Ming Liu, Tao Lin, Feng Chu, Feifeng Zheng, C. Chu
Scheduling-Location (ScheLoc) problem considering machine location and job scheduling simultaneously is a relatively new and hot topic. The existing works assume that only one machine can be placed at a location, which may not be suitable for some practical applications. Besides, the customer credit risk which largely impacts the manufacturer's profit has not been addressed in the ScheLoc problem. Therefore, in this work, we study a new and general stochastic parallel machine ScheLoc problem with limited location capacity and customer credit risk. The problem consists of determining the machine-to-location assignment, job acceptance, job-to-machine assignment, and scheduling of accepted jobs on each machine. The objective is to maximize the worst-case probability of manufacturer's profit being greater than or equal to a given profit (referred to as the profit likelihood). For the problem, a distributionally robust chance-constrained (DRCC) programming model is proposed. Then, we develop two model-based approaches: (i) a sample average approximation (SAA) method; (ii) a model-based constructive heuristic. Numerical results of 300 instances adapted from the literature show the average profit likelihood proposed by the constructive heuristic is 9.43% higher than that provided by the SAA, while the average computation time of the constructive heuristic is only 4.24% of that needed by the SAA.
{"title":"A new and general stochastic parallel machine ScheLoc problem with limited location capacity and customer credit risk","authors":"Ming Liu, Tao Lin, Feng Chu, Feifeng Zheng, C. Chu","doi":"10.1051/ro/2023016","DOIUrl":"https://doi.org/10.1051/ro/2023016","url":null,"abstract":"Scheduling-Location (ScheLoc) problem considering machine location and job scheduling simultaneously is a relatively new and hot topic. The existing works assume that only one machine can be placed at a location, which may not be suitable for some practical applications. Besides, the customer credit risk which largely impacts the manufacturer's profit has not been addressed in the ScheLoc problem. Therefore, in this work, we study a new and general stochastic parallel machine ScheLoc problem with limited location capacity and customer credit risk. The problem consists of determining the machine-to-location assignment, job acceptance, job-to-machine assignment, and scheduling of accepted jobs on each machine. The objective is to maximize the worst-case probability of manufacturer's profit being greater than or equal to a given profit (referred to as the profit likelihood). For the problem, a distributionally robust chance-constrained (DRCC) programming model is proposed. Then, we develop two model-based approaches: (i) a sample average approximation (SAA) method; (ii) a model-based constructive heuristic. Numerical results of 300 instances adapted from the literature show the average profit likelihood proposed by the constructive heuristic is 9.43% higher than that provided by the SAA, while the average computation time of the constructive heuristic is only 4.24% of that needed by the SAA.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"46 1","pages":"1179-1193"},"PeriodicalIF":0.0,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84701782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop a technique for exact simultane- ous upliftings of circuit inequalities of an independence system poly- tope. The resulting inequalities define new families of valid inequal- ities for this polytope. They are obtained by simultaneously adding the most appropriate set of variables with the highest possible values of the lifting coefficient that maintain the validity. More specifically, in this technique, we introduce a procedure to generate two conflict hypergraph structures types: hypertrees and clutter. In this setting, we use the hyperedges cardinalities of these structures to compute the suitable lifting coefficient values. We then give necessary and sufficient conditions for both the circuit inequalities and the new families of valid inequalities to be facet-defining.
