Integrating Bass model in a closed loop supply chain system with low and high product return scenario under carbon cap and trade policy

Abstract

Sustainability has become a major industry concern in the last decade to maintain the prosperity of current and future generations. A closed-loop supply chain (CLSC) is considered in line with sustainability because it involves the return of used products in manufacturing, which will reduce end-of-life product waste and the use of raw materials. This research has two contributions to the CLSC literature. First, demand and the quantity of returned products are estimated using the Bass model with a certain return rate, which will become the input of the product mix decision model. Second, carbon caps and trade policy is considered in the model to achieve sustainability. The analysis showed that carbon bought and sold are significantly affected by carbon cap threshold, manufacturing cost, and remanufacturing cost in both low- and high-return cases. The profit was not sensitive to the change in carbon cap threshold and remanufacturing cost but was significantly impacted by the change in manufacturing cost.

Keywords:

• Sustainable industry
• Bass model
• closed-loop supply chain
• remanufacturing
• carbon cap and trade

1. Introduction

Sustainability has become a major concern in the manufacturing industry in the last decade. The manufacturing company has to shift its focus from single consideration in terms of economics to triple bottom lines. Those additional considerations consist of social and environmental. Due to the rise of global environmental consciousness, manufacturing company has to increase their efficiency in raw material uses and energy consumption and develop strategies to decrease carbon emission, which has been acknowledged as the major source of climate change. According to the results of COP 26, the participant countries of the United Nations Climate Change Conference have agreed to limit the rise of the earth’s temperature to 1.5°C in 2060. In this context, the closed-loop supply chain (CLSC) is considered an effective way to lower the impact of industrial activities on the environment.

In a CLSC, once a product enters its end of life, it will be returned by consumers to the manufacturers for further reconditioning, repairing, or remanufacturing (Ijomah, 2009). Industries that fulfill demand from manufacturing and remanufacturing production are known as the hybrid manufacturing-remanufacturing production system. Carbon emission policies are also often used to achieve sustainability. Three carbon emission policies are widely adopted in developed countries: cap and trade, strict cap, and carbon tax. The government sets a carbon cap as the allowable limit on carbon emissions in a cap and trade policy. Then, the companies can sell the surplus of their carbon emissions or buy the carbon when the emitted carbon exceeds the cap.

One of the important decisions that should be made when an industry implements a hybrid manufacturing-remanufacturing system is how to determine the quantities of new and remanufactured products. In this paper, we developed an optimization model to determine the optimal product mix that maximizes the company’s net profit. The model can be used for an industry that implements a hybrid manufacturing-remanufacturing system by considering carbon caps and trade policy. The Bass model is used in this research to estimate the product demand and the quantity of returned products from consumers. The output resulting from the Bass model will be used as the input data for the mathematical optimization model.

The rest of this paper is organized as follows. Section 2 presents a literature review on the hybrid manufacturing-remanufacturing systems model and carbon emission policies. In Section 3, we describe the system description. Section 4 presents the model assumptions, notations, and model formulation. In Section 5, a numerical example is given to illustrate the models’ implementation along with the sensitivity analysis results. Lastly, the conclusions are drawn in Section 6.

2. Literature review

Many previous studies have discussed the implementation of a CLSC. In recent years, there has been a growing interest in CLSC issues in terms of reverse logistics, recycling, remanufacturing, and reusing of products or components due to the environmental concerns, economic issues, and legal obligations so that companies should take into account the recovery options, such as recycling and remanufacturing, while in the same time preparing their tactical plans (Subulan & Tasan, 2013). Remanufacturing is a viable way to prolong the useful life of an end-of-use product or its components. Despite its economic, environmental, and social benefits, remanufacturing is associated with many challenges related to core (used product or its components) availability, timing, and quality (Kurilova-Palisaitiene et al., 2018). The configuration of the reverse logistics network is complex comprising the determination of the optimal sites and capacities of collection centers, inspection centers, remanufacturing facilities, and recycling plants, including the product price and advertising decisions (Alumur et al., 2012; Asghari et al., 2022). Another aspect that makes the configurations more complex is the reshoring decisions.(Kim & Chung, 2022). The model helps a decision-maker to decide whether the production facilities must be relocated to the home country or still in the host country.

