28 research outputs found

    A Robust Two-Stage Stochastic Location-Routing-Inventory Model for Perishable Items

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    The aim of this study is to develop a robust two-stage stochastic location-routing-inventory model for perishable items. The proposed model is implemented in a two-stage structure. The first-stage decisions determine the establishment of distribution centres and the second-stage decisions identify the other variables of the problem. In order to reduce the effect of different scenarios on the outputs of the problem, the two-stage model is developed to a robust model. Two variability criteria called \u27Partial Lower Deviation from Mean\u27 (PLDM) and \u27Partial Lower Deviation from Target\u27 (PLDT) are considered for the problem. This robust model can manage the variability of different scenarios considering the variability needed for the problem. The summary of the results of the models indicate that the supply cost, the setup cost, the vehicle supply cost, and the production cost comprise 55%, 28%, 3%, and 14% of the total costs of the supply chain, respectively. Similarly, the ratio of net profit margin to the total revenue of the supply chain derived from the division of the objective function by the revenue function is 15%. Among free, fresher first, older first, and mixed policies, the free policy provides the decision maker with more profit than the other three policies since it imposes less constraints on the model

    Research Article Balancing the Production Line by the Simulation and Statistics Techniques: A Case Study

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    Abstract: A wide range of the real world problems in industries are related to misbalances of the production line and excessive Work in Process parts (WIP). Simulation is an effective method to recognize these problems with consuming least cost and time. Moreover, total system efficiency of a production line can be extremely improved by examining different solution scenario via the simulation techniques. In this research, we utilize the simulation technique founded upon the software Enterprise Dynamics (ED) for evaluating the cause of these problems and trying to find the improvement solutions in Sadid Pipe and Equipment Company (SPECO). Two parameters of diameter and thickness are important factors affecting the time of workstations. The effects of these factors on process time are evaluated by hypothesis tests. Two improvement scenarios have been presented. In the first scenario, the layout design of the factory has been improved with regard to production process and bottleneck station. In the second one, an essential improvement has been carried out by reduction in wastages. Regarding the accomplished simulations, it is concluded that it is possible to eliminate the existing bottleneck by implementing changes in the locations of production stations or reducing the waste in some stations. The improvements eventually result in balancing the production line

    Social Innovation: Towards a Better Life after COVID-19 Crisis: What to Concentrate On

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    We know that saving lives of people is the most important issue during COVID-19 crisis, but we should not forget that due to this crisis, the quality of life for many people will change and new social needs will appear and we must be prepared for that. The main purpose of this research is to find out the areas, which are the most affected ones by the pandemic and have a direct impact on citizensā€™ lives. This research is a quantitative study, which plans to use the opinions of business and management graduates in Iran to present the status of affected fields of better life index by COVID-19 crisis. A fuzzy TOPSIS method is used here to do this ranking. This research has ranked the most affected indicators of better life index by COVID-19 pandemic. In addition, the profile of this impact including the indicators of better life index and their change is also presented in this research. We found out that most affected indicators are Income, jobs, health, life satisfaction and education, respectively. The output of this research can be used for policy makers to start providing support on policies, infrastructures and social innovations on the most affected dimensions in order to reduce the impact of this pandemic on citizensā€™ everyday life and their quality of life. Also using fuzzy TOPSIS in recognizing the most affected dimensions of quality of life of citizens is a theoretical implication of this research for similar ideas of future researchers. This study is a pioneer in investigating the effects of COVID-19 pandemic on dimensions of life quality of citizens. Also linking the better life index, as a comprehensive index, which has a direct impact on peopleā€™s lives to social innovation is another novelty of this research. As it opens a new window for social innovators to know how they can use their innovation capacity to have higher impact on society by shedding light on the main challenges occurred in peopleā€™s lives. In this research we have decided to use primary data on perceptions of citizens as waiting to get the official secondary data might take long and, on that time, we might be deep in these societal problems and it might be late to make new directions on them. Research paper Keywords: Social innovation; Better life index; OECD; Fuzzy TOPSIS; Iran; COVID-19 Reference to this paper should be made as follows: Sharafi Farzad, F., Salamzadeh, Y., Bin Amran, A., & Hafezalkotob, A. (2020). Social Innovation: Towards a Better Life after COVID-19 Crisis: What to Concentrate On, Journal of Entrepreneurship, Business and Economics, 8(1), 89ā€“120

    Evaluating innovation capabilities of real estate firms: a combined fuzzy delphi and dematel approach.

