A Closed-Loop Supply Chain Inventory Model with Carbon Emissions and Green Technology Investment

. This paper proposes an inventory model that integrates a manufacturer and a retailer in a supply chain system. The model employs environmentally friendly technology investments to reduce the emissions produced in the process. Furthermore, the demand at the retailer's end is unpredictable, and green investments affect the average demand levels. This research aims to identify the optimal delivery lot, the number of deliveries, the Safety Factor, the level of green technology, and the collection level to maximize the joint total profit. Numerical examples illustrate the model's practical application, and algorithms are developed to solve the problem. Sensitivity analysis is used to determine the key model parameters' effect on the model's behavior. Green investments have been shown to reduce emissions and increase returns on second-hand goods, thus enhancing the environmental efficiency of supply chains.


I. INTRODUCTION 1
The closed-loop supply chain concept is gaining popularity among companies due to growing awareness among consumers about the environment and the reuse of used goods (Khorshidvand et al., 2023).In order to increase their sustainability performance, businesses are investing in green technology and remanufacturing to recover used products because consumers are prepared to pay more for environmentally friendly products (Jauhari et al., 2021).The process of recovering used products can help organizations conserve resources, reduce environmental risks, and bridge the gap between expected and actual performance., understand the practical usage of the product, and form proactive relationships with consumers, thereby increasing company profits (Dominguez et al., 2019;Maiti & Giri, 2015).Companies such as Xerox, Apple, and Hewlett-Packard have implemented remanufacturing processes into their manufacturing activities (Wei et al., 2019).
Remanufacturing is an effective way to save energy and raw materials, while reducing carbon emissions and production waste (Shu et al., 2017).For instance, Volkswagen is able to save up to 70% by using used car engines and parts.Similarly, Kodak can save between 40% to 60% of production costs by utilizing camera parts that return to the factory.Xerox also saves between 40% to 65% of production costs by reusing parts, components, and raw materials from products that return to the factory (Genc & Giovanni, 2017).
As the world's environmental concerns continue to grow, carbon emissions have become a significant issue for CLSC.Global warming and environmental change are putting the world's sustainability at risk.As a result, cooperation amongst all parties is essential to slowing the rate at which carbon emissions are rising in the Earth's atmosphere.The increasingly strict carbon policy regulations encourage CLSC companies to adopt various green technologies to reduce the emissions from their manufacturing operations.
Efficient management of operations is crucial for CLSC to remain competitive in the market.One of the key components to be considered in making decisions related to the recovery of scrap generated during manufacturing operations is the quality of the scrap product.This is because the emissions from manufacturing operations need to be controlled and monitored to ensure they are within the acceptable limits.High-quality scrap products still in good condition can be refurbished or remanufactured, and low-quality ones can be recycled.However, not all used products can be processed through recovery, so waste disposal is required (Hasanov et al., 2012).
According to the data above, although Closed-Loop Supply Chains (CLSC) have been the subject of numerous studies and in-depth discussions in the literature, carbon reduction, green investment, demand influenced by green technology level, and two recovery processes have received less attention.Therefore, given this context, we aim to address the following questions: 1.How can the inventory decision be determined in a CLSC system that involves manufacturers and retailers with regard to carbon emissions?2. What is the effect of investments in green initiatives and collection efforts on CLSC systems inventory decisions?
In order to address the aforementioned queries, our main effort is to create an inventory model for a manufacturers and retailers CLSC system, where demand is shaped by the degree of green technology.Green technology is something that manufacturers invest in to lower emissions produced during production and remanufacturing.Carbon tax laws are put into effect by regulators to lower CLSC emissions.Remanufacturing and recycling procedures are included in this model to save raw materials, energy, and emissions.

Assumptions
The following presumptions were made to create this study model: 1. Retailer demand is normally distributed with standard deviation σ and average demand  ( ) . 2. The green technology level influences the average demand.3. The quality of remanufactured goods is equal to that of manufactured goods offered at the same price in the main market.(Maiti & Giri, 2015;Taleizadeh et al., 2017) .4. The manufacturing system is still imperfect, so there are still defective products produced (Cárdenas-Barrón, 2008;Marchi et al., 2019). 5.All products that are defective are fixed, and the reworked items are of the same quality as the original items.(Jauhari et al., 2020;Marchi et al., 2019).6.The government implements a carbon emission tax policy to reduce emissions.7. Green investment can reduce emissions and increase the market share of manufacturers.(Bai et al., 2020).8. Manufacturers also collect used goods.To increase the number of returned goods, manufacturers invest in collection efforts (Maiti & Giri, 2015;Zhang et al., 2015).