A CLSC model has been developed in Jeihoonian et al. (2017) with remanufacturing for a single modular product, and a fuzzy multi‐objective mixed integer linear programming (FMOMILP) model was proposed in Pourjavad & Mayorga (2018) to simultaneously minimize cost and environmental effects and maximize social impacts for a multi‐echelon and multi‐period CLSC network. In a multi-product closed-loop system environment, a model has been developed by Shi et al. (2011) where the manufacturer has two channels for supplying products: producing brand-new products and remanufacturing the returned products into as-new ones. In a more complex problem with a similar environment (Shi et al., 2011), a model has been developed by incorporating uncertainty in the case of tire and shrimp products (Fatthollahi-Fard et al., 2021; Mosallanezhad et al., 2021). Another research by Subulan & Tasan (2013) developed a mathematical model to focus primarily on integrating remanufacturing as a recovery option into the tactical planning process. A product mix optimization model was developed by Bagalagel & ElMaraghy (2020) in Industry 4.0 with a hybrid manufacturing-remanufacturing system. The research aims to determine the optimal number of the product mix in such a manufacturing-remanufacturing system to maximize profit (Bagalagel & ElMaraghy, 2020).

An integrated optimization model for CLSC, which produces new and reconditioned products, has been developed by Gaur et al. (2017) with a real-world case study of a battery manufacturer. Zhong et al. (2017) established a hybrid manufacturing-remanufacturing production decision model for the product in a stable market environment by considering the update cycle of the product’s life cycle. An optimization model has been proposed to solve the problem of manufacturing-remanufacturing—transport–warehousing CLSC (Turki et al., 2017). The company is assumed to have two machines for manufacturing and remanufacturing, manufacturing stock, purchasing warehouse, transport vehicle, and recovery inventory. Three models have been developed by Su et al. (2018) to study the decision mechanism in a CLSC with different players (retailer, a third-party service, or retain it exclusively) that were selected to collect the used product.

Commonly, the quality and quantity of the returned products in a CLSC are considered as the input parameters (Zeballos et al., 2018). A model was proposed by Wang et al. (2017a, 2017b) to determine the number of components used in remanufacturing using Bass’ model, a product diffusion dynamics approach widely used to estimate the demand for a new product. The model has been used to predict the demand quantity of fashion (Tashiro, 2016), automotive (Fan et al., 2017), and solar water heaters (da Silva et al., 2020). In Rosyidi (2021), a framework was proposed to implement the models of Wang et al. (2017a, 2017b) in predicting the demand and the returned product. Hence, their quantity has a quantitative justification rather than being treated as a given input parameter.

According to Avenyo & Tregena (2022), China emitted the highest carbon dioxide compared to other countries such as Russia, South Africa, and India. This condition was resulted from the large population of China and the used of high level intensive productions. In average, the carbon emissions from the countries under study were more than 200,000 kilotons. Based on the data total Green House Gas emissions of Indonesia in 2012 were estimated at 1,454 million metric tons of carbon dioxide equivalent MtCO2e. Those study showed that many efforts must be made to globally reduce the carbon emissions. The research of Lamba & Singh, (2019) and Lamba et al. (2019) strengthened the importance of minimizing carbon emissions in a supply chain by determining the optimal combination of suppliers and their corresponding lot sizes. Using the same policies, Fareeduddin et al. (2015) developed an optimization model in a CLSC. A model was developed to design a logistics network in an environmentally friendly hybrid manufacturing-remanufacturing system industry by considering carbon emissions that include carbon emissions during the manufacturing/remanufacturing process and carbon emissions in transportation (Wang et al., 2013). In this research, we develop an optimization model to determine the product mix of a hybrid manufacturing-remanufacturing system in a single time horizon. The model is formulated using linear programming to maximize the profit. The quantity of the returned products will be estimated using the Bass model. This model also considers the carbon cap and trade policy. The decision variables in this model include the production quantity of the products by regular manufacturing, the number of products by remanufacturing, the quantity of discarded products, and the quantity of carbon emission, either bought or sold.

Other researchers in this area developed meta-heuristics and algorithms to solve the model efficiently. Several researchers implemented a hybrid algorithm to solve the models. Some of the interesting hybrid algorithms are the hybrid genetic algorithm and simulated annealing (Li et al., 2019), the combination of the red deer algorithm and whale optimization algorithm with genetic algorithm and simulated annealing (Fatthollahi-Fard et al., 2021), and the extension of particle swarm optimization using crowd learning theory (Asghari et al., 2022).