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    Due to strong competition, numerous technology advancements and the monetary policy of the government, the survival of Indian real estate firms now depends on their capacity to measure their existing innovation capabilities, rebuild them and adopt new ones. The aim of this study is to evaluate the technology and human resources innovation capabilities of Indian real estate firms by applying fuzzy Delphi and DEMATEL techniques. After identifying the innovation capabilities through an extensive literature review, a questionnaire is designed based on fuzzy linguistic scales to manage any vagueness of information received. Data has been collected from experts in the field, with capabilities then finalized by using a fuzzy Delphi method. To establish cause-effect relationships among capabilities, a DEMATEL method is applied to the data collected from a second questionnaire. Analysis of the data divides capabilities into two groups i.e. cause and effect. The results show that innovation management, robustness of product and process design capability, strategic planning and knowledge resources fall in the cause group; these are critical findings given the effect on the other capabilities. The study outcomes can help real estate firms to enhance their capabilities with the proposed model providing guidelines and direction in this regard.N/

    Social Innovation: Towards a Better Life after COVID-19 Crisis: What to Concentrate On

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    We know that saving lives of people is the most important issue during COVID-19 crisis, but we should not forget that due to this crisis, the quality of life for many people will change and new social needs will appear and we must be prepared for that. The main purpose of this research is to find out the areas, which are the most affected ones by the pandemic and have a direct impact on citizensā€™ lives. This research is a quantitative study, which plans to use the opinions of business and management graduates in Iran to present the status of affected fields of better life index by COVID-19 crisis. A fuzzy TOPSIS method is used here to do this ranking. This research has ranked the most affected indicators of better life index by COVID-19 pandemic. In addition, the profile of this impact including the indicators of better life index and their change is also presented in this research. We found out that most affected indicators are Income, jobs, health, life satisfaction and education, respectively. The output of this research can be used for policy makers to start providing support on policies, infrastructures and social innovations on the most affected dimensions in order to reduce the impact of this pandemic on citizensā€™ everyday life and their quality of life. Also using fuzzy TOPSIS in recognizing the most affected dimensions of quality of life of citizens is a theoretical implication of this research for similar ideas of future researchers. This study is a pioneer in investigating the effects of COVID-19 pandemic on dimensions of life quality of citizens. Also linking the better life index, as a comprehensive index, which has a direct impact on peopleā€™s lives to social innovation is another novelty of this research. As it opens a new window for social innovators to know how they can use their innovation capacity to have higher impact on society by shedding light on the main challenges occurred in peopleā€™s lives. In this research we have decided to use primary data on perceptions of citizens as waiting to get the official secondary data might take long and, on that time, we might be deep in these societal problems and it might be late to make new directions on them. Research paper Keywords: Social innovation; Better life index; OECD; Fuzzy TOPSIS; Iran; COVID-19 Reference to this paper should be made as follows: Sharafi Farzad, F., Salamzadeh, Y., Bin Amran, A., & Hafezalkotob, A. (2020). Social Innovation: Towards a Better Life after COVID-19 Crisis: What to Concentrate On, Journal of Entrepreneurship, Business and Economics, 8(1), 89ā€“120

    Strategic and Tactical Design of Competing Decentralized Supply Chain Networks with Risk-Averse Participants for Markets with Uncertain Demand

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    An integrated equilibrium model for tactical decisions in network design is developed. We consider a decentralized supply chain network operating in markets under uncertain demands when there is a rival decentralized chain. The primary assumption is that two chains provide partial substitutable products to the markets, and markets' demands are affected by tactical decisions such as price, service level, and advertising expenditure. Each chain consists of one risk-averse manufacturer and a set of risk-averse retailers. The strategic decisions are frequently taking precedence over tactical ones. Therefore, we first find equilibrium of tactical decisions for each possible scenario of supply chain network. Afterwards, we find optimal distribution network of the new supply chain by the scenario evaluation method. Numerical example, including sensitivity analysis will illustrate how the conservative behaviors of chains' members affect expected demand, profit, and utility of each distribution scenario