Retailer Model
Figure 1 shows the proposed CLSC system.In the proposed model, Retailers typically receive demand that is distributed with a mean D and standard deviation σ.This average demand depends on the green technology level,  ( ) =  +  .The retailer applies the continuous review method in its inventory control.The retailer will order nQ units of products to the manufacturer when the inventory reaches the reorder point (ROP).The delivery lead time is formulated as  =   +  ⁄ .The retailer's storage cost per unit is prepared as follows: In addition, retailers also incur ordering costs and transportation costs formulated as follows: If the retailer cannot fulfill consumer demand due to insufficient inventory, there is a backorder fee incurred by the retailer.Backorder costs are formulated as follows.: where () = { () − [1 −  ()]} The standard normal distribution's probability density function is denoted by  () and  () is the standard normal distribution's cumulative distribution function..The retailer will earn revenue from product sales with the following equation:  =  ( , )  (4) So, the total retailer profit, including product procurement cost, can be written as an equation:

Manufacturer Model
The setup cost per unit of time is formulated by considering the setup frequency D/nQ and setup cost K.The manufacturing inventory accumulation is subtracted from the accumulative shipments to determine the manufacturing inventory level.As a result, the storage and setup costs per unit of time for the manufacturer are: As was mentioned in the preceding section, there are flaws in the manufacturer's production system, which results in certain defective products.Even though the system produces good things at the beginning of production, there is a chance that it will go into an out-of-control state and make defective goods with a probability of γ.We assume an exponential distribution for the time that elapses before the production system enters an out-of-control condition.We assume that the system will remain in an out-of-control state until the batch has been created by Rosenblatt & Lee (1986).As a result, the following formula determines how many defective goods the production system produces.
The resulting defective goods will enter the rework process stage to improve their quality.The rework cost is formulated in equation ( 8) Electrical energy is required to run the production process studied by Bazan et al (2015) and Gutowski et al (2006). , and z are the energy consumption and idle power of the manufacturing and remanufacturing processes. , and  energy consumption and idle capacity during rework.This energy consumption equation can be written as: Formula ( 11) represents the cost of procuring raw materials and used products to be reprocessed.In contrast, formula (12) includes the costs for recycling, waste disposal, and inspection of used goods conducted by the invoice.
The manufacturer invests to increase the number of used products returned to the manufacturer.The collection effort investment is written with the following equation: Equation ( 13) is the cost of emission taxes manufacturers incur from manufacturing and remanufacturing processes, where this cost is generated from emissions per unit multiplied by the number of products processed in each process.
) Due to pressure from the government and consumers, manufacturers began switching to green technology.However, manufacturers are gradually replacing their facilities due to the high investment costs.Formula ( 14) is the formulation of green technology investment.
So, the total profit of the manufacturer can be written with the equation: Joint Total Profit The joint total profit of the proposed system can be calculated by combining the profits earned by the manufacturer and retailer, as described in the following equation:

Solution methodology
In finding the optimal solution in this model, partial derivatives of the total joint profit (JTP) for Q, S, k, and  are performed.The value of n is assumed to be fixed in this algorithm.
By setting the partial derivative of the total joint profit (JTP) for Q, S, k, and  equal to zero, the equations for Q, S, k, and  are obtained as follows

Algorithm
The following is a solution algorithm for the values of n, Q, k, τ, and S using Matlab 2022a software: 1. Set n=1 and  ( ,  ,  ,  ) 2. = 0 3. Set initial values for  dan S for the first iteration and determine the value of D.
12. set  ( ,  ,  ,  , ) as the maximum value of the total joint profit (JTP) with, ,  , , dan  as the optimal solution in solving the problem.

