A New Product Configuration Model for Low Product Cost and Carbon-Neutral Expenditure

Abstract

In the background of global carbon-neutral requirements, enterprises need to control carbon emissions in the process of product lifecycles in order to gain market competitive advantages. Previous product configuration studies, mostly focused on minimizing carbon dioxide emissions, have ignored the issue of carbon-neutral costs. This study quantifies the product costs borne by enterprises and the carbon-neutral cost borne by the government, respectively. A carbon-neutral cost model for suppliers, enterprises, customers, and recycling plants in the whole life cycle of products was constructed. The whole life cycle carbon emissions and the unit carbon removal costs were taken into account in the carbon-neutral cost model. By minimizing product and carbon-neutral costs, a bi-objective integer programming model was constructed. The NSGA-II algorithm was introduced to solve the Pareto front of the model. The feasibility and effectiveness of this method were then illustrated through a case study and results comparison. It showed that, compared with the scheme of carbon emissions reduction, the optimization scheme with carbon-neutral costs as the object had a significant change. Integrating carbon-neutral costs into product development activities was effective in reducing the enterprise’s product cost and the government’s financial expenditure on carbon removal simultaneously. The proposed model could provide a win–win product configuration scheme for the government and enterprises.

1. Introduction

Mass customization aims to provide customer satisfaction with increasing variety and customization, and it has been successfully applied in many industrial fields, such as residential architecture, electronics, food, and large engineering systems [1,2]. Product configuration is one of the supporting technologies for mass customization, which satisfies customer customization requirements by selecting module instances from candidate modules that combine into product variants [3]. Product configuration design can be abstracted into a mathematical optimization model. In recent years, many scholars have conducted in-depth research on the design of product configurations. Tong et al. [4] built a customer-oriented optimization configuration model, providing customers with multiple choices and reference schemes. Liu and Li [5] considered the effect of the coordination strategy and protection strategy on product family configuration, and the result showed that the two strategies could coordinate supplier capabilities and protect module instances against disruption, respectively. With the enhancement of customers’ awareness of environmental protection, they gradually favored greener products, which also made enterprises transform into product development.

Nowadays, with global warming, more and more people have begun to pay attention to the environmental field. Carbon neutrality was introduced in 2002 to ensure a sustainable and resilient economic recovery [6]. The ultimate goal of the Carbon-Neutral Protocol framework is to reach net zero emissions. With the development of carbon neutralization strategies, some countries have also introduced relevant carbon neutralization schemes and carbon compensation standards. The New Zealand government’s CarboNZero, based on ISO 14065, is the world’s first internationally recognized Greenhouse Gas (GHG) certification scheme. The Australian government put forward the National Carbon Offset Standard (NCOS) in 2009 and put forward the carbon-neutral program based on NCOS. The UK government has set the PAS 2060 specification for the demonstration of carbon neutrality to encourage more measures to tackle climate change. As carbon neutrality receives more attention in more countries, enterprises must also take measures to control the carbon-neutral cost of products. Low-carbon product design has become a hot issue in academic circles. Wang et al. [7] proposed a platform planning approach that considered the cost and greenhouse gas emissions of a product family to support a low-carbon product family design. In order to reduce the product’s carbon footprint and reuse the carbon footprint data, Zhang proposed a novel method for identifying connection units with high GHG emissions [8].

In previous studies, one of the main optimization objectives of product low-carbon configurations has been to reduce the carbon emissions of products [9,10]. Generally, the lower the carbon emissions, the lower the cost of carbon neutrality. However, due to the variant of the cultural, geographical, local environment, the economic development level, and other factors, different regions need to adopt different carbon dioxide removal technologies to achieve carbon neutrality. The differences in carbon dioxide removal technologies could lead to regional differences in unit carbon removal costs. In the process of product processing, enterprises need to select suppliers from different regions to purchase the required modules. This could result in a product with the lowest carbon emissions when its carbon-neutral cost is not necessarily the lowest. Toward this end, a carbon-neutral cost model needs to be constructed to reveal the impact of supplier selection when reducing carbon-neutral expenditure. In this study, we mainly focused on the product configuration problem for carbon removal costs. Our contributions are as follows. Firstly, the concept of carbon-neutral costs was proposed based on carbon dioxide removal technology and previous carbon emission studies. Secondly, the influence of carbon-neutral costs on product configuration results and product costs was analyzed and provided suggestions for decision makers to develop new green products.

This study proposes an integer programming model aimed at minimizing product costs and carbon-neutral costs. An improved genetic algorithm with a chromosome repair mechanism (NSGA-II) was used to solve the model. The difference from previous studies is that this study constructs a carbon-neutral cost model for the whole life cycle of products, which comprehensively considers carbon emissions and the unit carbon removal cost. With the consideration of the carbon-neutral cost, the proposed model provides more realistic guidance for low-carbon product configuration.

The structure of this paper is as follows: the next section briefly reviews the related work. Section 3 describes the optimization problem and establishes the mathematical models of product cost and carbon-neutral costs. Section 4 proposes an NSGA-II model with a chromosomal repair mechanism. Section 5 provides a case study to discuss and analyze the effectiveness of the proposed model. Conclusions and future research are proposed in the final section.

2. Related Work

2.1. Low-Carbon Product Design

Influenced by global warming, the concept of low-carbon design has attracted more scholars’ attention. Greenhouse gases produced by-products are one of the main sources of emissions, and designing low-carbon products is crucial to mitigating climate change [9]. In order to achieve the low-carbon design of products, carbon emissions in the product life cycle should be monitored. Kuo [11] established a collaborative design framework to assist companies in collecting and calculating their carbon footprint throughout the supply chain. He et al. [12] proposed a low-carbon design approach based on the mapping between the design solution and life cycle paths in the product life cycle. A feature-based carbon footprint element model was established to quantitatively estimate the carbon footprint at each stage of the product’s life cycle. Peng et al. [13] provided a low-carbon design method based on a multi-layer carbon footprint information model, which combined direct structural design elements with indirect design elements such as function and principle, and provided a qualitative/semi-quantitative carbon footprint calculation method.