    A Three-Echelon Multi-Objective Multi-Period Multi-Product Supply Chain Network Design Problem: A Goal Programming Approach

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    In this paper, a multi-objective multi-period multi-product supply chain network design problem is introduced. This problem is modeled using a multi-objective mixed integer mathematical programming. The objectives are maximizing the total profit of logistics, maximizing service level, and minimizing inconsistency of operations. Several sets of constraints are considered to handle the real situations of three-echelon supply chains. As the optimum value of conflictive objective functions of the proposed model cannot be met concurrently, so a goal programming approach is used. An illustrative numerical example is provided to show the mechanism of proposed model and the solution procedure. In a numerical example, 1 manufacture, 2 warehouses, 2 distribution centers (DCs), and 2 types of final products are considered in a planning horizon consists of 3 time periods. Products are shipped from the manufacturer to warehouses and then are shipped from the two warehouses to two distribution centers. The distribution centers are the point from which the product are shipped to final consumers. The Model is coded using GAMS software on a Core i7 CPU, using 8GB of RAM with MS-Windows 8.0. The optimum design of supply chain, inventory level for warehouses and distributors, and amount of shipments between echelons are determined

    Robust approach to DEA technique for supplier selection problem: A case study at Supplying Automotive Parts Company (SAPCO)

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    Abstract In many industries such as automotive industry, there are a lot of suppliers dealing with the final products manufacturer. With growing numbers of suppliers, the suppliers' efficiency measurement often becomes the most significant concern for manufacturers. Therefore, various performance measurement models such as DEA, AHP, TOPSIS, are developed to support supplier selection decisions. After an exhaustive review of the supplier selection methods, we employ data envelopment analysis (DEA) for computing the relative efficiency of the suppliers and introducing the most efficient supplier as a benchmark. In reality, there are large amounts of uncertainty regarding the suppliers' measurements; therefore, we propose the robust optimization approach to the real application of DEA (RDEA). In this approach, uncertainties about incomes and outcomes of decision making units (DMUs) are involved in the relative suppliers' efficiencies. The proposed RDEA approach is utilized for the selection of suppliers which manufacture the automotive safety components in Supplying Automotive Parts Company (SAPCO), an Iranian leading automotive enterprise. Numerical example will illustrate how our proposed approach can be used in the real supplier selection problem when considerable uncertainty exists regarding the suppliers' input and output dat

    A fuzzy leader-follower game approach to interaction of project client and multiple contractors in time/cost trade-off problem

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    In recent years, clients often employ multiple contractors to implement different activities of the projects. Each contractor manages and implements a subset of activities according to the deter-mined schedule and payments. In this situation, time/cost trade-off problem becomes a distributed decision making problem in which the client, as leader, and the contractors, as followers, pursue their own objectives. We establish a multi-objective, bi-level distributed programming model based on fuzzy mathematical programming for this time/cost trade-off problem. The model is then developed for three common behaviors of client i.e. profit seeking, minimization of project time, as well as combination of profit seeking and minimization of project time behaviors. As the solution approaches, we propose transformation method based on Karush-Kuhn-Tucker condi-tions projects to transform bi-level programming problem to a single level one. Numerical results reveal that the clientā€™s behaviors have measurable impact on time and cost of activities performed by contractors. Moreover, we found that when the client does not have complete information about the contractorsā€™ financial situations, the client should make trade-off between his confidence level and his profit

    Impact of government's policies on competition of two closed-loop and regular supply chains

