TECHNOLOGY LICENSE SHARING STRATEGY FOR REMANUFACTURING INDUSTRIES UNDER A CLOSED-LOOP SUPPLY CHAIN MANAGEMENT BONDING

. Remanufacturing is getting attention nowadays due to increasing waste and corresponding emissions. One of the important factors of remanufacturing is the quality of the remanufactured products. The collection and distribution of used products require proper management. Based on this situation, this study discusses a hybrid closed-loop supply chain management in cooperation with a hybrid production system. The vendor comes up with the policy of sharing remanufacturing responsibility by sharing the technology license with other supply chain players. The carbon cap restricts emissions from the entire hybrid production system of the vendor. Other factors of this proposed study are service by the retailer and quality, gift policy, and customer awareness by the vendor. This study examines the scenario under random market demand. Classical optimization provides the solution under the Stackelberg game policy where the vendor acts as leader and the retailer & third party act as followers. This paper considers two scenarios: Scenario A for a continuous distribution and Scenario B for no specific distribution. A comparison is drawn between various motivating factors-based policies to control supply chain management.

improvement is contributing to the economy though. Mentioning that, responsibility sharing policy is explored in this study. With consumer satisfaction, industries are leaning towards a customer-oriented green policy that helps to increase customer demand.
Various motivating factors have been discussed in the closed-loop supply chain management (CLSCM) for the growing market demand as the carbon tax, gift policy, and remanufacturing. Remanufacturing has a big role in the CLSCM that deals with remanufacturing of used products. The vendor allows the other supply chain players to remanufacturer the collected used products. This responsibility sharing happens in only one condition the supply chain player should maintain the quality of products as same as the vendor. This cooperation between supply chain management (SCM) players for remanufacturing has a huge impact on both economy and the environment [54]. Whenever there is a competition among SCM players, a game starts for decision making on behalf of the SCM.
Remanufacturing requires the repair or replacement of obsolete components of the used product. Spare parts subject to quality affect the performance of the product or the expected lifetime of the product changes. Here, the responsibility sharing for remanufacturing works. The vendor gives licenses to other supply chain players for remanufacturing. One of the benefits of sharing technology licenses is that it reduces the use of transportation. For example, suppose Company A situates at place A and Company B situates at place B. Company A does not have to carry all used products from place B to place A. Already Company B situates at place B. Then, Company A just can share the license with Company B and Company B can remanufacture used products with quality as good as Company A. As a result, extensive transportation can be saved as well as emissions. This research works helps to survey the following research quarries: -How cooperation between all SCM players works for responsibility sharing? How customer awareness is effective under the circumstances of remanufacturing and responsibility sharing? -How does gift policy affect the SCM when the vendor gives license to other players for remanufacturing used products by leveling the vendor's license? -How does stochastic demand affect the management when the demand depends on customer awareness, gift policy, and quality of remanufactured products?
The rest of the paper is structured as Section 2 consists of a literature review, Section 3 consists description of the problem, assumptions, and notation; after that, Section 4 introduces the proposed model under two scenarios, Section 5 introduces solution methodology, Section 6 explores numerical examples and managerial insights, and finally, Section 7 gives conclusions, respectively.

Selling price dependent demand
For the first time, Kotler and Zaltman [23] introduced the idea of a business strategy for decision making. They introduced the relationship between price and the economic order quantity (EOQ) inventory model. An EOQ inventory model with variations in the effect of selling price had been investigated by Ladany and Sternlieb [26]. Bhuniya et al. [4] introduced an EOQ model with the variable selling price. Again, Sepehri et al. [49] introduced a model, where the selling price influenced customers for purchasing items. Choosing an optimal pricing strategy for new and renewed products can help the manufacturer to achieve maximum profit. The retailer sells new products and collects returnable products, which are shipped for recycling and used as raw materials for other products. Retailers need to invest in branding and pricing for new and remanufactured products. Studies had shown that increasing unit purchasing and remanufacturing costs of used products increased the quality and decreases the brand investment. Kumar et al. [24] confirmed that the increasing cost of advertising provided a continuous increasing value of the total cost.