The carbon emissions monitoring of the product life cycle could assist designers in adjusting the structure and processing technology of products and reducing carbon emissions. He et al. [14] considered the interaction effects of solutions at each stage in the product life cycle. Additionally, the total carbon footprint of each stage was optimized by using a dynamic programming-based approach. Kuo et al. [15] reviewed the carbon emissions at each stage of the product and determined whether to optimize the product structure and consumption. This method improved the efficiency of the product carbon footprint calculation and provided convenience for enterprises to design low-carbon products.

By collecting carbon emissions during the life cycle of a product, a low-carbon design system could be established to facilitate the development of low-carbon products. Song and Lee [16] developed a low-carbon product design system to calculate the greenhouse gas emissions of products, which could assist designers in quickly evaluating the alternative parts of low-carbon products. Zheng et al. [17] presented a knowledge-based integrative framework for a low-carbon product design, which could assist designers to create an eco-friendly product. Lin et al. [18] developed a multi-layer integrated framework for low-carbon parts design, using a top-down approach to obtain a component carbon emission assessment model. This framework could help identify carbon-relevant information at the product design stage in terms of a systematic mapping mechanism between design features and carbon emissions.

In addition, low-carbon product design also considers customer demand, the supply chain, design methods, and other factors. Liu et al. [19] introduced the concept of customer-collaborative product innovation into the design process of low-carbon products. By analyzing the heterogeneity of customers, the low-carbon needs of customers were determined. Liu and Li [20] discussed joint carbon reduction and contract coordination in the supply chain. The results showed that introducing a low-carbon reference could promote carbon reductions in the supply chain. He et al. [21] regarded a low carbon footprint as an important benchmark for product performance and proposed lightweight product design under the constraints of a low carbon footprint. To sum up, researchers are paying more attention to the calculation of product carbon footprints and the development of low-carbon design systems; introducing low-carbon concepts at all stages of product design could eliminate the impact of product design and production activities on the environment.

2.2. Product Configuration

The product family configuration design aims to develop a modular product platform from which product family members can be derived by adding, substituting, and/or removing one or more functional modules [22]. Liu et al. [23] proposed a game-theoretic bilevel optimization approach, which revealed distributed collaborative decision-making inherent in the co-evolution of configuration design and supplier selection for a product family. Luo et al. [24] introduced supply risk into product configuration and proposed an optimization model that maximized the total profit and minimized the supply risk of the whole product family. The decision maker could interactively determine the best solution based on the non-dominant solution set obtained from the model. Liu et al. [25] considered customer satisfaction and the evolution of product families in product configurations. The result showed that this method could provide a more competitive product configuration scheme to customers in the future market.

Previous product configuration has focused on product cost, supplier selection, product family evolution, and other issues, while research on low-carbon product configuration has been less. Xiao et al. [26] incorporated low-carbon awareness into product family development activities, and the result showed that carbon emissions had a significant impact on the optimal product family architecting and manufacturing process configuration decisions. Yang et al. [10] explored the impact of carbon emissions on product configuration decisions and carbon procurement decisions and suggested a range of carbon caps for manufacturers and government agencies. Tang et al. [9] proposed a model that maximized customer satisfaction and minimized product GHG emissions and solved the product configuration problem with a two-stage modeling approach. Kim and Moon [27] proposed a method that could identify a sustainable product family configuration by integrating sustainability performance and a platform strategy. Badurdeen et al. [28] proposed a multi-lifecycle-based methodology to solve multi-objective product configuration design problems considering conflicting economic and environmental objectives. However, all the above models were optimized for carbon emissions, ignoring the impact of carbon-neutral costs on the government and enterprises.

2.3. Carbon-Neutral and Carbon Dioxide Removal Technologies

Carbon neutrality is a frontier of eco-compensation research with the presence of global climate change and low-carbon economic development [29]. CO₂ is one of the main greenhouse gases. Carbon neutralization aims to offset the emission and removal of CO₂. At present, most countries have not achieved this goal, and the path to carbon neutrality is still in the stage of exploration. Attahiru et al. [30] proposed that building roads and highways utilizing GHGs as feedstock for renewable energy could assist in reducing advanced GHG emissions in the highway construction industry. Kilian et al. [31] analyzed the impact of implementing carbon-neutral solutions on the company based on Dole Costa Rica’s situation. The result showed that the company not only needed to pay attention to its strategy, market share, and finances but also to decide which offsetting method it could use. Schoedel et al. [32] reviewed the use of metal–organic frameworks in the development of carbon-neutral energy cycles and introduced strategies and technologies that are used in the capture, storage, delivery, and conversion of GHG molecules. Current studies mostly focus on CO₂ capture technology, but there is little research on CO₂ capture costs. Therefore, it is necessary to quantify the cost of CO₂ capture from the perspective of carbon dioxide removal technology.

Carbon dioxide removal technology is an important means of achieving carbon neutrality. It is crucial to pay close attention to technologies and the materiality of carbon offsetting [33]. Terlouw et al. [34] emphasized that carbon dioxide removal technologies should meet the following requirements to result in negative GHG emissions. (1) Carbon removal technology can permanently remove GHGs from the atmosphere; (2) all upstream and/or downstream GHG emissions are quantified and presented in emissions balances for a specific carbon dioxide removal technology; (3) the total removal of GHG emissions must be larger than the total GHG emissions emitted to the atmosphere. So far, there have been many kinds of carbon neutralization technologies applied in daily life. Ten CO₂ utilization and removal approaches were summarized by Hepburn, including chemicals from CO₂, fuels from CO₂, products from microalgae, concrete building materials, CO₂ enhanced oil recovery, bioenergy with carbon capture and storage, enhanced weathering, forestry techniques, soil carbon sequestration techniques, and biochar [35].

From the above review, the research on product configuration in a carbon-neutral global context should not be limited to reducing CO₂ emissions but also needs to focus on the economic benefits of CO₂ removal. Therefore, we proposed a product configuration model for carbon-neutral costs based on existing carbon removal technologies to fill this gap. The breakthrough of the proposed model was to add the consideration of economic benefits on the basis of the previous low-carbon product configuration, only focusing on environmental issues.

