling approach, etc. Carbon tax and production subsidy are two main means of governments to promote the production of remanufactured products. [10] analyzed the impacts of carbon taxes and carbon caps on the remanufacturing decisions, and proposed the optimal carbon policy for the considered scenario. [11] considered remanufacturing subsidy policy and carbon tax policy in a dual-channel supply chain selling both remanufactured and new products. [12] discussed a tax policy, a subsidy policy, and a tax-subsidy policy for a remanufactured problem, and designed a proper regulatory policy. [13] considered both fixed carbon emissions and variable carbon emissions for remanufacturing products, and presented three production decision models.

The production process of the remanufactured product is crucial for a manufacturer. [14] discussed a two-period manufacturing process, in which the remanufacturing activities happen at the second period. [15] constructed two-period production decision models in which the manufacturer produces new products in the first period and makes new and remanufactured products in the second period, aiming to acquire the optimal carbon emission tax policy. [16] considered pure manufacturing and hybrid manufacturing systems, and obtained production and sustainability level decisions by analyzing multiple settings. Recycling mode is another focus of manufacturers. This paper involves manufacturer recycling and third-party recycling. [17, 18] discussed cases in which manufacturers are in charge of recycling. [19, 20] examined the third-party-recycling mode for the remanufacturing.

Despite the abundant literature, there are still some research gaps. First, the consumer’s preference for emission saving hasn’t been explored thoroughly. Some potential consumers who care about carbon emission reduction may be attracted by the emission saving of the remanufactured product. Moreover, some traditional consumers may accept the remanufactured product as a substitution, but others may don’t. This paper pays attention to this phenomenon and examines the impacts of the preference. Second, a binary-product strategy may not be better than a single-product strategy. We aim to determine the dominant region for each strategy. Similar to [21], we focus on production and pricing strategies in this study. The sales quantities (or production quantities) of both the new product and the manufactured product are formulated as a linear function with respect to the unified sales price, following [22]. Table 1 compares the proposed model and the existing models.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Summary of literature review.

https://doi.org/10.1371/journal.pone.0288225.t001

The remainder of this paper is organized as follows. In Section 2, we introduce the notations and make some assumptions for the given setting. Pricing models for a single-product market are constructed in Section 3. In Section 4, we propose a pricing model for a mixed-product market. Section 5 designs numerical illustrations to examine the sensitivity of the crucial parameters. Section 6 summarizes the study and shows the further research topics.

Model description and assumption

This paper discusses production and pricing strategies of new product and remanufactured product in the presence of consumers’ different preferences. For some traditional consumers, they prefer new products rather than remanufactured products. For other consumers who concern carbon emissions, the emission saving per remanufactured product will induce their purchase. We consider two types of markets in this study, i.e., a single-product market and a binary-product market. The manufacturer involved in this study is meanwhile a seller, which means he produces products and then sells by himself.

The notations used in the following discussion are given by Table 2.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Model parameters.

https://doi.org/10.1371/journal.pone.0288225.t002

We make precise explanation for Assumption 2. According to [23], d − δc − δλe > 0 is a necessary condition to guarantee that the demand of the new product is positive in the single-product market. Actually, this condition always holds for almost all literatures with regard to pricing. Assumption 2 needs more stringent requirements, i.e., and

If these conditions don’t hold, some sales models are infeasible. In the following discussion, we will show this judgment.

According to the above setting, we first show the demand quantity of each product when only one type of product is sold. The demand quantity of the new product is

And the demand quantity of the remanufactured product is

Further, the demand quantity of each type of product is formulated according to Assumption 1 when new products and remanufactured products are sold at the same time. The demand of a product decreases with the increase in retail price [24]. Following [25, 26], we adopt an item involving price spread to describe the cross influence on demand quantities. Thus, the demand quantity of the new product is formulated as

And the demand quantity of the remanufactured product is

In addition, we assume that the demand information is complete for the manufacturer, and the recyclable waste products are sufficient so as to guarantee that the manufacturer can produce enough remanufactured products to meet the consumers’ demand.

Pricing models for a single-product market

In practice, multiple-product strategies are not always optimal. In this section, we consider issues that the manufacturer only produces and sells one type of product.

First, we consider the situation in which only new products are sold. The objective function of the manufacturer is

This is a quadratic function with a negative quadratic term. According to the properties of quadratic functions, the solution of max π_n is (marking “*” at the top right corner, similarly hereinafter) (1)

The demand quantity of the new product under (1) is

According to Assumption 2, q_n > 0.

By substituting (1) into π_n, we have (2)

Second, we consider the situation in which only remanufactured products are sold. The objective function of the manufacturer is

This is a quadratic function with a negative quadratic term. According to the properties of quadratic functions, the solution of max π_r is (3)

The demand quantity of the remanufactured product under (3) is

According to Assumption 2, q_r > 0.