Production model
The study of defective production systems and the quality of products with unreliable machines had been considered in many papers so far. Sarkar et al. [42] proved that SCM was effective for variable production and maximized the profit of the supply chain. Sarkar et al. [47] simultaneously considered environmental risks associated with innovative green product manufacturing, while both the return rate and the demand were random with insufficient information on the distribution function. Rosenblatt and Lee [39] considered an economic production cycle and found the effect of the degradation of the traditional economic manufacturing quantity (EMQ) model on the imperfect production process. Porteus [38] discussed optimal lot-sizing in an imperfect production process, improving process quality, and reducing setup costs. Taleizadeh et al. [54] discussed that the SCM was effective for improving product quality and maximizing profits of the supply chain. Kang et al. [21] considered the effects of imperfect production for work-in-process inventory.

Remanufacturing
It is very difficult to make 100% perfect products by maintaining a sustainable manufacturing system [2]. Garai and Sarkar [13] proposed a model that simultaneously considered the production of second-generation biofuel from used products in the reverse-chain and the re-manufacturing of casing soil as returnable items in the manufacturing-chain to address the environmental concerns. That ensured long-term sustainability within the SCM. Every manufacturer should be responsible to save the environment when they made renewable items, namely biofuel. Sarkar et al. [46] discussed a model for biofuel manufacturing from renewable biomass through a smart manufacturing system. The biofuel was an important alternative to fossil fuels, which helped to decrease dependability on fossils fuel and decreased carbon emissions. Sarkar et al. [45] proposed a model that aimed to reduce waste by reworking defective products and maximizing profit. The uncertain situation within a production-inventory model was discussed by Mahapatra et al. [29]. Minner and Lindner [30] introduced a model that collectively optimized the production order of new and remanufactured batches, as well as the size and number of those batches. They allowed multiple setups within the same production cycle for both new and remanufactured items. Taleizadeh et al. [52] discussed a multi-item production system to redefine defective item policy. Considering the level of service and budget constraints, they found the total cost which was globally minimum. Shi et al. [50] introduced maximum profit for uncertain income. They reworked the items and sold them in the market as brand new. Another noteworthy matter was that the introduction of a smart manufacturing framework rose the percentage of green investment utilization [40].

Inventory management
A sustainable inventory management model under controllable carbon emissions from by reducing pollution was developed by Yadav et al. [56]. An animal fat-based renewable supply chain model was recently designed by Habib et al. [17], where the SCM was solved by robust possible programming. Still, the authors did not take the optimum selling price of biofuel and variable production rate. In the make-to-order policy, the vendor produced items in case of insufficient inventory in storage and sent them to the retailer, which was discussed by Mahajan et al. [28]. Sarkar et al. [41] discussed a model where inventory holding costs consisted mainly of two components, financial and operational. In the traditional system, the total inventory holding cost was paid by the retailer. in consignment stock, the inventory holding cost of the retailer was paid by the vendor. Adida and Ratinsoontorn [1] analyzed how competition among retailers affects supply chain decisions and profits under different price agreements. Again, Corbet and DeCroix [7] created a supply chain model with asymmetric information including consignment stock, cycle time, and safety stock. Gerchak and Khmelnitsky [14] had tested a consignment policy, where there was no opportunity to verify the retailer's sales report. Braglia and Zavanella [5] worked on an industry strategy for managing supply chains and inventory, including consignment stock. Yi et al. [57] had developed an integrated inventory model with retailer's space constraints and controllable lead time under the consignment stock policy. Yu et al. [58] considered a single-vendor multi-retailer consignment model and solved those models with a uniform and normal distribution. As'ad et al. [3] discussed a model on the consignment agreement and the CLSC was adopted due to its economic and environmental benefits. Murmu et al. [34] discussed a production-inventory model for perishable items by considering a manufacturing facility and warehouse.

