GREEN DUAL-CHANNEL SUPPLY CHAIN MODEL WITH CONSIDERING PRODUCT RETURNS AND REMANUFACTURING PROCESS

Article History: The development of information and communication technology causes internet users to increase, so consumers are increasingly accustomed to buying products through online channels. This can encourage business people to carry out a sales strategy using two channels (offline and online) or commonly called Dual-Channel Supply Chain (DCSC). In its application, it is hoped that business people will create an environmentally friendly company to reduce carbon emissions. Therefore, business people create companies that implement the Green Dual-Channel Supply Chain (GDCSC) model. GDCSC in online channels has one drawback, namely that consumers cannot evaluate products accurately. This allows consumers to obtain defective products resulting in product returns. Returned defective products can be reprocessed through the remanufacturing process. To provide solutions to these conditions, centralization scenario is used to determine the optimal solution so that maximum profit is obtained. Based on the analysis, it shows that changes in price elasticity and product returns cause system profits to get smaller, while changes in price elasticity and energy efficiency levels cause system profits to get bigger.


INTRODUCTION
Climate change is a growing problem that has a major impact on life.One indicator of climate change is the increase in carbon dioxide gas and other gases, causing the greenhouse effect [1].In paper [1] was also argued that greenhouse gases cause the earth to heat up due to the emergence of gas emissions produced by human activities, one of which is industrial activities.Industrial activities are one of the main factors that participate in the destruction of nature because the raw materials used contain various chemicals and emissions that are emitted [2].Raw materials used contain various chemicals and emissions that have the potential to pollute the air [3].One of the strategies that can be used to reduce the greenhouse gas effect is by implementing green investment.
Eyraud et al [4] stated that green investment is the investment needed to reduce greenhouse gases and air pollution and includes the technology needed to provide products and services.Sani [5] applied green technology that can help address environmental issues.To support the successful launch of green products or environmentally friendly products, Waskito [6] argues that manufacturers must realize that consumers are not only focused on the issue of environmentally friendly products, sales strategies also affect consumer attractiveness.The rapid development of information and communication technology has caused the number of internet users to increase, so consumers are increasingly accustomed to buying products online.This can encourage manufacturers to carry out sales strategies using two channels, namely offline and online channels [3], [7], [8].The sales strategy with two channels is called Dual-Channel Supply Chain (DCSC).
In 2019, Ranjan and Jha [9] explained that DCSC can encourage manufacturers to build online sales media to meet consumer demand that cannot be reached through offline sales channels.According to Dumrongsiri et al [10], consumers can choose purchasing channels based on price and service quality.Purchasing on online channels has the disadvantage that consumers cannot evaluate products accurately, allowing consumers to obtain defective products so that the product return process can occur.Li et al [11] showed that there are four return strategies consisting of manufacturers and retailers, namely no refunds in both channels, full refunds in offline channels only, full refunds in online channels only, and full refunds in both media.Defective products returned from consumers can be reprocessed through the remanufacturing process.Statham [12] states that remanufacturing is a process where used or returned defective products can be reprocessed into new products with minimum expenditure on materials and energy.Remanufacturing describes a recycling process that produces products of the same quality and price as new products.
Zhang et al [13] conducted research on the DCSC model with manufacturers and retailers serving green product returns.Then, Reiman et al [14] researched the remanufacturing process carried out by manufacturers or retailers and manufacturers have the opportunity to reduce remanufacturing costs.Based on these two studies, a GDCSC model will be developed by considering product returns and remanufacturing processes.

RESEARCH METHODS
The research method used in this research is the literature review method.Literature review was carried out using references in the form of books and articles in journals regarding the GDCSC model.The operational steps carried out in this research are as follows.first, constructing the GDCSC model with two structures, namely remanufacturing products that are resold through offline media in model (a) and remanufacturing products that are resold through online media in model (b).After obtaining the GDCSC model in a centralized scenario, it was then determined that the model obtained was a strict concave function to guarantee a single solution.The next step is to determine the optimal solution for model (a) and model (b) using the first partial derivative of the model to the independent variable equal to zero.Next, the model and optimal solution obtained are applied to a case and a sensitivity analysis is carried out.
In this research, optimization theory is used to determine the minimum and maximum extreme points in multivariable functions without constraints from Taha [15] and Winston [16].To determine the optimal solution, the necessary and sufficient conditions theorem is used for a function to have extreme points.Given a multivariable function () with  = (  ,   , ⋯ ,   ) ∈  ⊆ ℝ  .Theorem 1.The necessary condition for  0 to be the extreme point of the function () is ( 0 ) = 0. Definition 2. The Hessian matrix of () is an  ×  matrix with the -th row and -th column elements as  2      .Theorem 3. The sufficient condition for a stationary point  0 to become an extreme point is to determine the Hessian matrix  at  0 so that it fulfills the following conditions, 1.  is positive definite if point  0 is the minimum extreme point, 2.  is negative definite if point  0 is the maximum extreme point.Definition 4. The  th principal minor determinant of an  ×  matrix is the determinant of a matrix of size  ×  obtained by deleting  −  rows and  −  columns related to the Hessian matrix .Theorem 5.If ′′() is continuous for all  ∈ , then () is a concave function on  if and only if for every  ∈  and all non-zero principal minor determinants have the value (−1)  with  = 1 ,2,3, ⋯ , .