3. System description

The mathematical model proposed in this paper addresses a manufacturing-remanufacturing production planning for a hybrid manufacturing-remanufacturing system to fulfill the company’s demands. The company follows a carbon cap and trade policy in its production process. Demand and the quantity of returned products are estimated using the Bass model with a certain return rate. Figure 1 shows the system under consideration. The company’s demands are fulfilled by manufacturing and remanufacturing products. In the manufacturing process, the manufacturer buys raw materials from suppliers and then processes them into finished products and sold to customers through distribution dealers. In remanufacturing, customers return their used products to the company through distribution dealers. Those used products will be disassembled and inspected at the company facility and then processed with raw materials obtained from suppliers to produce remanufacturing products, which are finally sold to customers through distribution dealers. Meanwhile, the used products that do not pass the quality inspection will be disposed of with no salvage values.

Figure 1. System Description.

4. Model development

4.1. Model assumption

The assumptions of the model are as follows:

1. The model covers production planning for the hybrid manufacturing-remanufacturing system, with the demand for each period and the quantity of the used products estimated using the Bass’ diffusion model approach with a certain return rate.

2. Product demand is fulfilled either by manufacturing or remanufacturing production.

3. Remanufactured products are produced using one component from the returned product.

4. Product materials are purchased from a single supplier.

5. The new products, as well as remanufactured products, are sent to a single distribution dealer who is the collector of returned products from customers.

6. The unit transportation cost from the manufacturer to the distribution dealer has the same value as the transportation cost of the returned products back to the disassembly-inspection facility.

7. The disassembly-inspection facility is located at the manufacturer’s site.

4.2. Model notations

Table

Indices
t	Time period	year
Decision Variable
$Q_{ma{n}_t}$	Quantity of manufactured product in time period t	unit
$Q_{re{m}_t}$	Quantity of remanufactured product in time period t	unit
$Q_{dis{p}_t}$	Quantity of a product to be disposed in time period t	unit
$E_{s_t}$	Carbon emissions sold in time period t	kgCO2
$E_{b_t}$	Carbon emissions purchased in time period t	kgCO2
Parameters
$d_t$	Demand in time period t	unit
$Q_{re{t}_t}$	Quantity of returned product (quantity of end-of-life products returned by customers) and acquired by the manufacturer in time period t. It is calculated through the product diffusion dynamic approach, and there are two conditions, low return and high return.	unit
$P_{\mathit{man}}$	Price of manufactured product per unit of product	$
$P_{\mathit{rem}}$	Price of remanufactured product per unit of product	$
$M_{\mathit{man}}$	Material cost of manufactured product per unit of product	$
$M_{\mathit{rem}}$	Material cost of remanufactured product per unit of product	$
$T_{\mathit{mat}}$	Transportation cost of material from supplier to manufacturer per unit of product	$
$C_{\mathit{man}}$	Production cost of manufacturing product per unit	$
$T_{\mathit{prod}}$	Transportation cost of product from manufacturer to distribution dealer per unit of product	$
$C_{\mathit{ret}}$	Cost of acquiring returned products from customers per unit of product	$
$T_{\mathit{ret}}$	Transportation cost of returned product from distribution dealer to the manufacturer (disassembly and inspection facility) per unit of product	$
$C_{\mathit{dis}}$	Cost of disassembling and inspecting returned product per unit of product	$
$C_{\mathit{rem}}$	Production cost of manufacturing product per unit of product	$
$T_{\mathit{disp}}$	Transportation cost of not used returned product from manufacturer to disposal site per unit of product	$
$C_{\mathit{disp}}$	Cost of disposal per unit of product	$
C	Carbon Cap	kgCO2
$\mathit{P}{C}_s$	Carbon selling price	$/kgCO2
$\mathit{P}{C}_b$	Carbon purchase price	$/kgCO2
$\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{man}}}$	Carbon emissions in the transportation of material manufactured products per unit of product	kgCO2
$\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{rem}}}$	Carbon emissions in the transportation of material remanufactured products per unit of product	kgCO2
$\mathit{E}{T}_{\mathit{ret}}$	Carbon emissions in the transportation of returned products from distribution dealers to manufacturer per unit of product	kgCO2
$\mathit{E}{T}_{\mathit{disp}}$	Carbon emissions in the transportation of disposal products per unit of product	kgCO2
$\mathit{E}{T}_{\mathit{prod}}$	Carbon emissions in the transportation of manufactured or remanufactured products from the manufacturer to distribution dealers per product unit	kgCO2
$E_{\mathit{man}}$	Carbon emissions resulting from the manufacturing process per unit of product	kgCO2
$E_{\mathit{rem}}$	Carbon emissions resulting from the remanufacturing production process per unit of product	kgCO2
$E_{\mathit{dis}}$	Carbon emissions resulting from the disassembly process and inspection of each product unit	kgCO2
γ	Yield rate or percentage of returned products that still meet quality standards to be manufactured	%
$\mathit{F}{C}_{\mathit{man}}$	Fixed cost of manufacturing production facilities per time period	$
$\mathit{F}{C}_{\mathit{rem}}$	Fixed cost of remanufacturing production facilities per time period	$
$\mathit{F}{C}_{\mathit{dist}}$	Fixed cost dealer distribution facility per time period	$
$\mathit{F}{C}_{\mathit{dis}}$	Fixed cost of disassembly & inspection facilities per time period	$
$U_{\mathit{man}}$	Manufacturing production facility capacity per time period	unit
$U_{\mathit{rem}}$	Capacity of remanufactured production facilities per time period	unit
$U_{\mathit{dis}}$	Disassembly & inspection facility capacity per time period	unit
Nomenclatures in product diffusion dynamics; Bass model
Notation
M	Potential market or total products sold in the planned time horizon	unit
P	Internal influences coefficient	-
Q	External influences coefficient	-
R	Return rate	%
Τ	Time delay, which is the accumulation between the time when the product is used to reach the end-of-life and the reverse logistics process time	year