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    Abstract With progressing technologies and new features of production, new products compete with older ones in markets. Also new products initiate contest with olden ones and this process repeats in different productions life time for several times. In this situation recycling the olden products seems to be significant for supply chains. Governments often levy special tariffs for these products as a control tool which aims to incentive production recovery. In the real world, government purposes financial incentive plans for recoverable productions, and also punitive plans for unrecoverable products. This paper tries to model the competition of a closed-loop supply chain and an ordinary supply chain using a game theory approach. In next step, the effects of persuasive and punitive governmental plans are modeled. Optimal retail and wholesale prices of the products are found in two chains. Numerical examples including sensitivity analysis of some key parameters will compare the results between different models of this study. Keywords: Game theory; competition; closed-loop supply chain; government intervention. 1-Introduction Nowadays, competition is evolved among supply chains (SCs). For example, Google and Samsung both have constituted a supply chain that competes with the existing supply chain consisting of Microsoft and Nokia. The decisions of members in one SC affect the decisions of members in its rival supply chain. In this paper the competition between two supply chains under government financial intervention (environmental protection, revenue seeking on and revenue seeking policies) is studied. Green supply chain management (GSCM) criteria have been used to control flow of information and material. Researchers have applied GSCM criteria to expand a green strategy. (Vachon and Klassen, 2008). In a GSCM, manufacturer and customers work together to reduce the environmental effects of processes. That is, the supplier and the manufacturer both set some goals in order to limit the environmental effect with the help of GSCM approach. (Tseng et al., 2009; *Corresponding author. ISSN: 1735-8272, Copyright c 2015 JISE. All rights reserved Journal of Industrial and Systems Engineering Vol. 8, No. 4, Autumn 2015 87 Due to global environmental concerns, reverse supply chain becomes extremely important. Many firms design products that can be reused. Furthermore, Japanese and American governments use green legislation and financial instruments, to extent the product life cycles and promote recycling the products (Robeson, 1992; Fleischmann et al., 2002). In this paper the competition between two supply chains under government financial intervention (environmental protection, revenue seeking on and revenue seeking policies) is investigated. The remainder of this paper is organized as follows. A review is provided in Section 2 while the notations and assumptions underlying these models are discussed in Section 3. Section 3 also presents model formulation. Section 4 provides some numerical results. Finally, the paper concludes in Section 5 with some suggestions for future works in this field. 2-Literature Review This paper is closely related to closed-loop supply chains, green supply chain management, government intervention and game theory. Therefore, let us first review the literature on closed-loop supply chains. Qiaolun et al. (2007) have introduced a closed-loop supply chain with a supplier, retailer, and recycler. In the reverse supply chain, the recycler collects products with different scenarios, so that the rate of return for the used products is related to the consumption of customer. In a forward supply chain the optimal wholesale and retail prices are determined. There are a few papers on green supply chain management related to this paper. Green supply chain management involves customization and coordination of the flow of information and materials between the manufacturers and the customers. Vachon and Klassen (2008) have studied environmental collaboration within organizational interactions of supply chain members. The obtained results have shown that the upstream practices are related to the process-based performance, whereas the downstream collaboration is associated to the product-based performance. Zhu et al. (2008) found that Chinese firms tend having greater environmental awareness than the other firms because they are under pressure of green regulations of European countries. Zamarripa et al. (2013) have improved the tactical decision-making of a supply chain under an uncertain competition scenario. They evaluated different optimization criteria with the help of game theory. The consequence of global pollution, environmental concern is growing that the key members of supply chain and reverse supply chain should be managed to maximize the profit and manage the product life cycle. Robeson (1992) has studied the governmental financial tools. Green legislation was used in Europe, Japan, and North America to promote the awareness of extended producer responsibility. Advanced recycling fees (ARFs) and government subsidies are important to encourage manufacturer to recycle their products. Several studies on the game theory investigate the influence of government financial instrument related to this paper. Governments often use motivation and penalties to exert positive and negative effects, respectively Many scientists have conducted research on the game theory to study the impact of government financial involvements on green supply chain. 