3. Optimization Model

3.1. Problem Description

Suppose that an enterprise has developed a modular architecture product that can provide customized products for customers and achieve the mass customization of products. We defined the set of replaceable components in an interface as a replaceable component set (RCS); that is, each RCS consisted of module instances with similar functionalities but different features [36]. Suppose that the module instances in each RCS were screened to satisfy customer requirements. The enterprise would need to select module instances in the RCS for each product variant to satisfy the customer’s customized product requirements. Module instances were purchased from external suppliers s (s = 1, 2, …, S), and the product was assembled by the enterprise company. The bi-objective optimization design of the product cost and carbon-neutral cost was described as follows: The enterprise developed a modular product family architecture, in which the product family variant i (i = 1, 2, …, I) contained j (j = 1, 2, …, J) RCS, each RCS has k (k = 1, 2, …, K) module instances M_jk. In the process of product configuration, module instances that satisfying the constraints could be replaced arbitrarily. Suppose that product carbon emissions generated during manufacturing, assembly, transportation, use, and recycling could be neutralized by carbon dioxide removal technologies. The product configuration optimization problem was defined as the bi-objective optimization of the low-carbon product family to minimize product costs and carbon-neutral costs.

Decision variables x_ijk, y_jks, z_q, and o_s were expressed as follows for the convenience of modeling. x_ijk is a binary decision variable that indicates whether (1) or not (0) the kth module instance of the jth RCS is assigned to the ith product variant. y_jks is a binary decision variable that indicates whether (1) or not (0) the kth module instance of the jth RCS is provided by the sth supplier. z_q is a binary decision variable that indicates whether (1) or not (0) the location chooses the qth carbon dioxide removal technology. o_s is a binary decision variable that indicates whether (1) or not (0) the sth supplier is selected.

3.2. Constraints

Module instances were constrained by functions, compatibility, and dependencies. Three main types of constraints were considered in this paper.

3.2.1. Decision Variables Constraints

For each RCS of a product variant, only one module instance could be selected. For each module instance of RCS, only one supplier could provide it. The constraint was formulated as follows:

$${\displaystyle \sum _{k=1}^{K_j}{x}_{ijk}}=1$$

(1)

$${\displaystyle \sum _{s=1}^S{y}_{jks}}=1$$

(2)

3.2.2. Compatibility Constraints

Some module instances were incompatible with each other, and these incompatible modules could not be assembled in the same product variant. It was assumed that the module instances M_ab and M_cd were incompatible with each other. This constraint relationship is described below:

$$x_{iab}+x_{icd}\le 1$$

(3)

3.2.3. Dependence Constraints

During product configuration, some module instances were strongly dependent on each other. In other words, when a module instance was assembled into a product variant, the module instances with dependencies had to be configured simultaneously. It was assumed that there was a dependency between the module instances Mab and Mef, and the constraint relationship is described below.

$$x_{iab}-x_{\mathrm{ief}}\le 0$$

(4)

3.3. Product Cost Model

In order to improve market competitiveness, enterprises need to reduce the cost of the product family. Variable costs and the fixed cost model were used to calculate the product cost [24,36,37]. The product cost $C_i^{\mathrm{p}}$ of the ith product variant consisted of the inner-company production cost $C_i^{\mathrm{in}}$ and outsourcing cost $C_i^{\mathrm{out}}$.

$$C_i^{\mathrm{p}}=C_i^{\mathrm{in}}+C_i^{\mathrm{out}}$$

(5)

The inner-company production cost could be further divided into fixed costs and variable costs. The fixed inner-company production cost $C_i^{\mathrm{in}\left(\mathrm{fix}\right)}$ included the equipment depreciation cost, infrastructure cost, management cost, etc. Additionally, the variable inner-company production cost $C_i^{\mathrm{in}\left(\mathrm{var}\right)}$ included the costs of assembly, storage, transportation, and so on. The variable inner-company production cost model refers to Steiner’s method [38].

$$C_i^{\mathrm{in}}=C_i^{\mathrm{in}\left(\mathrm{fix}\right)}+C_i^{\mathrm{in}\left(\mathrm{var}\right)}$$

(6)

$$C_i^{\mathrm{in}\left(\mathrm{var}\right)}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^{K_j}{c}_{jk}^{\mathrm{in}\left(\mathrm{var}\right)}}}{x}_{ijk}$$

(7)

where $c_{jk}^{\mathrm{in}\left(\mathrm{var}\right)}$ is the variable unit production cost for the kth module instance of the jth RCS.

Similarly, outsourcing costs could also be divided into fixed costs and variable costs. The fixed outsourcing costs $C_i^{\mathrm{out}\left(\mathrm{fix}\right)}$ included the costs of negotiation, communication, contract signing, quality assurance, etc. The variable outsourcing costs $C_i^{\mathrm{out}\left(\mathrm{var}\right)}$ mainly referred to the purchase cost of module instances that were provided by suppliers. Thus, the variable outsourcing cost for a single product variant could be determined by the total price of selected module instances.

$$C_i^{\mathrm{out}}=C_i^{\mathrm{out}\left(\mathrm{fix}\right)}+C_i^{\mathrm{out}\left(\mathrm{var}\right)}$$

(8)

$$C_i^{\mathrm{out}\left(\mathrm{fix}\right)}=\frac{{\displaystyle \sum _{s=1}^S{g}_s{o}_s}}{n}$$

(9)

$$C_i^{\mathrm{out}\left(\mathrm{var}\right)}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{s=1}^S{c}_{jks}^{\mathrm{out}\left(\mathrm{var}\right)}}}}{x}_{ijk}{y}_{jks}$$

(10)

where g_s is the cost related to adopting the sth supplier; $c_{jks}^{\mathrm{out}\left(\mathrm{var}\right)}$ is the price of the kth module instance of the jth RCS provided by the sth supplier; n is the order quantity.