Closed-loop supply chain management
In commerce, SCM is the management of the flow of items and services between SCM players. This included the movement and storage of raw materials, work-in-process inventory, finished goods as well as end to end order fulfillment from point of origin to point of consumption. Interconnected, interrelated, or interlinked networks, channels, and node businesses combine for supplying products and services required by end customers in a supply chain. The study of Chung et al. [11] had shown a multi-unit structure, where the industry was restored to a reconditioning facility and then given back to the retailer. They analyzed an integrated system consisting of a single supplier, a manufacturer, a retailer, and a third party. Lee et al. [27] discussed the benefit of carbon emissions during manufacturing and transportation. Multi-objective optimization in logistics problem for multiproduct supply chain network model was introduced by Gupta et al. [16]. But the authors did not consider the rate of manufacturing and the impact of power for renewable items.
Jaber et al. [20] first considered a two-echelon vendor-retailer CLSC with a consignment stock strategy, where a batch was delivered to the retailer as soon as the production was completed. Although they had created mathematical models for equal and unequal batch sizes, the sequencing of batches was considered a priority where remanufactured batches were produced first and then batches were produced. The management should take care of a sustainable production system with variable reliability [33]. The transportation of biofuel for a smart manufacturing system played an essential role in a bioenergy supply chain network [18]. By utilizing a smart manufacturing [45], the defective products could be reduced. A partial backorder was studied by Park [36] while backordering was purchasing-price depended. Sarkar et al. [44] discussed a artificial neural network with multithreading as a solution policy. Sarkar et al. [43] discussed a CLSCM for waste reduction in a singlestage supply chain. They discussed the effectiveness of reducing carbon emissions and the total cost of the two-stage supply chain. Choi et al. [10] described a model where the selling price of the product varied with different channels. That helped to determine the demand for the product for the entire supply chain. Vandana et al. [51] discussed a green SCM for agile manufacturing. They used a trade-credit policy for maintaining the relationship between both SCM players.

Customer awareness and gift policy
In this paper, customer awareness is the more important part to buy that product. By awareness, customers are easily able to know about their consumer rights. There are no such disadvantages to customer awareness. In this present situation, awareness is necessary for production planning. Here, in this paper, the market demand for products is depending on customer awareness. Several researcher developed models where demand depends on customer awareness. Sen and Bhattacharya [48] analyzed a model where they focused on the customer channel and examined the role of customer awareness in promoting the firm's sales and its financial performance. Cárdenas-Barrón [6] introduced sustainable practices for maximum profit. A gift policy is an effective approach to inventory management. Here, the vendor invests for the purpose of an additional gift policy for promoting products through the SCM. Generally, through this policy, the market demand for the product increases. In this policy, the vendor gives an additional gift voucher for a certain amount of products sold to the retailer. This policy provides information and guidelines for employees and the company's expectations when those vouchers are accepted by retailers. Gifts can be used to build goodwill between the vendor and retailer. In this policy, the vendor acts as a company that does business with the SCM players. Khouja et al. [22] analyzed that the gift policy was more effective in SCM to increase profit.

Research gap
Different researchers considered many models, where demand was depended on selling price and demand was depended on customer awareness. Here, this study considers a comparison between the continuous distribution and the distribution-free approach, where the vendor shares the technology license with the SCM players. Table 1 gives a glimpse of recent researches and defines the research gap. Here, this model distinguishes the optimal decision procedure of supply chain and inspect the results in two scenarios based on stochastic approach and uses a competitive scenario under game policy. Based of authors knowledge, this is the very first time in the literature that discusses two different stochastic scenarios under technology license.

Problem description, notation, and assumptions
The problem description is explained in this section along with notation, and assumptions to understand the research problem.