3-Notation and Problem Formulation The competition between two supply chains, namely regular and closed loop, is investigated in this study under two different scenarios. In the first scenario, the regular supply chain includes a supplier and a retailer, while the closed loop one involves a supplier, a retailer and a recycler. The supplier sells his product with wholesale price to the retailer and the retailer also delivers the same product with the retail price to customers. In return, the third part adopts to collection of used products and sends them to the supplier for recycling. In the second scenario the competition is between a regular supply chain (i.e. supplier and retailer) and a closed loop supply chain (i.e. supplier and retailer which acts also as the collector). The supplier sells his product with the whole sale price, while the retailer delivers the same product with the retail price. In return, the retailer who also plays the collection role collects the products and sends them to the supplier for recycling. Meanwhile, the government sets tariffs to control the market and protect the environment. In real world, the government adopts its financial policies by defining subsidies or taxes. The tariff parameter is considered to be variable and the problem is solved for both of these scenarios in terms of two policies which will be adopted by the government. The policies which are adopted by the government are listed below: 1. Revenue seeking policy: The government aims to maximize its income by setting this policy. 2. Environmental protection and revenue seeking policy: By following this policy, the government intends to increase its net income in addition to mitigate the adverse environmental effects. is indicative of the government's approach toward environmental effects. A stackelberg model is utilized in this section to solve the problem and to find optimal values of the governmental tariffs. Then, both of the scenarios will be solved in terms of two governmental policies taking into account stackelberg model (game theory) and using a backward approach. This section introduces the notation and formulation used in competition of two supply chains under two proposed scenarios. All variables and assumptions underlying the proposed models will be stated. 3-1-Notation Parameters: the potential size of market for product , = 1, 2; b the fixed cost parameter of collection; the production cost of supply chain i per unit product, = 1, 2; 2 the cost of reproduction of supply chain 2 per unit product; the fixed parameter of tax ratio, d the substitution rate of two products (0ā‰¤ ā‰¤ 1); 2 the retail price of a unit product from recycler to supplier in closed loop supply chain; 2 the collection cost per unit product by recycler in closed loop supply chain ( 2 ā‰„ 2 ); the environmental risk aversion coefficient of government, ā‰„ 0. The larger the coefficient , the higher the environmental protection tendency of government will be; environmental impacts of regular products; environmental impacts of closed-loop products; the product demand for supply chain , = 1, 2 Decision variables: the retail price of product of supply chain , = 1, 2; 2 the rate of collection of used product by recycler of supply chain 2; the tariff imposed by government for supply chain i , i=1,2; the wholesale prices of product manufactured by supply chain i, i=1,2. Decision functions: the profit of retailer in supply chain i , = 1, 2; the profit of recycler in supply chain i, = 1, 2; the profit of supplier in supply chain i, = 1, 2; GNR the government's net revenue obtained from tax and subsidy on supply chains' products; EIS the total environmental impacts of supply chains' products; U the government's net revenue obtained from tax and subsidy on supply chains' products and the total environmental impacts of supply chains' products. 90 3-2-Assumptions The proposed models are established upon the following assumptions: 1. It is assumed that the consumer demand functions for retailer i, i = 1, 2 are a linear function of the two retailers' prices. The linear demand functions can be written as = -+ ; ( , = 1,2; ā‰  ) (Wei and Zhao, 2011). 2. The amount of the supply is the same as demand. 3. The products of two suppliers are differentiated and each supplier sells products to customers through his retailers. 4. All companies have common knowledge about substitution rates, demand density, taxes, and other parameter values. 5. Each member of supply chains has rational behavior and seek to maximize his profit. 6.The and represent environmental impacts of regular and green products, respectively. For generalization purpose of the model, the environmental impacts of products are not restricted to a specific factor. The environmental impacts are industry-dependent and they can embrace air, soil, or water pollutions. They may also be measured by various factors such as reversible index of products, reproduction or recycling index, annual exhausting CO2 or NOx of products, or even a combination of different factors 7. Based on the article from Wei and Zhao (2013), the total cost needed to collect the used product is shown as c( )=b Where b. 2 is the constant part of the cost and . . is its variable part. is the total number of used products which are collected. The model is examined under two following scenarios with respect to the above mentioned explanations. 