According to Equations (5)–(10), the total cost of a single product could be expressed as follows. Controlling the product cost enabled enterprises to pursue more profits and market price advantages. Therefore, minimizing the product cost was regarded as one of the main optimization objectives.

$$C_i^{\mathrm{p}}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^{K_j}{c}_{jk}^{\mathrm{in}\left(\mathrm{var}\right)}}}{x}_{ijk}+\frac{C_i^{\mathrm{in}\left(\mathrm{fix}\right)}}{n}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{s=1}^S{c}_{jk}^{\mathrm{out}\left(\mathrm{var}\right)}}}}{x}_{ijk}{y}_{jks}+\frac{{\displaystyle \sum _{s=1}^S{g}_s{o}_s}}{n}$$

(11)

3.4. Carbon-Neutral Cost Model

In the process of product configuration, different module instances of the same module have different manufacturing materials, processing times, and weights, which can lead to different carbon emissions in the production and processing of module instances. In other words, the combination of different module instances makes the total carbon emissions of the product variant different. In addition, product variants with different configuration schemes produce different carbon emissions due to different customer usage habits and recycling plant recycling methods. Therefore, different product configuration schemes can affect the carbon emissions of product variants throughout the life cycle.

Carbon neutrality requires enterprises, organizations, or individuals to offset their direct or indirect CO₂ emissions through carbon dioxide removal technology within a specified period and ultimately achieve net zero emissions. We defined the cost of CO₂ captured from enterprises, organizations, and individuals through carbon dioxide removal technology as the carbon-neutral cost. Different from the concept of a carbon tax, the carbon-neutral cost is not the same as the tax levied on CO₂ emissions, but the cost generated by the country’s CO₂ governance. Carbon-neutral cost is one of the bases for the important reference of carbon tax designation. Carbon emissions and unit carbon removal costs are important factors affecting carbon-neutral costs. As shown in Figure 1, the CO₂ generated in the whole product life cycle was composed of suppliers, enterprises, consumers, and recycling plants. The carbon emissions of the product in the whole life cycle were estimated by collecting the energy consumption (e.g., electric energy consumption in processing, fuel consumption in transportation, fuel consumption generated by using products, etc.) of the product in different stages. The carbon-neutral cost of the product was calculated as follows.

$$C^{\mathrm{cn}}=C^{\mathrm{cn}\left(\mathrm{s}\right)}+C^{\mathrm{cn}\left(\mathrm{e}\right)}+C^{\mathrm{cn}\left(\mathrm{c}\right)}+C^{\mathrm{cn}\left(\mathrm{r}\right)}$$

(12)

$$C^{\mathrm{cn}\left(\mathrm{obj}\right)}=G^{\mathrm{obj}}{C}^{\mathrm{rem}\left(\mathrm{obj}\right)}$$

(13)

where C^cn is the total carbon-neutral cost; C^cn(s), C^cn(e), C^cn(c), and C^cn(r) represent the carbon-neutral cost of suppliers, enterprises, consumers and recycling plants, respectively; C^cn(obj) is the carbon-neutral cost for the object; G^obj is the carbon emissions of the object; C^rem(obj) is the unit carbon removal cost for the object.

3.4.1. Carbon Emissions

(1)

G^s

G^s is the carbon emissions generated by the supplier, which consists of the raw materials stage G^raw(s), the manufacturing stage G^man(s), and transportation stage G^tr-m(s) of the module instance. The manufacturing stage could be divided into direct emissions $G_{jk}^{\mathrm{man}\left(\mathrm{dir}\right)}$ (e.g., exhaust emissions) and indirect emissions $G_{jk}^{\mathrm{man}\left(\mathrm{indir}\right)}$ (e.g., energy consumption). The carbon emissions of a module instance were estimated using the average manufacturing carbon emissions of all module instances in the same batch. This could lead to different carbon emissions for different module instances. Then, the module instances of the product variant with different configuration schemes were counted, and the total carbon emissions of the product variant were calculated. The carbon emissions generated by the supplier were calculated as follows.

$$G^{\mathrm{s}}=G^{\mathrm{raw}\left(\mathrm{s}\right)}+G^{\mathrm{man}\left(\mathrm{s}\right)}+G^{\mathrm{tr}\text{-}\mathrm{m}\left(\mathrm{s}\right)}$$

(14)

$$G^{\mathrm{raw}\left(\mathrm{s}\right)}={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{G}_{jk}^{\mathrm{mat}}}}{x}_{ijk}}$$

(15)

$$G^{\mathrm{man}\left(\mathrm{s}\right)}={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K(G_{jk}^{\mathrm{man}\left(\mathrm{dir}\right)}}}+G_{jk}^{\mathrm{man}(\mathrm{indir})})x_{ijk}}$$

(16)

$$G_{jk}^{\mathrm{man}\left(\mathrm{dir}\right)}=\frac{G_{jk}^{\mathrm{unit}\left(\mathrm{dir}\right)}{T}^{\mathrm{man}}}{n}$$

(17)

$$G_{jk}^{\mathrm{man}\left(\mathrm{indir}\right)}=\frac{G_{jk}^{\mathrm{unit}\left(\mathrm{indir}\right)}{T}^{\mathrm{man}}}{n}$$

(18)

$$G_{jk}^{\mathrm{unit}\left(\mathrm{indir}\right)}={\displaystyle \sum _{v=1}^{V}E{F}_v}{G}_v^{\mathrm{E}}$$

(19)

$$G^{\mathrm{tr}\text{-}\mathrm{m}\left(\mathrm{s}\right)}={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{G}^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{m}\right)}}}{D}_{jk}{m}_{jk}{x}_{ijk}}$$

(20)

where $G_{jk}^{\mathrm{mat}}$ represents the carbon emissions of M_jk using the raw materials stage; $G_{jk}^{\mathrm{unit}\left(\mathrm{dir}\right)}$ and $G_{jk}^{\mathrm{unit}\left(\mathrm{indir}\right)}$ represents the direct and indirect carbon emissions per unit of time in the process of manufacturing M_jk, respectively. T^man is the total manufacturing time of n module instances M_jk; EF_v is the carbon emissions factor of vth energy; $G_v^{\mathrm{E}}$ represents the amount of vth energy consumption per unit time in the process; $G^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{m}\right)}$ represents the unit carbon emissions of transportation; D_jk is the distance between the supplier of M_jk and the enterprise; m_jk is the mass of M_jk.