Model Construction
The green two-channel supply chain (GDCSC) model consists of one manufacturer and one retailer.Manufacturers sell products to retailers through offline channels and directly to consumers through online channels and retailers sell products to consumers through offline channels.In this study, the strategy of returning product return strategy.The returned products are then reprocessed by the manufacturer through the remanufacturing process.The structure of product return and remanufacturing process in the green dualchannel supply chain model is shown in Figure 1.  1. Based on the structure in Figure 1 and the notation in Table 1, the assumptions used in the modeling are given as follows.
1.The number of products produced is equal to the amount of demand, so there is no shortage of products and no storage costs.
2. The product price   is greater than the product price  and less than the product price   so  <   <   .
3. The selling price of the product from the manufacturer contains production costs and remanufacturing costs.
4. Refunds on product returns are made in full.
5. In the offline channel, product returns to the manufacturer correspond to consumer product returns to the retailer with   =   = .
6.The elasticity of the energy efficiency level is smaller than the elasticity of demand ( < ).
7. The demand elasticity, energy efficiency elasticity, and cross-price sensitivity are in the interval (0,1).
8. The value of min{  ,   } > max{} to satisfy the negative Hessian matrix.
9. The cost of remanufacturing is less than the manufacturing cost (  <   ).
10.All parameters are positive.
Based on the assumptions that have been made, we can determine the amount of demand for manufacturers and retailers.The amount of demand in the green dual-channel supply chain structure consists of the amount of demand on the online channel and the amount of demand on the offline channel.

A. Amount of Demand on Online Channels
Consumer demand to producers is expressed by   and potential market demand on online channels is   .Demand is linear to the price elasticity at the producer by   .Demand in the online channel decreases as the selling price of the product from the producer increases by   so that     is obtained.In addition, demand on the online channel is also affected by the cross-price sensitivity  between offline and online channels.The selling price in the online channel   is affected by the selling price in the offline channel   , so the demand in the online channel increases by   .Then, the demand increases with the energy efficiency level denoted by  multiplied by the elasticity of the energy efficiency level denoted by , resulting in .Thus, the total demand for the online channel is   =   −     +   + . (1)

B. Amount of Demand on Offline Channels
Retailers sell products to retailers through offline channels with consumer demand to retailers expressed by   and potential market demand by   .The linear elasticity of demand concerning the price at the retailer is   .Consumer demand in the offline channel decreases when the selling price of the product from the retailer   increases, resulting in     .The selling price from retailers to consumers is affected by the cross-price sensitivity  and the selling price from producers to consumers   , so demand in the offline channel increases by   .Furthermore, the demand in the offline channel is affected by the energy efficiency level and the elasticity of the energy efficiency level, so the demand at retailers increases by .Thus, the total demand in the offline channel is   =   −     +   + . (2) At this stage, the amount of demand on the online and offline channels has been obtained.The next step is to determine the amount of profit for manufacturers and retailers in the model (a) and model (b).
Profit is obtained from total revenue minus total expenditure.The total profit in the green dual channel supply chain structure consists of the total profit of the manufacturer and the total profit of the retailer.

C. Manufacturer Profit Amount
The manufacturer's profit is earned from selling products through the online channel at a price   for   and through the offline channel at a price  for   , so the total revenue of the manufacturer is The manufacturer conducts production activities at a cost of   .The cost incurred by the producer is   multiplied by the total demand from online and offline channels, so the production cost is   (  +   ).
Eyraud said that the cost of green technology is usually assumed to be a quadratic function, where  2  2 represents the cost of energy efficiency.The producer receives   of returned products directly from consumers at a return cost of   .In addition, the manufacturer also receives   of returned products from retailers with a return cost of   .The manufacturer remanufactures the returned products with a remanufacturing cost of   ( +   ), so the total cost incurred by the manufacturer is ( In model (a), remanufacturing products are resold through offline channels at the same selling price as the selling price of new products, which is , so the cost of selling remanufacturing products obtained by the manufacturer is Based on Equation ( 5) and Equation ( 6), the total manufacturing profit for model (a) is obtained, namely Then in model (b), remanufacturing products are resold through online channels at the same selling price as the selling price of new products, which is   , so that the manufacturer earns the cost of selling remanufacturing products amounting to From Equation (5) and Equation ( 8), the total manufacturing profit in model (b) is obtained =   (  + ) + (  − ) −   (  +   ) −   (  + ) −  2  2 .