3-3-Scenario No1 Via this scenario the competition occurs between a regular and a closed loop supply chains. The closed loop supply chain includes a supplier, a retailer and a recycler, while the regular supply chain incorporates one retailer and one supplier. The government is placed at a higher level and tries to balance the market and meets his requirements by following the mentioned policies and by properly setting the tariffs 1 and 2 . The profit function of each member can be defined as below: 1 1 Solution of this problem is described below with respect to Stackelberg model: Step Step Step (3): Considering the wholesale price and the government's tariff, each retailer as the follower, determines the optimal value of * . Step (4): The recycler acting as the game follower, indicates the return rate of collection of used product according to the wholesale price, retail price and tariff. Now, the problem can be solved by backward approach. Proposition (1) can determine the optimum rate of collection of used product. Proposition 1. If the profit function of a recycler is a concave function, the return rate of the used products will be calculated from first derivative conditions of the recycler function as below: Taking into account concavity of the profit function and the retail sell, Proposition 2 calculates the amount of the optimal retail sells. Proposition 2. If the profit function of a retailer is a concave function, the optimal retail price will be calculated from the first derivative conditions of the retailer functions as following: where, = 2 + 4āˆ’ 2 (i,j=1,2) , 1 = 2 4āˆ’ 2 and 2 = 4āˆ’ 2 . By replacing equations (8) to (10) in the profit functions of the suppliers, the profit functions of the producer can be presented as below: 2 2 ==( 2 āˆ’ ļæ½1 āˆ’ āˆ’ ( 1 + 2 2 2 + 1 1 1 + 1 1 + 2 2 ) āˆ’ ( 2 + 1 2 2 + 2 1 1 + 2 1 + 1 2 )ļæ½ āˆ’ ļæ½ 2 + 2 ļæ½ļæ½ āˆ’ ( 1 + 2 2 2 + 1 1 1 + 1 1 + 2 2 ) āˆ’ 92 If ( 2 āˆ’2)(2+ļæ½ 2 āˆ’ 2 ļæ½ļæ½2āˆ’ 2 ļæ½ļæ½ļæ½4āˆ’ 2 ļæ½ 2 2 āˆ’ļæ½ 2 + 2 ļæ½ļæ½) (4āˆ’ 2 ) < 0, then the profit function of the suppliers will be a concave function, with the optimal values of the wholesale price being obtained by establishing the first derivative conditions of equations are calculated by a mathematical software. By replacing the optimal values of w i * , * and (i=1,2) in the profit functions of the government, these functions are calculated as follows under two following policies which are chosen by the government: a) Revenue seeking policy In this case the government intends to maximize his profit. If the equation Proposition 4. If equation (16) holds, the optimal values of 1 and 2 can be found by establishment of the first derivative conditions of equation (15). b) Environmental protection and revenue seeking policy In this case, the government decides to maximize his profit and protect the environment. The profit function of the government is described as below: In this case, if equation Problem Statement in Scenario 2 As discussed earlier, the competition takes place between a regular supply chain and a closed-loop one. In this case the closed-loop supply chain includes a supplier and a retailer who is the collector as well, but the regular supply chain involves a retailer and a supplier. The government acts as the leader at a higher level, which determines the proper tariffs in accordance with his policies by selecting various policies (i.e. income-oriented and environment protection). The objective function of supplier in regular supply chain can be written as below: (19) Similar to Wie and Zhao (2013), the objective function of the recycler-retailer in the closed-loop supply chain can be formulated as follows: The objective function of supplier in the closed-loop supply chain can be stated as: This problem is solved with respect to Stackelberg model and the following steps can be followed to address the optimal values: Step Step Step (3): The retailer of regular supply chain and the retailer-recycler addresses the return rate of products as well as the retail price as the game follower. For this purpose, a backward approach is utilized considering the optimal tariff rate and considering the defined response functions from suppliers, retailers and retailer-recycler. Noteworthy is considering the competition of the supply chain members outside the chain and also taking the government as the main leader. 94 Proposition 6. If 4b>ļæ½ 2 āˆ’ 2 ļæ½ holds, then the optimal retail prices and the return rate collection of used products are calculated as below. and 2 = ļæ½āˆ’ļæ½ 2 āˆ’ 2 ļæ½ 2 +2 ļæ½(2 2 + 1 ) . By replacing equations If ļæ½ 2 āˆ’ 2 ļæ½ 2 (1 āˆ’ )< (4b-2bd) holds, the profit function of the first producer will be concave on w1, and if (āˆ’ 2 + 1 )(1 + 3 2 āˆ’ 3 )ļæ½ 2 + 2 ļæ½ < 0 holds, the profit function of the second producer will become concave on 2 , and the optimal values of (i=1,2) are obtained from Proposition (7). Proposition7.If(āˆ’ holds, the optimal values of w i c (i=1,2) can be found as follows: We can write the linear wholesale price variables as the following. ( , and ( = 1,2) are calculated by a mathematical software). 