(2)

G^e

The enterprise purchases module instances from suppliers and assembles them into products for sale. The carbon emissions generated by the enterprise in the process of products assembly G^as(e) and transportation G^tr-p(e) is G^e, as described below.

$$G^{\mathrm{e}}=G^{\mathrm{as}\left(\mathrm{e}\right)}+G^{\mathrm{tr}\text{-}\mathrm{p}\left(\mathrm{e}\right)}$$

(21)

$$G_i^{\mathrm{as}\left(\mathrm{e}\right)}=\frac{G_i^{\mathrm{unit}\left(\mathrm{as}\right)}{T}^{\mathrm{as}}}{n}$$

(22)

$$G_i^{\mathrm{unit}\left(\mathrm{as}\right)}={\displaystyle \sum _{w=1}^{w}E{F}_w}{G}_w^{\mathrm{E}}$$

(23)

$$G^{\mathrm{tr}\text{-}\mathrm{p}\left(\mathrm{e}\right)}={\displaystyle \sum _{i=1}^I{G}^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{p}\right)}}{D}_i{m}_i$$

(24)

where $G_i^{\mathrm{unit}\left(\mathrm{as}\right)}$ represents carbon emissions per unit time in the assembly process; T^as is the total assemble time of n products; EF_w is the carbon emissions factor of wth energy; $G_w^{\mathrm{E}}$ represents the amount of wth energy consumption per unit time in the product assembly; $G^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{p}\right)}$ represents the unit carbon emissions of transportation; D_i is the distance between the enterprise and market; m_i is the mass of the product.

(3)

G^c

The products produced by the enterprise flow into the market and can be sold to consumers. The carbon emissions G^c generated by consumer use in the product life cycle were calculated as follows.

$$G^{\mathrm{c}}={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{h=1}^H(E{F}_h}}}{G}_{jkh}^{\mathrm{E}}{x}_{ijk})T^{lc}}$$

(25)

where EF_h is the carbon emissions factor of hth energy; $G_{jkh}^{\mathrm{E}}$ represents the amount of hth energy consumption of M_jk per unit time in the use process; T^lc is the total operating time of the product in the whole life cycle.

(4)

G^r

At the end of product life, the product needs to be recycled and destroyed. The carbon emissions G^r generated by the recycling plant can be calculated as follows.

$$G^{\mathrm{r}}={\displaystyle \sum _{u=1}^U{G}_u^{\mathrm{rec}}}{m}_u$$

(26)

where $G_u^{\mathrm{rec}}$ represents the number of carbon emissions for disposal per unit of the uth raw material; m_u is the amount of the uth raw material in the product.

3.4.2. Unit Carbon Removal Cost

The unit carbon removal cost estimate mainly depends on the carbon dioxide removal technologies adopted in a region. Hepburn et al. [35] summarized 10 approaches to carbon utilization and removal and gave the carbon dioxide removal potential, utilization potential and profit and loss cost range of each technology. Eight of these technologies with carbon dioxide removal potential were considered in this study. The median values of carbon dioxide removal potential, and breakeven costs represented the overall level of the technology, and the results are shown in

Table 1. Carbon dioxide removal potential and breakeven cost.

No.	Carbon Dioxide Removal Technology	Carbon Dioxide Removal Potential (Mt CO2/yr)	Breakeven Cost ($)
1	Chemicals from CO2	20	120
2	Concrete building materials	750	20
3	CO2 enhanced oil recovery	950	−7.5
4	Bioenergy with carbon capture and storage	2750	110
5	Enhanced weathering	3000	100
6	Forestry techniques	2050	−15
7	Soil carbon sequestration techniques	3800	−55
8	Biochar	1150	−65

. A negative breakeven cost indicated that the technology was already profitable without any incentive to utilize CO₂. Since it was difficult to deploy all technologies in each region, only the first four technologies were counted to estimate the regional unit carbon removal cost. The weight of each technology was estimated based on its carbon dioxide removal potential, and the calculation method is described below.

$$C^{\mathrm{rem}\left(\mathrm{obj}\right)}={\displaystyle \sum _{q=1}^Q{w}_q}{C}_q^{\mathrm{rem}}{z}_q$$

(27)

$$w_q=\frac{cr{p}_q}{{\displaystyle \sum _{q=1}^{Q}cr{p}_q{z}_q}}$$

(28)

where w_q is the weight of qth technology; $C_q^{\mathrm{rem}}$ is the cost of the qth carbon dioxide removal technology; crp_q is the carbon dioxide removal potential of qth technology.

3.4.3. Carbon-Neutral Cost

According to Equations (14)–(28), the carbon-neutral costs of suppliers, enterprises, consumers, and recycling plants could be, respectively, described as follows. The carbon-neutral cost of the product life cycle was the sum of the above four objectives. The carbon-neutral cost model comprehensively considered the carbon emissions and unit carbon removal costs of different objectives. Minimizing the carbon-neutral cost needed to be optimized for objective carbon emissions and unit carbon removal costs. Minimizing the carbon-neutral cost as the optimization objective was beneficial in reducing the government’s carbon neutralization expenditure and the enterprise’s potential carbon tax risk.

$$\begin{array}{l}{C}^{\mathrm{cn}(s)}=({\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{G}_{jk}^{\mathrm{mat}}}}{x}_{ijk}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K(\frac{G_{jk}^{\mathrm{unit}\left(\mathrm{dir}\right)}{T}^{\mathrm{man}}}{n}}}+\frac{({\displaystyle \sum _{v=1}^{V}E{F}_v}{G}_v^{\mathrm{E}})T^{\mathrm{man}}}{n})x_{ijk}\\ \hspace{1em}\hspace{1em} +{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{G}^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{m}\right)}}}{D}_{jk}{m}_{jk}{x}_{ijk})\times {\displaystyle \sum _{q=1}^Q(\frac{cr{p}_q}{{\displaystyle \sum _{q=1}^{Q}cr{p}_q{z}_q}})}{C}_q^{\mathrm{rem}}{z}_q\end{array}$$