4.3. Model formulation

First, we have to determine the demand for each period, which is estimated using the Bass’ diffusion model approach as suggested by (Zhong et al., 2017):

(1) $\mathit{d}\left(\mathit{t}\right)/\left[\mathit{m}-\mathit{D}\left(\mathit{t}\right)\right]=\mathit{p}+\mathit{qD}\left(\mathit{t}\right)/\mathit{m}$(1)

In Equation (1)(1) $\mathit{d}\left(\mathit{t}\right)/\left[\mathit{m}-\mathit{D}\left(\mathit{t}\right)\right]=\mathit{p}+\mathit{qD}\left(\mathit{t}\right)/\mathit{m}$(1) , p denotes the coefficient of innovation (external influence), and q denotes the coefficient of imitation (internal influence). The values of both p and q may be obtained from historical data.

After some delay times (τ) representing the product use time, the product will be returned by customers to the company with a certain return rate (r). Hence, the quantity of the returned product for each period can be calculated as follows (Zhong et al., 2017):

(2) $Q_{re{t}_t}=\mathit{r}\times \mathit{d}\left(\mathit{t}-\mathit{\tau }\right)$(2)

The value of r will determine the quantity of $Q_{re{t}_t}$. There are two possibilities in $Q_{re{t}_t}$, namely low return and high return. A low return will occur if the value of $\mathit{r}\le \frac{1}{\mathit{\gamma }{\mathit{e}}^{\left(\mathit{p}+\mathit{q}\right)\tau }}$ and a high return will occur if the value of $\mathit{r}>\frac{1}{\mathit{\gamma }{\mathit{e}}^{\left(\mathit{p}+\mathit{q}\right)\tau }}$. Those two possibilities will be used as the basic scenarios in the model development. The results of the above estimations constitute the product demand at each period and the quantity of the returned product $\left(Q_{\mathit{ret}}\right)$ will be used as the input data for the optimization model.