Problem description
A vendor, retailer, and 3PL form a hybrid CLSCM. The 3PL collects used products from the market at a unit price (Fig. 1). 3PL remanufactures portion of the total collected used product ( , ) and sends remaining (1 − ) portion to the vendor at a unit price . The vendor gives the license to the 3PL to remanufacturer products on behalf of maintaining the same quality as the vendor. The vendor remanufactures the remaining (1− ) portion of the collected used products. Now, the retailer purchases remanufactured products from the 3PL and vendor. That is, the retailer buys new and remanufactured products from the vendor. Investments for quality improvement and gift policy are used by the vendor. All CLSCM players are environment conscious and they share the remanufacturing responsibility subject to the condition that the quality of remanufactured products will be the same as the vendor's product quality. This remanufacturing-cooperation between SCM players has an effect on their decentralized decision. This complex concept of cooperative-decentralized decision-making is explored in this study. A portion of the market demand of the retailer is fulfilled by the remanufactured products. Along with the hybrid CLSCM, the vendor operates a hybrid production system for the production process of new products and remanufacturing process of used products. The vendor has the carbon cap for carbon emissions from the hybrid production system. Thus, the carbon tax is only payable for emitting more carbon into the environment than the carbon cap.

Notation
Following notation is used to understand the mathematical model.

Assumptions
To construct the mathematical model, the following assumptions are used.
(1) A single-period hybrid CLSCM consists of a single-retailer, single-3PL, and single-vendor. The vendor produces a single type of product using a hybrid production system consisting of both production and remanufacturing facilities. The vendor assembles and transports products without adequate inventory to meet the retailer's demand [28]. (2) The following condition ≤ ≤ should hold in order to ensure the convergence and profit of the system. The retailer's demand is fulfilled by both new and remanufactured products. To ensure the convergence of the reverse chain, 1 , 2 < should follow. The vendor's unit production cost is a function of production rate of new products (3) The 3PL collects all used products from the market. Only a fraction ( ) of collected used products are remanufactured by the 3PL. Rest fraction (1 − ) is remanufactured by the vendor. = 0 indicates that 3PL does not participate in remanufacturing and = 1 implies that 3PL remanufacturers all collected used products [55]. Scaling parameters of demand for carbon emission reduction rate (>0) 4,5 Scaling parameters of demand for purchasing cost of used product (>0) 6,7 Scaling parameters of demand for quality improvement (>0)   [54]. (5) Carbon emissions from the hybrid production system are controlled by a carbon cap. The vendor pays carbon tax when the emissions exceed the projected carbon cap. Investment for carbon reductions is used to reduce the carbon tax [9]. (6) The vendor uses additional investments for quality improvement, customer awareness, and gift policy whereas the retailer invests for additional service to customers.
The next section gives a detailed explanation of the mathematical model based on these assumptions.

Model formulation
Market demand is stochastic and it has two segments: one is variable and another one is random. Variable demand segment is dependent upon decision variables as the selling price of the product ( ), quality improvement ( ), carbon emissions reduction ( ), purchasing price of collected used products ( ), service ( ), customer awareness ( ), and gift policy ( ). The random demand is denoted as . The demand is expressed as The random demand has the random variable that follows uniform distribution, i.e., ∼ [ 2 , 1 ]. For random demand , an additional inventory level of the retailer is added as such that either [ ] > or [ ] < . Due to remanufacturing and 1 , 2 < , savings of the vendor from per unit remanufacturing cost is and savings of the retailer ( 3 ) from per unit remanufacturing cost is Now, the collected used products ( ( , )) is variable and is a function of unit purchasing cost of used products ( ) and the quality of the product ( ) [54]. It has a fixed market size . ( , ) is shown in Equation (4.4) as The scaling parameter has a negative impact on the collection of used products. More good quality products imply less collection of used products.