(29)

$$C^{\mathrm{cn}(e)}=(\frac{({\displaystyle \sum _{w=1}^{w}E{F}_w}{G}_w^{\mathrm{E}})T^{\mathrm{as}}}{n}+{\displaystyle \sum _{i=1}^I{G}^{\mathrm{unit}\left(\mathrm{tr}\text{-}\mathrm{p}\right)}{m}_i}{D}_i)\times {\displaystyle \sum _{q=1}^Q(\frac{cr{p}_q}{{\displaystyle \sum _{q=1}^{Q}cr{p}_q{z}_q}})}{C}_q^{\mathrm{rem}}{z}_q$$

(30)

$$C^{\mathrm{cn}\left(\mathrm{c}\right)}=({\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{h=1}^H(E{F}_h}}}{G}_{jkh}^{\mathrm{E}}{x}_{ijk})T^{lc})\times {\displaystyle \sum _{q=1}^Q(\frac{cr{p}_q}{{\displaystyle \sum _{q=1}^{Q}cr{p}_q{z}_q}})}{C}_q^{\mathrm{rem}}{z}_q$$

(31)

$$C^{\mathrm{cn}\left(\mathrm{r}\right)}=({\displaystyle \sum _{u=1}^U{G}_u^{\mathrm{rec}}}{m}_u)\times {\displaystyle \sum _{q=1}^Q(\frac{cr{p}_q}{{\displaystyle \sum _{q=1}^{Q}cr{p}_q{z}_q}})}{C}_q^{\mathrm{rem}}{z}_q$$

(32)

4. Utilized Algorithm

The optimization model can be expressed as a nonlinear mixed integer programming model. The configuration optimization model mentioned above is a combinational optimization problem and, thus, is an NP-hard problem. The meta-heuristic algorithm is more effective than traditional algorithms in solving such problems [10]. In addition, since the solution space of the proposed model rapidly expands when the number of RCS and suppliers increases, we eventually considered using the metaheuristic algorithm, NSGA-II, to achieve a near-optimal solution for the optimization problem. NSGA-II could deal with high-dimensional and more difficult multi-objective optimization problems, which is suitable for product family design problems [27,39]. NSGA-II, as the second generation of a multi-objective evolutionary algorithm, uses a fast non-dominated sorting mechanism, an elite protection strategy, and crowding distance to solve the Pareto frontier solution of multi-objective optimization [40]. The flow of the proposed algorithm is shown in Figure 2 and is briefly described below.

4.1. Encoding of Chromosome

In this study, the integer coding technique of chromosomes was used. Individuals in the initial population were randomly created to maintain the diversity of the population. The index of module instances and suppliers was encoded as integers in the gene, ranging from [1, K] to [1, S], respectively. A chromosome consisting of J units corresponded to the product configuration scheme. The front part of the jth unit meant that the kth module instance of the jth RCS was selected, and the back part meant that the kth module instance selected by the front part could be provided by the sth supplier. Figure 3 shows an example of chromosomal coding. The chromosome contained four RCSs, which were configured as follows. The first RCS used the second module instance sourced from the first supplier; the second RCS used the third module instance sourced from the third supplier; the third RCS used the second module instance sourced from the sixth supplier; the fourth RCS used the first module instance sourced from the eighth supplier. Each module instance contained information about the module’s price, the carbon emissions of raw materials, weight, manufacturing time, and distance from the enterprise. In addition, carbon dioxide removal technology options were included in the supplier information to estimate the local carbon-neutral cost. As shown in Figure 3, the sixth suppliers of the third RCS chose the second and third carbon dioxide removal technologies.

4.2. Population Initialization and Chromosome-Repairing

As described in Section 3.2, there were some constraints in the product configuration problem. We mapped these constraints to the gene sequence of the chromosome. Chromosomes should be repaired when there is a conflict between genes. The gene sequence of each chromosome can be detected during the generation of the initial chromosome population. If the chromosome gene does not satisfy the constraint conditions, the repair method is as follows. The first step is to identify and mark the conflicting gene point indexes. Then, the sequence indexes of conflicting gene points are randomly selected, and the index is randomly mutated, as shown in Figure 4. Finally, the repaired chromosomes can be detected again. If the constraint conditions are still not satisfied, the repair method mentioned above is repeated until the chromosome gene sequence satisfying the constraint is obtained. The chromosome-repairing method also applies to chromosome crossover and variation.

4.3. Crossover and Mutation

Crossovers and mutations are genetic manipulations that mainly affect evolution. In this study, a two-point crossover and a single-point mutation were used. In Figure 5, two crossover points were randomly selected for chromosome crossing. Offspring 1 and offspring 2 were generated by exchanging genes between the crossing points of parent 1 and parent 2. The generated offspring chromosomes were new configuration schemes. The single-point mutation is shown in Figure 6. A mutation point was randomly selected, and the gene at the selected point was mutated to generate new chromosomes. To ensure that the module instance and supplier corresponding to the mutation point matched each other, both of them needed to be re-selected. It should be noted that the chromosome gene sequence needed to be detected when the crossover and mutation were completed. If the chromosome gene sequence did not satisfy the constraint conditions, the method mentioned in Section 4.2 was used to repair the chromosome.

4.4. Selection Mechanism and Elitist Strategy

A binary tournament and elite save strategies were used for selection operations in this study. According to the fitness value of the binary tournament selection results, elite individuals were reserved for the next generation with a certain probability.

5. Case Study

5.1. Problem Context

This section uses a motorcycle case to illustrate the proposed approach. The motorcycle had been designed as a modular structure consisting of seven RCS, including steering (RCS1), front wheel suspension (RCS2), rear-wheel suspension (RCS3), electrical system (RCS4), engine assembly (RCS5), seat (RCS6) and chassis (RCS7), as shown in Figure 7. Each RCS contained a set of module instances with similar functionality that could satisfy a variety of customer needs. The module instances number of RCSs was 4, 5, 5, 3, 3, 5, and 3, and the corresponding number of product variants was 13,500 (4 × 5 × 5 × 3 × 3 × 5 × 3). It was assumed that each module instance was provided by only one supplier, and different module instances of the same supplier were transported in the same way. In order to avoid involving some commercially sensitive data, data masking was carried out in this study.

Table 2. Supplier information.