The model’s objective function is to maximize the net profit of the manufacturing-remanufacturing activities on the manufacturer side. The net profit can be expressed simply by Equation (3)(3) $\mathit{Profit}=\mathit{Total}\mathit{revenue}-\mathit{Total}\mathit{cost}$(3) :

(3) $\mathit{Profit}=\mathit{Total}\mathit{revenue}-\mathit{Total}\mathit{cost}$(3)

The complete model can be formulated as follow:

(4) $\mathit{Max}\sum _{\mathit{t}=1}^T{P}_{\mathit{man}}{Q}_{{\mathit{man}}_t}+P_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}+{\mathit{PC}}_s{E}_{s_t}-M_{\mathit{man}}{Q}_{{\mathit{man}}_t}-T_{\mathit{mat}}{Q}_{{\mathit{man}}_t}-C_{\mathit{man}}{Q}_{{\mathit{man}}_t}-T_{\mathit{prod}}{Q}_{{\mathit{man}}_t}-C_{\mathit{ret}}{Q}_{{\mathit{ret}}_t}-T_{\mathit{ret}}{Q}_{{\mathit{ret}}_t}-C_{\mathit{dis}}{Q}_{{\mathit{ret}}_t}-M_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{mat}}{Q}_{{\mathit{rem}}_t}-C_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{prod}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{disp}}{Q}_{{\mathit{disp}}_t}-C_{\mathit{disp}}{Q}_{{\mathit{disp}}_t}-{\mathit{PC}}_b{E}_{b_t}-{\mathit{FC}}_{\mathit{man}}-{\mathit{FC}}_{\mathit{rem}}-{\mathit{FC}}_{\mathit{dis}}-{\mathit{FC}}_{\mathit{dist}}$(4)

s.t.

(5) $Q_{re{t}_t}=Q_{re{m}_t}+Q_{dis{p}_t},\mathrm{\forall t}$(5)

(6) $D_t=Q_{ma{n}_t}+Q_{re{m}_t},\mathrm{\forall t}$(6)

(7) $Q_{ma{n}_t}\le U_{\mathit{man}},\mathrm{\forall t}$(7)

(8) $Q_{re{m}_t}\le U_{\mathit{rem}},\mathrm{\forall t}$(8)

(9) $Q_{re{t}_t}\le U_{\mathit{dis}},\mathrm{\forall t}$(9)

(10) $Q_{re{t}_t}+D_t\le U_{\mathit{dist}},\mathrm{\forall t}$(10)

(11) $Q_{re{m}_t}\le \mathit{\gamma }\times Q_{re{t}_t},\mathrm{\forall }\mathit{t}$(11)

(12) $\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{man}}}{Q}_{ma{n}_t}+\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{rem}}}{Q}_{re{m}_t}+\mathit{E}{T}_{\mathit{ret}}{Q}_{re{t}_t}+\mathit{E}{T}_{\mathit{disp}}{Q}_{dis{p}_t}+\mathit{E}{T}_{\mathit{prod}}{Q}_{ma{n}_t}+\mathit{E}{T}_{\mathit{prod}}{Q}_{re{m}_t}+E_{\mathit{man}}{Q}_{ma{n}_t}+E_{\mathit{dis}}{Q}_{re{t}_t}+E_{\mathit{rem}}{Q}_{re{m}_t}+E_{s_t}\le C_{\mathit{cap}}+E_{b_t}$(12)

(13) $Q_{re{m}_t},Q_{ma{n}_t},Q_{dis{p}_t},E_{s_t},E_{b_t}\ge 0$(13)