Scenario A: Uniform distribution model
In the traditional policy, the cost of carrying the total inventory is borne by the retailer. The retailer buys the total lot from the seller at the wholesale price, retains ownership of it, and sells the item to the customer at the sale price. The seller takes no responsibility for the product and does not incur any cost to retain the item after delivery at the retailer's end.

Retailer
In this case, the total account holding amount is obtained by the retailer. The retailer buys the total lot from the seller at the wholesale price, retains ownership of it, and sells the item to the customer at the sale price. The seller assumes no responsibility for the product and does not incur any costs for retention after the item is delivered to the retailer's end. The total cost of the retailer is given below: The distributor takes major roles in the supply chain to product selling and helps to maximize profit in the supply chain. The distributor always gives holding costs and shortage costs and receives retrieve the value. In two scenarios, the retailer remanufactures the used products as new by his technical ability along with the vendor and sells them in the market to earn a profit margin along with new products. To increase the demand for products in the market the distributor expands customer awareness investment costs. Here distributor's optimal profit is calculated by subtracting all his costs from his revenue.

Revenue of the retailer (RN)
( ) is the expected amount of sold out products, i.e., the retailer sells this amount of products in market. This can be calculated by the following equation.
Now, the demand ( , , , , , , ) has two segments: one is variable in nature and another is random in nature ( ). During the use of probability theory, the variable segment of the demand has no effect. Only random demand segments will change. That is why can be replaced by inventory level of the retailer for integration to avoid the complexity [54]. The random demand segment is calculated with respect to this inventory level . Then Equation (4.5) can be written as Purchasing cost (PC) is the total ordered quantity of the retailer. This quantity is fulfilled from both the new products and remanufactured products. The retailer purchases new products from the vendor and remanufactured products from both the vendor and 3PL. But, as all the remanufactured products have similar quality as new products, the unit purchasing cost for all products is the same. If is the unit purchasing cost, then the total purchasing cost is PC = .

Holding cost (HC)
Retailer holds products if there are some products that are still in inventory system. ℎ is the unit holding cost of those products which are not sold yet in market [47,54]. The expected leftover inventory [ ] can be calculated as Thus, the expected holding cost is HC = ℎ [ ].

Shortage cost (SC)
The retailer pays a shortage cost only when a shortage occurs. Unit shortage cost of the retailer is [47,54].

Investment for service to customers (SI)
The retailer provides a service to customers for increasing market demand of the product. It helps to improve the goodwill of the retailer among customers. It has a direct impact on market demand. The service investment is Expected total profit of the retailer under uniform distribution (︀ )︀ Thus, the ordered quantity of the retailer can be expressed as and the expected total profit of the retailer is given by

Third-party logistics (3PL)
The vendor ties a not with the 3PL and it formulates a hybrid CLSCM. The 3PL collects used products ( , ) from the market with a unit purchasing cost . Now, the vendor shares a technology license with the 3PL such that the 3PL is able to remanufacture portion of collected products ( , ). The remaining portion of the collected products is sent to the vendor.

Revenue of 3PL from the retailer (RN 3PL )
After remanufacturing, the remanufactured products are labeled as new products. Thus, the price of these remanufactured products are same as the new products. The 3PL sells ( , ) amount of remanufactured products to the retailer. Then, the revenue of the 3PL is RN 3PL = ( , ). (4.12)

Technology license fees (TL)
The 3PL gives as unit license fees to the vendor for getting the permit of remanufacturing from the vendor. Then, the total technology license fees [54] of the 3PL is TL = ( , ). (4.13) Remanufacturing cost of 3PL (RC 3PL ) 3PL remanufactures ( , ) amount of used products. If 3 is the unit remanufacturing cost of the 3PL, then the remanufacturing cost is (4.14) Now, if these amount of products are produced as new products, then the unit production is = 1 + 2 and > 3 , then unit savings is given by Equation (4.3). Thus, the savings from the remanufacturing is RC 3PL = 3 ( , ).