Supplier	Module Instance	The Distance Between Supplier and the Company (km)	Transportation Time (h)	Carbon Dioxide Removal Technology Number
S1	M11, M12	530	66	1, 4, 5, 8
S2	M13, M14	640	84	1, 2, 4, 5
S3	M21, M31	720	104	2, 4, 5, 7
S4	M22, M32	485	72	2, 4, 5, 6
S5	M23, M33	620	83	1, 3, 4, 8
S6	M24, M34	690	77	1, 2, 5, 6
S7	M25, M35	780	90	3, 4, 5, 7
S8	M41	390	56	2, 3, 5, 8
S9	M42	550	74	3, 4, 5, 6
S10	M43	530	68	1, 5, 6, 8
S11	M51, M52	460	78	1, 2, 5, 7
S12	M53	580	87	2, 4, 5, 7
S13	M61, M62	300	18	3, 4, 5, 7
S14	M63, M64, M65	470	22	2, 4, 6, 8
S15	M71	375	69	2, 4, 7, 8
S16	M72, M73	310	66	1, 3, 5, 7

and

Table 3. Candidate module instance information.

Instance	Variable Unit Cost ($)	Purchase Cost ($)	Mass (kg)	Manufacturing Time (h)	Carbon Emission (kg)
M11	0.4	47.74	7.8	9.5	6.8
M12	0.3	44.02	7.2	10.7	6.4
M13	0.2	46.5	7.9	12.6	7
M14	0.3	41.385	7.3	12.1	5.7
M21	0.2	89.59	8.4	17.6	7.2
M22	0.1	86.025	8.7	15.1	7.9
M23	0.2	86.8	8.6	18.4	7.2
M24	0.1	87.73	8.5	18.7	7.8
M25	0.2	78.12	8.9	17.7	7.5
M31	0.2	91.605	11.1	19	9
M32	0.2	89.745	11.1	18.9	7.6
M33	0.1	92.38	11.7	17.5	8.1
M34	0.4	97.96	10.7	18.6	7.7
M35	0.4	95.945	11.4	16.7	8.9
M41	0.2	78.74	9.5	22.8	8
M42	0.2	87.575	7.8	20.1	9.1
M43	0.2	74.865	8.1	21.1	9.3
M51	0.4	232.5	66.7	46.1	21.2
M52	0.2	258.85	68.9	45.4	20.8
M53	0.1	226.3	70	43.5	22.4
M61	0.3	50.685	6.9	7.8	5.2
M62	0.2	50.84	6	7.5	5.3
M63	0.2	47.585	6.7	9	5.6
M64	0.2	49.135	6.3	9.2	5.1
M65	0.1	48.98	7.6	6.7	5.8
M71	0.1	154.535	28.6	27.6	14.9
M72	0.4	145.855	32.6	30	14.2
M73	0.4	157.015	26.8	26.7	15.2

show the supplier information and candidate module instance information, respectively.

The compatibility and dependencies between the module instances are shown below.

$$\left\{\begin{array}{l}{x}_{i11}+x_{i23}\le 1\\ x_{i12}+x_{i23}\le 1\\ x_{i14}+x_{i21}\le 1\\ x_{i13}+x_{i22}\le 1\\ x_{i31}+x_{i72}\le 1\\ x_{i33}+x_{i71}\le 1\end{array}\right.$$

(33)

$$\left\{\begin{array}{l}{x}_{i33}-x_{i42}\le 0\\ x_{i51}-x_{i72}\le 0\end{array}\right.$$

(34)

It was assumed that all module instances had the same direct carbon emissions (0.04 kgCO₂e/h) and indirect carbon emissions (4.5 kgCO₂e/h) per unit time in manufacturing. The unit carbon emissions of the module instances and product variants were 0.0005 kgCO₂e/kg·km. The assembly time of the motorcycle was 2.5 h, and the carbon emission per unit of time in the assembly process was 0.8 kgCO₂e/h. The distance between the company and the market was 20 km. The carbon emissions of the motorcycle were mainly caused by gasoline energy. It was assumed that the consumer rode for 3000 h in the whole life cycle of a motorcycle, and the average fuel consumption of the motorcycle was 1.1 L/h. The unit of carbon emissions caused by gasoline combustion was 2.3 kgCO₂e/L. The carbon emissions per unit of raw material disposal at the end of the motorcycle’s life was 0.2 kgCO₂e/h. The unit carbon removal cost at the location of the enterprise, consumer, and recycling plant locations is shown in

Table 4. Unit carbon removal cost for different object.

Object	Carbon Dioxide Removal Technology	Unit carbon Removal Cost ($/t CO2)
Enterprise	1, 2, 5, 6	49.25
Consummer	2, 5, 6, 7	7.84
Recycling plants	1, 3, 4, 7	11.81

.

5.2. Implementation and Results

The NSGA-II algorithm was used to construct the product cost and carbon-neutral cost bi-objective optimization model (PC-CNC). NSGA-II was coded in the programming language Matlab and was run on a desktop computer (8 GB RAM, 3.60 GHz CPU using Windows 10). The population size of NSGA-II was set to 100, and the number of iterations was 100. The crossover rate and mutation rate were set to 0.9 and 0.1, respectively. Figure 8 shows the Pareto frontier after 10 repeated solutions. The first solution had the lowest product cost and the highest carbon-neutral cost. The 17th solution was the opposite, with the highest production cost and the lowest carbon-neutral cost. Through a comparison of 17 schemes, it was found that if the enterprise reduced the product cost, the carbon-neutral cost borne by the government would increase correspondingly.

The optimal configuration results when the government’s carbon emissions control budget for the products was $80, $82, $84, and $86, respectively, are shown in

Table 5. Optimal configuration results.