The model’s objective function is to maximize the net profit as formulated in Equation (4)(4) $\mathit{Max}\sum _{\mathit{t}=1}^T{P}_{\mathit{man}}{Q}_{{\mathit{man}}_t}+P_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}+{\mathit{PC}}_s{E}_{s_t}-M_{\mathit{man}}{Q}_{{\mathit{man}}_t}-T_{\mathit{mat}}{Q}_{{\mathit{man}}_t}-C_{\mathit{man}}{Q}_{{\mathit{man}}_t}-T_{\mathit{prod}}{Q}_{{\mathit{man}}_t}-C_{\mathit{ret}}{Q}_{{\mathit{ret}}_t}-T_{\mathit{ret}}{Q}_{{\mathit{ret}}_t}-C_{\mathit{dis}}{Q}_{{\mathit{ret}}_t}-M_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{mat}}{Q}_{{\mathit{rem}}_t}-C_{\mathit{rem}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{prod}}{Q}_{{\mathit{rem}}_t}-T_{\mathit{disp}}{Q}_{{\mathit{disp}}_t}-C_{\mathit{disp}}{Q}_{{\mathit{disp}}_t}-{\mathit{PC}}_b{E}_{b_t}-{\mathit{FC}}_{\mathit{man}}-{\mathit{FC}}_{\mathit{rem}}-{\mathit{FC}}_{\mathit{dis}}-{\mathit{FC}}_{\mathit{dist}}$(4) . Equation (5)(5) $Q_{re{t}_t}=Q_{re{m}_t}+Q_{dis{p}_t},\mathrm{\forall t}$(5) ensures that the total number of remanufactured products and the disposed of products equals the number of returned products. The sum of manufactured and remanufactured products should equal the market demand as indicated by Equation (6)(6) $D_t=Q_{ma{n}_t}+Q_{re{m}_t},\mathrm{\forall t}$(6) . The capacity constraints for the manufacturing facility, remanufacturing facility, disassembly and inspection facility, and distribution dealer facility are given by Equations (7)(7) $Q_{ma{n}_t}\le U_{\mathit{man}},\mathrm{\forall t}$(7) , (8(8) $Q_{re{m}_t}\le U_{\mathit{rem}},\mathrm{\forall t}$(8) ), (9(9) $Q_{re{t}_t}\le U_{\mathit{dis}},\mathrm{\forall t}$(9) ), (10(10) $Q_{re{t}_t}+D_t\le U_{\mathit{dist}},\mathrm{\forall t}$(10) ), and (11(11) $Q_{re{m}_t}\le \mathit{\gamma }\times Q_{re{t}_t},\mathrm{\forall }\mathit{t}$(11) ) respectively. Equation (12)(12) $\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{man}}}{Q}_{ma{n}_t}+\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{rem}}}{Q}_{re{m}_t}+\mathit{E}{T}_{\mathit{ret}}{Q}_{re{t}_t}+\mathit{E}{T}_{\mathit{disp}}{Q}_{dis{p}_t}+\mathit{E}{T}_{\mathit{prod}}{Q}_{ma{n}_t}+\mathit{E}{T}_{\mathit{prod}}{Q}_{re{m}_t}+E_{\mathit{man}}{Q}_{ma{n}_t}+E_{\mathit{dis}}{Q}_{re{t}_t}+E_{\mathit{rem}}{Q}_{re{m}_t}+E_{s_t}\le C_{\mathit{cap}}+E_{b_t}$(12) limits the number of carbon emissions from the company activities and determines how much carbon should be bought or can be sold by the manufacturer. The last constraint in Equation (13) ensures that all product and carbon emission quantities are non-negative.

5. Numerical example and analysis

The numerical example in this research is adopted from Pourjavad & Mayorga (2018), which presented a case of washing machine products with some adjustments from the related literature. The values of p and q used in this research were set at the values of 0.03 and 0.38, as suggested by Sultan et al. (1990) as the average values of both p and q. We assume that the potential market of the product is 150,000 units. The transportation cost is assumed to depend on the traveled distance, unit size, and weight. The parameters of the model are taken from the most relevant research (Bagalagel & ElMaraghy, 2020; Wang et al., 2017b; Wang et al., 2013) and shown in Table 1. The demand data that the manufacturer should fulfill are shown in Table 2. The demand data result from the Bass model. We forecast the demand for 20 years, assuming that the product is still marketable for at least the next 20 years and the delay time is set at 10 years, meaning that the customers return their used products after 10 years of use. Hence, the returned products with low- and high-return rates are shown in Table 3. The value of r represents the low return rate, and the high-return rate is set at 0.01 and 0.2, respectively.