Selling price remaining collected used products (SCP)
The 3PL sells remaining (1 − ) portion of the collected products ( , ) to the vendor at a unit price . Then, total selling price of used products is Total profit of 3PL ( ) Total profit of the 3PL is given by (4.16)

Vendor
The vendor uses a cooperation policy for remanufacturing by sharing licenses. Along with this hybrid CLSCM, the manufacturer uses a hybrid production system that produces new products as well as remanufactured products. For the convergence, the price and costs follows the relation ≤ ≤ . Carbons are emitted from the hybrid production system of the vendor at a rate , 0 ≤ ≤ 1. Other intriguing factors are described below.

Revenue (RN )
The vendor makes the revenue by selling the new products and remanufactured products. As both types of products have the same quality, the unit wholesale price is the same. If is the unit wholesale price, the revenue of the vendor is RN = ( − ( , )). (4.17)

Investment for carbon emission reduction ( ( ))
As the vendor has a carbon cap, the vendor tries to reduce the emissions rate such that the total emissions can be restricted within the carbon cap. To reduce the emissions rate, the vendor invests the following amount.

Carbon tax (CT)
If emissions from the system does not follow the reduced emissions rate , then total emissions may exceed the total carbon cap [15]. For that excess emissions, the vendor has to pay a carbon tax. If the unit carbon tax is , then total carbon tax is This tax gives a positive effect on reducing CO 2 emissions.

Investment for quality improvement ( ( ))
The vendor invests on quality improvement ( ) for products. This investment has an inverse effect on remanufactured products as the quantity of collected used products depends on . The investment [8] for quality improvement is (4.20) Purchasing cost of used products from 3PL (PC ) The vendor buys (1 − ) portion of used products from the 3PL for remanufacturing. If the unit purchasing cost of used products is , then total purchasing cost is (4.21)

Remanufacturing cost of vendor (RC )
Now, the vendor remanufactures all purchased used products. But the quality of these remanufactured products remains as good as new. If the unit remanufacturing cost of the vendor is 1 , then < 1 . This implies that the vendor saves 1 unit cost per unit product (Equation (4.1)) by using remanufacturing. Total remanufacturing cost is (4.22)

Production cost of new products (NPC)
Vendor produces ( − ( , )) amount of new products for retailer. Rest order is fulfilled by the remanufactured products. Unit production cost of new products is = 1 + 2 . Unit production cost depends upon the production rate. Then, the total production cost of new product is

Investment for customer awareness (AC)
Customer awareness is one of the CLSCM driving factors that help to achieve green and sustainable practice. Vendors actively take part in customer awareness programs such that the process of reuse through remanufacturing goes well. Then the investment for customer awareness is

Investment for gift policy (GP)
The vendor uses gift policy to boosts up the market demand. This helps to attract more customers. Then, the investment for gift policy is GP = 2 2 · (4.25)

Total profit of vendor under uniform distribution (︀ )︀
Thus, the total profit of the vendor is given by

Scenario B: Distribution-free model
Scenario B considers that the random variable of the market demand does not have any known distribution function. Thus, the expected shortage quantity 1 ( ) of the retailer can not be calculated using the distribution function. Then, a minimum-maximum distribution-free approach is used [12,15] to find the expected shortage quantity. and 1 are the mean and standard deviation of , respectively. Then, 1 ( ) is found from the following expression as Then, 1 ( ) is the of the retailer's leftover for holding, which can be expressed as Thus, expected shortage cost of retailer is )︂]︂ .
Further, the upper limit of the upper inequality is tight [12]. Hence, the expected total profit of the retailer is The ordered quantity is the same as in equation (4.10). Profit functions of the 3PL ( DF ) and vendor ( DF ) will be same as in equations (4.16) and (4.26), respectively. That is, (4.32) Solutions to the objective functions are given in the next section.