By substituting (3) into π_r, we have (4)

Profits gained by selling new products and remanufactured products are compared by (2) and (4). We have

Clearly, whether the value of (π_n−π_r) is positive or negative, depends on (5)

According to the above result, we draw the following conclusion:

Proposition 1 In a single-product market: selling new product is better when

Otherwise, selling remanufactured product is better when

We expound the reasonability of Proposition 1 by making analysis for (5). Clearly, (1 − β)d denotes the decreased demand of remanufactured product, φ∆e denotes the increased demand of remanufactured product brought by carbon emission reduction, δs denotes the increased demand of remanufactured product brought by low production cost, and δλ∆e denotes the increased demand of remanufactured product brought by low carbon tax. Hence, when the decreased demand of remanufactured product is larger than the increased demand, which means selling new product is better than selling remanufactured product.

A pricing model for a mixed-product market

This section considers a mixed-product market, in which both new products and remanufactured products are sold. The price spread works. We will show the necessary condition for this mode to be practicable.

In this situation, the objective function of the manufacturer is

The following equation set is obtained by differentiating π:

By solving the above equation set, we have (6)

The Hessian matrix of π is

Apparently, H is negative definite. Hence, the concavity of π is demonstrated, and the solution given by (6) is the solution of max π. Next, we examine the demand quantity of each type of product.

The demand quantity of the new product under (6) is

According to Assumption 2, q_n > 0.

The demand quantity of the remanufactured product under (6) is

Clearly, whether q_r > 0 or not, depends on the value of (7)

According to [27], the manufacturer produces and sells one type of product when (7) is negative, which degenerates to the case proposed in Section 3. In order to maintain a mixed-product market, it is a necessary condition that (7) is positive. Actually, an equivalent form of q_r > 0 is (8)

By (8), we have which is one condition of Assumption 2. Hence, Assumption 2 is the premise and necessary condition of this discussion.

The profit of the manufacturer in a mixed-product market is

Clearly, it is hard to compare π with the profits gained in the single-product market π_n and π_r. We present the following suppose, and verify it in the next section by numerical examples.

Suppose 1 A multiple-product strategy is not always optimal.

Suppose 1 reveals the following fact: although a mixed-product market retains consumers that reject remanufactured products and meanwhile attracts extra consumers by the emission saving, the price competition between new products and remanufactured products droves away some consumers.

Numerical study

As is shown above, there are two crucial parameters in this study, i.e., the percentage of the tradition demand which is willing to purchase remanufactured products, and the demand coefficient generated by the emission saving. In order to explore the impacts of β and φ over the decisions, we design three numerical illustrations.

The common parameters are given as follows: the tradition demand quantity d = 1000 units, the production cost of a new product c = $100, the cost saving of a remanufactured product s = $50, the carbon emission of a new product e = 100 g, the emission saving of a remanufactured product ∆e = 50 g, the carbon tax λ = $1, the linear price-sensitive rate δ = 2, and the price substitution rate θ = 1.

First, we examine the impact of β under β∈[0.2, 0.8], and set φ = 6. In this situation, the given parameters meet Assumption 2. According to (2), the profit for selling new products in a single-product market is π_n = $45000. According to (4), the profit for selling remanufactured products in a single-product market is

Given the above results, we depict the following curves:

According to Fig 1, β is an important factor for the profit of new products. When the value of β is low, producing and selling new products is better in the single-product market. Otherwise, producing and selling remanufactured products is a better choice.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. The impact of β.

https://doi.org/10.1371/journal.pone.0288225.g001

Second, we examine the impact of φ under φ∈[6, 12] and set β = 0.4. The profit for selling new products in a single-product market is still π_n = $45000. According to (4), the profit for selling remanufactured products in a single-product market is

Given the above results, we depict the following curves:

By Fig 2, it is shown that φ has a similar effect on the profit of new products in a single-product market. The difference is that the sensitivity of φ is relatively low than the one of β.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. The impact of φ.

https://doi.org/10.1371/journal.pone.0288225.g002

By the above two examples, we show that β and φ determine which is the optimal strategy in a single-product market.

Finally, we examine the optimal selling strategy by comparing the three strategies under β∈[0.2, 0.8] and φ∈[6, 12]. The profit for selling new products in a single-product market remains unchanged. The profit for selling remanufactured products in a single-product market is

And the profit for selling both new products and remanufactured products in a mixed-product market is where

According to the above results, we present the following picture:

Fig 3 shows the following fact: different from the intuition, the multiple-product strategy (coloured by blue) is not optimal in most region, which is of practical meaning for a manufacturer to formulate production and pricing strategies. Apparently, Suppose 1 is demonstrated by this example.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Regions of domination for each strategy.

https://doi.org/10.1371/journal.pone.0288225.g003

Conclusions

This paper proposes pricing models for both the single-product market and the binary-product market in the presence of consumers’ preference. The impacts of crucial factors are explored and three production and pricing strategies are compared so as to analyze the superiority of single-product market and mixed-product market.

Our study draws some managerial insights. By setting an emission sensitive demand, we show the superiority of the remanufactured product when the extra demand attracted by the emission saving is relatively large. In the mixed-product market, the price competition between new products and remanufactured products droves away some consumers. When the extra demand attracted by the emission saving is large and the traditional demand ratio that accepts remanufactured product is high, a single-product market of remanufactured product is optimal.

This paper only considers production and pricing strategies in a single-layer framework. In the further research, it is worth to consider the following aspects: (a) the collection process of the waste product; and (b) multi-structural framework. The impact of the collection ratio over carbon emission will be revealed by considering these factors.