95 By replacing the optimal values of w i c , (i=1,2) and 2 in profit functions of the government under two scenarios adopted by the government, these profit functions can be calculated as below and the optimal values can be obtained accordingly. a) Revenue seeking policy: The government tries to increase his income following this policy. The profit function of the government is a concave function and by establishing the first derivative conditions for the profit function of the government, the optimal values of 1 and 2 are obtained from Proposition (8). Proposition 8. If equation 2 )) > 0 holds, the profit function of the government is a concave function. b) Environment Protection and Income-oriented Policies: In this case, the government decides to maximize his profit and protect the environment, so that his profit function is found as below: 2 ) + 2 2 (āˆ’2 + 4 ) + 2 (āˆ’2 + 4 2 )) > 0 holds, the profit function of the government is a concave function and the optimal values of 1 and T 2 C are obtained by considering the first derivative conditions. 4-Numerical Example The problem under study is examined in terms of a numerical example. For this purpose, the following parameters are used: = 0.5, = 1, = 0.5, 2 = 2, 2 = 1, 2 = 1, 2 = 1, ( = 1,2) 96 Two supply chains start to produce the same product with equal quality and potential market size. By adoption of profit-oriented and environment protection policies by the government, the wholesale price in the regular supply chain becomes greater than that of the close-loop supply chain. Nevertheless, the supplier's profit in the regular supply chain is smaller. However, the retail price of the regular supply chain is below than the closed-loop supply chain, with the retailer's profit of the closed-loop supply chain being smaller. The retailer's profit from the regular supply chain is negative here. It means that she/he will lose something, which is expectable considering the policies adopted by the government. In this case, where the government aims to get his profit and protect the environment at the same time, the set of tariff values for the closed-loop supply chain were a little greater than those of the regular supply chain. This time, the contribution of government is not greater than the previous case, while the recycler's profit is also increased. When the government decides to follow the income-oriented and environment protection policies, all the wholesale prices and retail prices rise, and the profit function of all the members grow except for the retailer of the first supply chain. By adoption of the profit-oriented policy by the government, the wholesale price in the regular supply chain is greater than that of the closed-loop, while the supplier's profit is greater in the regular SC as well. Moreover, the retail price of the regular supply chain is greater than that of the closedloop. However, the retailer's profit in the regular supply chain is smaller despite its higher prices, so that she/he will lose something. In this case, since the only objective of the government is to acquire his own profit, the set of tariff values of the closed-loop supply chain are almost twice of the regular one, and the government allocates some subsidies to this regular supply chain. Following the profit-oriented and environment protection policies by the government, the wholesale price in the supply chain is still more than the closed-loop supply chain, with the supplier's profit being greater in the regular supply chain. Furthermore, the retailer price of the regular supply chain is greater than that of the closed-loop, with the retailer's profit of the closed-loop being greater than that of the retailer-recycler. In this case, the government prefers to acquire his profit and to protect the environment as well. The set of tariff values for the closed-loop supply chain are a bit greater than those of the open loop supply chain. Here, the contribution of the government is somehow smaller than the previous case. The profit of the government decreases in the second scenario through both approaches (and the government has even lost in some instances). This indicates that the cooperation between the retailer and the recycler was not in favor of the government. Total contribution of the 97 retailer and the recycler in the first scenario is smaller than the retailer-recycler profit, which indicates providing some benefits for them both. Once the government selects profit-oriented and environment protection policies, all the retail and wholesale prices will increase and the profit functions of all members grow, except for that of retailerrecycler and that of government. As can be observed from 5-Conclusion This research provides a competitive model for competition of two supply chains, namely closedloop and regular, under intervention of the government. By the means of the games theory concepts, the optimal values of wholesale, retail sale, collection of used products parameter and tariff can be obtained for each of the supply chains in order to model these supply chains in terms of Stackelberg game. It is shown that the profit of the chain members is completely influenced by the government as the main leader of the game. Moreover, by selecting various scenarios, the government can influence the profit of each of the chain members, and can persuade the regular supply chain to withdraw. At the end, one of the potential subjects for being developed in the future can be eliminating the dominant assumptions of the current work. Some of the possible suggestions for future works are considering the costs of inventory, maintenance, ordering or shortage
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