Carbon Emission Control Budget	86$	84$	82$	80$
Optimal configuration result	M14, M25, M32, M43, M51, M65, M72	M14, M25, M35, M43, M51, M63, M72	M12, M25, M35, M43, M51, M63, M72	M12, M25, M35, M43, M52, M63, M71
Total product cost ($)	713.25	718.36	720.99	755.52
Carbon emission amount (kgCO2e)	8418.81	8421.78	8415.68	8402.34
Carbon-neutral cost ($)	85.80	82.80	81.17	79.98

. It could be seen that the product configuration with a relatively low cost but high carbon dioxide emissions tended to be selected when the carbon emissions control budget was abundant ($86 or $84). On the other hand, when the carbon emissions control budget was low ($80 or $82), the product configuration with a relatively high cost but low carbon dioxide emissions were often selected. Carbon emissions fluctuate with the increase in the carbon-neutral cost, but the overall trend is upward, as shown in Figure 9. This shows that the carbon-neutral cost model fully considers the carbon emissions in product configuration and can effectively help designers to develop a low-carbon product family.

5.3. Comparison and Discussion

In order to confirm that the PC-CNC model was more suitable for the product configuration requirements under the background of carbon neutrality, two traditional optimization methods were compared: (1) the single objective optimization model considering only product cost (PC-SINGLE), and (2) the bi-objective optimization model considering product cost and carbon emissions (PC-CE). The calculation of the product cost and carbon emissions was based on the method provided in Section 3.4.1. The solving algorithms and parameters of PC-Single and PC-CE models are shown in

Table 6. Solving algorithms and parameters.

Model	PC-SINGLE	PC-CE
Solving algorithm	GA	NSGA-II
Population size	150	100
Number of iterations	50	100
Crossover rate	0.8	0.9
Mutation rate	0.2	0.1

. Figure 10a,b shows the optimal solution of the PC-SINGLE model and the Pareto frontier solution of the PC-CE model after 10 repeated solutions, respectively. As a single objective optimization model, PC-SINGLE had only one product cost-optimal solution, which was 711.96$. The PC-CE model and PC-CNC model had almost the same product cost (710$–760$) for the enterprise.

The carbon emissions and carbon-neutral cost of the three models’ solutions are shown in Figure 11. The results show that, compared with the PC-SINGLE model, both the PC-CNC and PC-CE models could effectively reduce the carbon emissions of the whole product life cycle. Since carbon emissions are considered in the PC-CNC and PC-CE models, these two models have certain similarities. Therefore, the PC-CNC and PC-CE models have two identical configuration schemes. The remaining configuration schemes indicate that the carbon emissions of the PC-CNC model are relatively high, but the carbon-neutral cost is significantly lower than that of the PC-CE model. PC-CNC model provides a quantitative method to estimate the carbon-neutral cost of products based on the low-carbon product configuration and more practically considers the impact of the carbon-neutral cost on the government and enterprises.

The PC-CNC solution increased carbon emissions compared to the PC-CE model but reduced the total carbon-neutral cost for the government. Reducing carbon dioxide emissions is an important measure to alleviate the greenhouse effect. However, too much pursuit of the lowest carbon emissions could lead to an increase in carbon-neutral costs. An increase in carbon-neutral costs could not only increase the government’s financial expenditure but also increase the penalty factor for enterprises’ excessive carbon emissions, which would directly affect the net profit of enterprises. Achieving carbon neutrality is a long-term process in which the government and enterprises aim to reduce their carbon emissions in a more gradual manner. Especially for some countries that have not reached peak carbon dioxide emissions, appropriately increasing their carbon peak could reduce the financial expenditure of carbon removal to a certain extent. This also means that the government would reduce the punishment for the carbon emissions of enterprises. Therefore, it is not comprehensive to only consider the carbon emission factors in the low-carbon product configuration, and it would have more realistic significance to integrate the carbon-neutral cost into the product configuration model.

Based on the PC-CNC model, when enterprises develop a low-carbon product family, they need to obtain the distribution of major carbon dioxide removal technologies in different regions through investigation. Generally, suppliers of module instances are distributed in a wide span of regions, and the unit carbon removal cost varies significantly in different regions. Enterprises should consider the unit carbon-neutral cost of module instances provided by suppliers to select the best assembly mode for each product variant. The regional distribution of enterprises, consumers, and recycling plants is stable, and the unit carbon removal cost is relatively fixed; therefore, the carbon emissions of products should be reduced. Therefore, appropriate suppliers should be selected to achieve the lowest cost of carbon neutrality, while enterprises, consumers, and recycling plants also need to reduce their carbon emissions. The impact of carbon-neutral costs on the government and enterprises means that both the government and enterprises need to make joint decisions to achieve low-carbon product development. In summary, the PC-CNC model provides optimized product configuration solutions that can effectively reduce carbon-neutral costs to achieve a win–win situation for the government and enterprises.

6. Conclusions

With the increase in the greenhouse effect, the issue of carbon emissions has attracted the attention of the government and enterprises. Many researchers have focused their attention on environmental issues in product configuration. However, the carbon neutral-cost has always been ignored due to the immaturity of current carbon dioxide removal technologies. So far, most countries have yet to achieve carbon neutrality. It also gives countries more time to choose carbon-neutral solutions.

In this study, a new bi-objective optimization model was developed to integrate the carbon-neutral cost into product configuration. The PC-CNC model takes product cost and carbon-neutral cost as optimization objectives. The product cost, carbon emissions, and regional unit carbon removal cost models were established, respectively, and the product configuration scheme was generated based on the NSGA-II algorithm. The motorcycle case study demonstrated the reasonableness and superiority of the proposed approach. Compared with the optimization object of carbon emissions, the PC-CNC model demonstrated a similar ability to reduce carbon emissions. It assisted decision makers’ reduction in carbon emissions and the development of green products at an early stage of product design. In addition, the PC-CNC model provided a quantitative method to estimate the carbon-neutral cost of products. Reducing carbon-neutral costs not only reduces the financial expenditure on governments but also reduces the potential carbon tax penalty for enterprises. Consequently, to achieve a win–win situation between the government and enterprises, enterprises are required to choose the best supplier in the product configuration process.

Despite the above benefits, this study has its limitations. We only considered the interests of the government and business in this study. However, customers’ preferences for products can also affect the configuration of products in the real market. Therefore, one of the future research directions is to bring customer factors into product configuration optimization to achieve a win–win situation between the government, enterprises, and customers. In addition, carbon dioxide removal technology continues to evolve as technology advances. Future work may consider the impact of more carbon dioxide removal technologies on the carbon-neutral cost.