Numerical Example
The parameter values used to perform numerical analysis are adapted from the research of Ahmad Jauhari (2022) and Bai et al (2020) Table 2 shows that the optimal number of deliveries, delivery size, and safety factor are 3, 100.03, and 2.28.For the green technology level, the collection rate and demand are 3.78, 0.651, and 243.02 units.Based on these results, the manufacturer must invest $179.09for green investment and $466.32 for collection effort investment.By making these investments, the resulting emissions are 10,091 Kg .The total benefits to retailers, manufacturers, and the supply chain are $16,783, $8,477, and $25,260, respectively.

Green Technology Coefficient Analysis
The level of green technology increases significantly as y increases.As a result, the profits of manufacturers, retailers and total combined profits increase.Table 3 illustrates how y .affects profit.In the real system, producers will increase the level of green technology to attract more customers when the technology significantly affects the level of demand.Producers should increase investment to increase the level of green technology presented in Figure 2.

Green Investement Coefficient Analysis
The impact of green investment costs on model behavior is also investigated in this model.Table 4 shows that if the green investment parameter increases, the green technology level will decrease from 3.78 to 1.45 (160% increase).This happens because of the large cost burden of making investments.The increase in green investment costs makes manufacturers reduce their investment so that the emissions released will increase.In addition, the profits earned by manufacturers and retailers decrease.

Collection Effort Coefficient Analysis
The of testing the investment coefficient of scrap collection are shown in Table 5 and Figure 4.The variables Q, k, and S do not change when the coefficient of investment in scrap collection (g) increases; the only variable that changes is τ, which decreases from 0.651 to 0.232, which is a 180% increase.This result is consistent with the system, where the collection rate only affects when a manufacturer attempts to collect scrap.In order to avoid losing money, the manufacturer will lower its collection rate if the investment cost is higher.A high collection rate will cause the manufacturer and retailer to make more money, which means the total combined profit will be lower.Furthermore, manufacturers make more regular products than remanufactured products because there are not many used goods that are reprocessed.The amount of regular product production rather than remanufacturing increases the emissions produced by the manufacturer, as shown in Figure 5.  Carbon Tax Analysis Table 6 and Figure 6 illustrate how the suggested model is affected by the carbon tax.As the cost of the carbon tax rises, manufacturers are incentivized to decrease their emissions, as the graphic illustrates.The manufacturer will cut emissions by 3.7% if the carbon tax is raised to 0.1608.Manufacturers improve the degree of green technology from 3.78 to 4.23, which reduces these pollutants.and producers raise the rate of collection from 0.65 to 0.98.this is a result of manufacturers' increased interest in creating remanufactured goods with lower emissions as they are being offered.Furthermore, as a result of a decline in manufacturer earnings, the overall combined profits have also by 4.9%.This is a result of manufacturers making more investments in green projects.

IV. CONCLUSION
This study proposes a CLSC model considering carbon emissions and green technology.This study considers emissions resulting from manufacturing and remanufacturing By optimizing the model, the maximum profit of the manufacturerretailer can be obtained by setting several decision variables at the optimal level, namely the number of shipments, lot size, factor, green technology level, and collection rate simultaneously.
The sensitivity analysis results provide some interesting insights.Managers should be able to consider decision variables to balance carbon emissions and profit.First, the model allows managers to increase their green technology level to attract more customers.Second, managers need to consider green investment if the government increases the tax value of carbon emissions.Green investment must be increased to reduce the emissions produced by manufacturers.Third, with the change in collection effort costs, manufacturing managers need to consider the carbon emission tax that will be generated.If the collection rate of used goods is low, the manufacturer must produce more regular products to meet market demand.The large of regular products rather than remanufacturing can increase excess carbon emissions.
future research, emissions from each process also need to be considered, such as emissions from transportation, rework, recycling, waste disposal, etc.In addition, in this proposed model, there is no inventory control on storing used goods that return to the manufacturer.In the next model, other emission policies such as carbon cap and trade and carbon cap can also be applied.

Figure 1 .
Figure 1.Schematic diagram of the proposed system

Figure 4 .
Figure 4. Effect of collection effort investment cost on emissions manufactur and remanufacture

Table 1 .
Comparison of the proposed model with existing models : Parameter of the green technology level on lessening carbon emissons generated from remanufacturing process (Kg )

Table 3 .
Effect of changing the green technology coefficient parameter on the proposed model

Table 4 .
of changes in green investment costs on the proposed model

Table 5 .
Effect of changes in green investment costs on the proposed model

Table 4 .
Effect of changes in carbon tax on the proposed model