D. Retailer Profit Amount
Retailers sell their products to consumers through offline channels at a price of   .Retailer revenue is obtained from selling products to consumers multiplied by the amount of consumer demand, namely   .Furthermore, on product returns, the retailer gets a refund from the manufacturer of , so that the retailer's income is obtained, Retailers buy products from manufacturers at a price of w multiplied by the amount of demand in the offline channel of   .The retailer uses operating costs of co, so the cost incurred by the retailer in selling products to consumers is   multiplied by the amount of demand from consumers in the offline channel.The retailer receives returned products from consumers of  with a return cost of   , so the total cost incurred by the retailer is From Equation (10) and Equation ( 11), the total profit of the retailer is obtained In model (a), the product that has been processed by the manufacturer through the remanufacturing process is purchased by the retailer at a price of , so the retailer incurs a product purchase cost of (  + ).Then the retailer uses operating costs of   (  + ), so the total cost incurred by the retailer is The retailer resells the product purchased from the manufacturer to the consumer at a price of   multiplied by the amount of product reprocessed which is   + .The total cost earned by the retailer is Based on Equation ( 12), ( 13) and ( 14), the total profit of retailers in model (a) is obtained, namely In model (b), the sales of remanufacturing products are only resold through online channels, so the total profit of retailers in the model (b) is the same as Equation ( 12), namely In the centralized scenario, manufacturers and retailers make pricing decisions together.The resulting profit is obtained from the combined profit of the manufacturer and retailer.Based Equation (7),and ( 15), the GDCSC model in the model (a) is obtained, max Π  (  ,   , ) = Π   + Π . (17) Then in the model (b), the GDCSC model in the decentralization scenario can be constructed by using Equation ( 9) and ( 16), thus obtaining max Π  (  ,   , ) = Π   + Π   .(18) In this section, the GDCSC model has been obtained in model (a) and model (b) using the centralized scenario.Next, the optimal solution for each model obtained is determined.

Optimal Solution
The optimal solution in the centralization scenario can be determined by maximizing the profit of the system consisting of manufacturers and retailers.Since the profit function in the centralization scenario that has an optimal solution must have a strictly concave function, then in the model (a) and model (b), the Hessian matrix obtained from the second partial derivative of Equation (17) and Equation (18) on   ,   , and  can be constructed, where From the Hessian matrix in Equation ( 19), the principal minor determinant is obtained, namely Based on the 8 th assumption, the values of  11 < 0, 22 > 0, and  33 < 0 with the condition that , so it can be said that the system profit function is strictly concave and there is a single optimal solution.The optimal solution is obtained by deriving Equation ( 17) and Equation ( 18) concerning   ,   , and  which are then made equal to zero.The optimal solution in the model (a) is written as At this stage, the optimal solution has been obtained for model (a) and model (b) in the centralization scenario.Next, the model and optimal solution obtained are applied to a case and sensitivity analysis is carried out on changes in product return sensitivity parameters to the optimal solution model.

Application
An application is given by performing numerical simulations on a green dual-channel supply chain model considering product returns and remanufacturing processes.The parameter values are taken from the research of Chang et al. [17] and Zhang et al. [18], and numerical simulations.The parameter values used in this study are presented in Table 2.The optimal selling price in the centralized and decentralized scenarios is determined by substituting the parameter values in Table 2 into Equation (21) and Equation (23).The energy efficiency level is obtained by substituting into equations Equation (21) and Equation (23).The optimal demand function and optimal profit function are obtained by substituting Equation (22) and Equation (24).The optimal solution of the green dual-channel supply chain model is presented in Table 3.Based on Table 3, the optimal values of   , ,   ,Π  and total profit for model (b) are greater than model (a).While the values of ,   ,   , and Π  model (b) are smaller than model (a).When viewed from the total profit and manufacturer's profit obtained, model (b) gains greater profits than model (a).However, this does not apply to retailers' profits.Model (a) provides more profits for retailers than model (b).Furthermore, a sensitivity analysis was conducted to determine the effect of product return sensitivity changes on the solution of the GDCSC model.
Product returns can be made by consumers to retailers through offline channels and directly to manufacturers through online channels.The number of returned products affects the amount of demand and profit of each actor.The effect of changes in the number of product returns in the centralized scenarios is shown in Table 4. Based on Table 4, it can be seen that the number of returned products increases, the profitability of the system decreases.Based on the 2 nd assumption, in the centralization scenario the value of   <    <    is obtained when the value of   ≤ 12 and the value of    <    <    is obtained when the value of b ≤ 5.In the centralization scenario model (a) the maximum return of consumer products to the manufacturer is 7.35% and the return of consumer products to retailers is 6.41%, while in the model (b) the maximum

Figure 1 .
Figure 1. Green Dual-Channel Supply Chain Structure Figure 1(a) is a model (a) with a green dual-channel supply chain structure where remanufacturing results are resold through offline channels.While Figure 1(b) is a model (b) with a green dual-channel supply chain structure where remanufacturing results are resold through online channels.The notation used in the green dual-channel supply chain structure is presented in Table1.

Table 1 . Notation and Description Notation Description
Number of product returns from retailers   Number of product returns from online consumers   Number of product returns from offline consumers   Selling price elasticity of the manufacturer (  +   ) +     +  +   (  + ) +