Table 1. Parameters of the model

Parameter	Value	Parameter	Value
$P_{\mathit{man}}$	$1500/Unit	$\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{rem}}}$	0.011096 kgCO2
$P_{\mathit{rem}}$	$1400/Unit	$\mathit{E}{T}_{\mathit{ret}}$	0.013114 kgCO2
$M_{\mathit{man}}$	$100/Unit	$\mathit{E}{T}_{\mathit{disp}}$	0.013114 kgCO2
$M_{\mathit{rem}}$	$40/Unit	$\mathit{E}{T}_{\mathit{prod}}$	0.013114 kgCO2
$T_{\mathit{mat}}$	$2/Unit	$E_{\mathit{man}}$	2.198 kgCO2
$C_{\mathit{man}}$	$150/Unit	$E_{\mathit{rem}}$	0.785 kgCO2
$T_{\mathit{prod}}$	$2/Unit	$E_{\mathit{dis}}$	0.3925 kgCO2
$C_{\mathit{ret}}$	$30/Unit	Γ	0.85
$T_{\mathit{ret}}$	$2/Unit	$\mathit{F}{C}_{\mathit{man}}$	$33000
$C_{\mathit{dis}}$	$4/Unit	$\mathit{F}{C}_{\mathit{rem}}$	$25000
$C_{\mathit{rem}}$	$100/Unit	$\mathit{F}{C}_{\mathit{dist}}$	$500
$T_{\mathit{disp}}$	$2/Unit	$\mathit{F}{C}_{\mathit{dis}}$	$20000
$C_{\mathit{disp}}$	$2/Unit	$U_{\mathit{man}}$	20000 units
C	15000 kgCO2	$U_{\mathit{rem}}$	20000 units
$\mathit{P}{C}_s$	$0.3/kgCO2	$U_{\mathit{dis}}$	20000 units
$\mathit{P}{C}_b$	$0.5/kgCO2	$U_{\mathit{dist}}$	30000 units
$\mathit{E}{T}_{\mathit{ma}{\mathit{t}}_{\mathit{man}}}$	0.013114 kgCO2

Table 2. Demand on time horizon

Year	Demand	Year	Demand
2021	0	2032	10675
2022	4500	2033	7773
2023	6024	2034	5296
2024	7903	2035	3434
2025	10089	2036	2150
2026	12420	2037	1316
2027	14582	2038	794
2028	16123	2039	475
2029	16572	2040	282
2030	15661	2041	167
2031	13522	-	-

Table 3. Quantity of returned product in each period

Year	Quantity of Returned Product at Low Return	Quantity of Returned Product at High Return
2032	45	900
2033	60	1205
2034	79	1581
2035	101	2018
2036	124	2150
2037	146	1316
2038	161	794
2039	166	475
2040	157	282
2041	135	167

The optimization results for low- and high-return cases are shown in Tables 4, which shows the optimal product mix production planning of manufactured and remanufactured products with the maximum profit. The optimization model resulted profit in low-return and high-return cases of $39,526,560 and $39,256,230, respectively. The last two columns of the table show the carbon sold and bought in both low return and high return case. The manufacturer experiences the deficit in carbon emission only in the first 2 years of operation. The high return gives lower deficit of carbon emission compared to the low return. For the rest of periods, the manufacturer experiences surplus of carbon emission so the emission can be sold to other manufacturer who needs it. On the other side, the profit of low return is 0.6% higher than high return. Hence, with sustainability concern, the manufacturer has to make decision regarding which scenario will be implemented (i.e. the low or high return scenario) and trading off between the profit and carbon emission.

Table 4. Results of the optimization model

Year	Demand (units)	Qret (units)		Qman (units)		Qrem (units)		Qdisp (units)		Es (KgCO2)		Eb (KgCO2)
		Low Return	High Return	Low Return	High Return	Low Return	High Return	Low Return	High Return	Low Return	High Return	Low Return	High Return
2032	10675	45	900	10637	9910	38	765	7	135	0	0	8708	8028
2033	7773	60	1205	7722	6749	51	1024	9	181	0	0	2241	1331
2034	5296	79	1581	5229	3952	67	1344	12	237	3283	4478	0	0
2035	3434	101	2018	3348	1719	86	1715	15	303	7442	8967	0	0
2036	2150	124	2150	2045	323	105	1828	19	323	10317	11928	0	0
2037	1316	146	1316	1192	197	124	1119	22	197	12189	13119	0	0
2038	794	161	794	657	119	137	675	24	119	13362	13865	0	0
2039	475	166	475	334	71	141	404	25	71	14075	14321	0	0
2040	282	157	282	149	42	133	240	24	42	14498	14597	0	0
2041	167	135	167	52	25	115	142	20	25	14736	14761	0	0
Net Profit		Low return $39,526,560
		High return $39,256,230

A sensitivity analysis was performed to study the model’s behavior toward the uncertainty of its parameters. In this research, we study the effect of the cap threshold, manufacturing cost, and remanufacturing cost on the carbon bought, sold, and company profit. The results of such analysis are shown in Figures 2–4. Figures 2(a-b) show the result of sensitivity analysis of carbon threshold on high and low returns, respectively. From the figure, we can see that both scenarios result in the same linear pattern in which the increasing or decreasing threshold of the carbon cap affects the carbon bought and sold significantly. The increase of the threshold will decrease the amount of money that the company must spend in buying the carbon while at the same time increasing the company earnings from selling the carbon quota. Conversely, the decrease of the threshold will increase the company’s spending on buying carbon while at the same time decreasing the company’s earnings from selling its carbon quota. The change in the carbon threshold does not significantly affect the resulting profit.