Solution methodology
Both the models of Scenario A and B are solved for the decentralized case and it is solved by the Stackelberg game policy. The vendor acts as Stackelberg leader and retailer-3PL acts as Stackelberg follower. A backward Stackelberg policy is used where the vendor gives an opportunity to the followers to optimize their decisions. Based on those decisions, the vendor optimizes his decisions.

Scenario A
[See Appendix C]. The obtained optimal solutions are for the retailer and 3PL in Scenario A (Equations (4.11) and (4.16)) based on the Theorems 5.2 and 5.3. Proof. See Appendix B.

Scenario B
Optimum values of decision variables for distribution-free approach are given in Propositions 5.6 and 5.9. Retailer and 3PL's decisions are given in Proposition 5.6. Proposition 5.6. Applying equilibrium conditions on retailer and vendor's profit function of the CLSCM, the optimum values of decision variables * , * , * , and * are given in Equations (5.10), (5.11), (5.12), and (5.13), respectively.
[See Appendices A and C]. The obtained optimal solutions are for the retailer and 3PL in Scenario A (Equations (4.30) and (4.31)) based on the Theorems 5.7 and 5.8.

Numerical experiment
This investigation uses data from Sarkar et al. [41], Taleizadeh et al. [54], and Bhuniya et al. [4]. Two examples are provided two test the analytic model of Scenario A and Scenario B, respectively.

Example 1
Example 1 gives numerical results for Scenario A. Table 2 gives input values of parameters. Total profit and optimum values of decision variables for Scenario A are shown in Table 3. Table 3 shows that the profit of the vendor is maximum, which is $98 309.23, followed by the 3PL $43 161.94, and the retailer $887.15. Each CLSCM player optimizes their decisions individually as a decentralized case. Thus, the sum of these three profits is $142 358.32, which is treated as total profit for giving an overall aspect of the CLSCM profit.    Table 4 shows the result for above scenario.
Profit of the supply chain continuously decreasing in the sequence of no customer awareness, no gift policy and no customer awareness & gift policy, respectively. This implies that the proposed study with both the policies helps to generate more market demand when the CLSCM uses remanufactured products as a brand new products.

Example 2
Example 2 gives numerical results for Scenario B. Table 2 gives the parametric values for Example 2. Maximum profit and optimal values of decision variables are given in Table 5. Table 5 shows that the vendor has the maximum profit $97 209.09 followed by the 3PL $42 789.35, and the retailer $42 789.35. A centralized case is not discussed here. Thus, the total profit of the CLSCM is just the sum of the profits of three CLSCM players as 140 885.60. Results show that Scenario A has more profit than Scenario B. This happens because Scenario A has a known distribution function. Thus, all information about demand is known to the management and thus, it is easy to optimize the objective. But, in reality, there are a lot of risks and uncertainties that evolve along with information. Then, the management needs to justify that information more than the known case, as Scenario A.
A comparison between Scenario A and Scenario B is given to clarify the difference between the two Scenarios.

Comparative study between Scenario A and Scenario B Expected value of additional information (EVAI)
EVAI is found to compare two discussed scenarios in this study. If the optimal values of Scenario B are used as an input for Scenario A, then the total profit of Scenario A becomes $140 904.46, i.e., the difference is $(140 904.46−140 885.60) = $(18.86). This implies that Scenario B with a distribution-free approach has $(18.86) less profit. This amount of money is needed for gathering information in the case of no distribution. This amount of money is used for EVAI purposes, which is less than 1%, i.e., EVAI < 1%.

Sensitivity analysis
A sensitivity analysis of Example 1 for Scenario A are conducted with respect to the cost parameters. Table 6 gives the changes of sensitivity analysis. As game policy is used, cost parameters of one CLSCM player has effect on the the profit of other players.
(1) Minimum selling price of the product min is the most sensitive parameter for the retailer. 50% increment of minimum selling price increases the profit 226.36%. This implies that the retailer can earn more profit if the minimum selling price increases. This happens because the remanufacturing cost of used products is less than the production cost of new products. Thus, it gives a huge profit range. (2) Production cost of new products is the second most sensitive cost parameter for the 3PL. It has a direct impact on the profit of 3PL. 50% increment of production cost increases 90.97% profit of the 3PL. Other parameters are less sensitive.