Figure 2. Sensitivity analysis on the carbon threshold parameter.

Figures 3(a-b) show the sensitivity of manufacturing cost on carbon bought, carbon sold, and company profit both for low- and high-return scenarios. From the figure, the carbon bought and profit have a similar pattern as the impact of manufacturing cost. The higher the manufacturing cost, the lower carbons bought and the company’s profit. While for carbon sold, in low return, the manufacturing cost reduction will decrease the carbon sold, while in high return, the manufacturing reduction cost will make the carbon sold higher. Figures 4(a-b) show the effect of remanufacturing cost on carbon bought, carbon sold, and company profit in low-return and high-return scenarios. The figures show the same pattern for the sensitivity effect of remanufacturing cost. The magnitude of the effects looks higher in the high return scenario compared to the low return.

Figure 3. Sensitivity analysis on manufacturing cost.

Figure 4. Sensitivity analysis on remanufacturing cost.

Besides the carbon cap and trade, several developed countries have implemented other carbon policies. They can be incorporated into future research, namely carbon cap and trade, carbon tax, carbon cap, and carbon cap offset. The adoption of those four carbon policies has been discussed in the research of Wang et al. (2013). The research concluded that carbon tax and carbon cap and trade are effective in reducing carbon emissions but give a great challenge to the economic development of the company. In the case of the other two policies, the cap and trade performed better than the cap offset. Hence, it is interesting to incorporate the other carbon policies and compare the results to determine the most effective policy regarding the closed-loop model in this research.

6. Conclusions

In this research, we developed a product mix optimization model for a hybrid manufacturing-remanufacturing system to maximize profit. The product demand is estimated using the Bass model, while the returned product is represented as the proportions of the demand. Optimization results showed that the model could determine the optimal manufacturing-remanufacturing product mix planning by considering the carbon cap and trade policy. A sensitivity analysis was performed on three parameters: carbon cap threshold, manufacturing cost, and remanufacturing cost. The sensitivity analysis results showed that the threshold in both the low- and high-return cases significantly affected carbon bought and sold. Manufacturing cost also significantly affected the carbon bought and sold and the company profit for both low- and high-return cases. While remanufacturing cost resulted from the same pattern in both low- and high-return cases, the magnitude of the effect was higher in high-return cases. As the extensions of this work, we can consider parameters uncertainty, multi-products and components, sources of carbon emission from other activities in manufacturer operations such as inventory and delivery. Other future research can be directed in the development of meta-heuristics methods and the implementation of artificial intelligence to tackle the uncertainty of demand. Lastly, future research can be directed to consider other carbon policies such as carbon tax, carbon cap, and carbon cap offset.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Cucuk Nur Rosyidi

Cucuk Nur Rosyidi is a professor in Industrial Engineering Department of Universitas Sebelas Maret. He received doctoral degree in 2010 from Industrial Engineering Department of Institut Teknologi Bandung. Currently, he serves as the Doctoral Program in Industrial Engineering of Universitas Sebelas Maret and also the head of Production System Laboratory. He is one of the Members of Center for Research in Manufacturing Systems (CRiMS), a Research Group at Faculty of Engineering Universitas Sebelas Maret which focusing on the research of problem solving and mathematical modeling in make or buy decision, inventory management, quality engineering, product design and development, and other related research.

Rachmi Mustika Sari

Rachmi Mustika Sari is the alumni of Undergraduate Program of Industrial Engineering Universitas Sebelas Maret. She served as one of the Production System Laboratory assistant and graduated in 2022. During her position as the assistant of the laboratory, she was responsible for several laboratory practices such as Production Planning and Control and also held several webinars conducted by the laboratory. Currently, she works at the Financial Services Authority (OJK) Republic of Indonesia.