Managerial insights
After analyzing the results and hypotheses, the following insights are drawn from this study.
(1) Production managers should focus on the hybrid production process, where both 3PL & vendor can remanufacturer used products and the retailer can focus on selling new and remanufactured products. Thus, the retailer does not have to make decisions on used products collection and send those to the vendor. Instead, the retailer can promote the product by using additional services, which helps the vendor to receive more ordered quantities from the retailer. This responsibility sharing policy through cooperation is an effective management strategy. (2) As the demand varies with several factors, the vendor receives clear information about market demand and how customers react to the ongoing policy. Even though all remanufactured products have the highest quality as new products as well as gift policy, there is always a risk. Thus, industry managers focus on customer awareness. This only can help to sell more remanufactured and to save more production costs.
(3) Thus, this hybrid production process with hybrid CLSCM is a smart management policy. This can promote both environments as well as the economic purpose of sustainable development. Besides, the effort for emissions rate reduction with a carbon cap is another positive decision for management toward emissions reduction.
Finally, the conclusions of this study if describes in the next section.

Conclusions
Customer awareness and the gift policy had positive effects on the ordered quantity of the retailer. In addition, quality management positively affects the profitability of the CLSCM. This investigation helped to gain optimal policies for a hybrid production system. 0.0134% of the total profit of uniform distribution requires more to gather information if there is a lack of proper distribution functions for information. Thus, 0.0134% profit is less in the distribution-free approach. Even the [ 2 , 1 ] provided more profit, but it was almost impossible that all information always followed uniform distribution or any other known distribution. It was found that the proposed hybrid CLSCM helped to execute the purpose of the hybrid production system very well. Few limitations of this study can be overcome by extending it. Lead time issues and monetary policy are two of them. In the future study, a monthly installment (EMI) policy can be used as a monetary policy such that the 3PL can pay with a credit period. Other motivation factors like an advertisement, and credit policy for customers can be used in a future study. In addition, while a single-channel was used in this study, a dual-channel policy can be used for further investigation. A comparison between traditional and consignment policies can be incorporated into future research. Sustainability issues based on this context [2] can be an interesting future extension.
Equating the first order partial derivative of Equation (4.31) with zero, the optimum value of is obtained as These are the optimum solutions for the retailer and 3PL for the distribution-free approach.
Proof of Proposition 5.9. The optimum values of decision variables are obtained from the first order partial derivatives of Equation (4.26) with respect to , , , , and , respectively. Then, the optimum values are found by equating the first order partial derivatives with zero as Hence, these are the optimal values of decision variables of the vendor for the distribution-free approach.

Second order partial derivatives
Second order partial derivatives of Equation (4.11) are given below: Second order partial derivative of Equation (4.16) is Second order partial derivatives of Equation (4.26) are given below: Second order partial derivatives of Equation (4.30) are given below: Second order partial derivative of Equation (4.31) is given below: Second order partial derivatives of Equation (4.32) are given below:

Appendix B.
Proof of Theorem 5.2. The third order Hessian matrix can be written as The first order principal minor is Hence, the first order principal minor is negative. The second order principal minor is The aforementioned principal minor of the second order is positive. The third order principal minor is as det( 22 ) > 0. The calculated third order principal minor is less than zero. (See Appendix A for all second order partial derivatives). The first and third minors are negative, and the second order principal minor is positive. Thus, it can be concluded that the total profit, obtained by the CLSCM, has the global maximum profit.
Proof of Theorem 5.3. The second order partial derivative of with respect to is 2 2 = −2 < 0 as > 0. Thus, the total profit of the 3PL is global maximum.