{"title":"Conflict hypergraphs to define new families of facets for the independence system polytope","authors":"Chafia Boughani, Méziane Aïder","doi":"10.1051/ro/2023015","DOIUrl":"https://doi.org/10.1051/ro/2023015","url":null,"abstract":"In this paper, we develop a technique for exact simultane-\u0000ous upliftings of circuit inequalities of an independence system poly-\u0000tope. The resulting inequalities define new families of valid inequal-\u0000ities for this polytope. They are obtained by simultaneously adding\u0000the most appropriate set of variables with the highest possible values\u0000of the lifting coefficient that maintain the validity. More specifically,\u0000in this technique, we introduce a procedure to generate two conflict\u0000hypergraph structures types: hypertrees and clutter. In this setting,\u0000we use the hyperedges cardinalities of these structures to compute the\u0000suitable lifting coefficient values. We then give necessary and sufficient\u0000conditions for both the circuit inequalities and the new families of valid\u0000inequalities to be facet-defining.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"5 1","pages":"631-648"},"PeriodicalIF":0.0,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84799473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Information is important market resource. High-quality information is beneficial to increase enterprise’s reputation and reduce consumer’s verification cost. This paper constructs a two-layer dynamic model, in which enterprises simultaneously conduct price and information game. The goal of profit maximization integrates two types of games into one system. The complex evolution of the two-layer system are studied by equilibrium analysis, stability analysis, bifurcation diagram, entropy and Lyapunov exponent. It is found that improving the information quality through regulations will increase involution and reduce stability of the market. Then, the block chain technology is introduced into the model for improving information quality of the market. It is found that increasing enterprises’ willingness to adopt block chain can improve the information quality quickly and effectively, and that is verified by entropy value. Therefore, the application and promotion of new technologies are more effective than exogenous regulations for improving information quality in market .
{"title":"The complex evolution of information quality improvement in competitive market","authors":"Fang Wu, Bing Liu, Na Fu","doi":"10.1051/ro/2023013","DOIUrl":"https://doi.org/10.1051/ro/2023013","url":null,"abstract":"Abstract. Information is important market resource. High-quality information is beneficial to increase enterprise’s reputation and reduce consumer’s verification cost. This paper constructs a two-layer dynamic model, in which enterprises simultaneously conduct price and information game. The goal of profit maximization integrates two types of games into one system. The complex evolution of the two-layer system are studied by equilibrium analysis, stability analysis, bifurcation diagram, entropy and Lyapunov exponent. It is found that improving the information quality through regulations will increase involution and reduce stability of the market. Then, the block chain technology is introduced into the model for improving information quality of the market. It is found that increasing enterprises’ willingness to adopt block chain can improve the information quality quickly and effectively, and that is verified by entropy value. Therefore, the application and promotion of new technologies are more effective than exogenous regulations for improving information quality in market .","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"33 1","pages":"351-369"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76621449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note we introduce new characterizations for the optimal solution of the identical coupled tasks scheduling problem. We also develop three lower bounds and formulate useful observations about the choice of the test instances.
{"title":"New characterizations for the identical coupled tasks scheduling problem","authors":"Hatem Hadda, Mhamed Abdessalem","doi":"10.1051/ro/2023014","DOIUrl":"https://doi.org/10.1051/ro/2023014","url":null,"abstract":"In this note we introduce new characterizations for the optimal solution of the identical coupled tasks scheduling problem. We also develop three lower bounds and formulate useful observations about the choice of the test instances.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"18 1","pages":"325-332"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89657888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the context of subsidy phase-out and the tightening of credit trading policy tools, enterprises producing internal combustion engine passenger cars have also started to produce new energy passenger cars, creating a competitive market with new energy passenger car enterprises. To explore the operation strategies and profit fluctuations of two enterprises in passenger car market and credit trading market, this paper develops a duopoly competition game model. Based on solving a multi-objective equilibrium problem, and performing numerical simulations with real data on Chinese passenger car market, this paper analyzes the interactive impact of policy tools on market competition. The conclusions point out that the numerical relationship between the price of positive new energy credits and credit deficit penalty is decisive to enterprises' pricing strategies. As the subsidy recedes, the competitiveness of new energy passenger car enterprise will decline. The policy tools at corporate average fuel consumption credit regulation level only have a negative interactive effect on hybrid energy passenger car enterprise's pricing and production strategy. There is a threshold for the difference between corporate average fuel consumption up-to-standard value and actual value, below which hybrid energy passenger car enterprise will produce more new energy passenger cars than internal combustion engine passenger car. The tightening of policy tools at new energy credit regulation level will drive both enterprises to raise price and reduce yield.
{"title":"Impact of subsidy phase-out and credit trading policy tools on the competitive strategies of Chinese passenger car enterprises","authors":"Bing Sun, Xueting Yang, Shen Zhong, Minjung Kang, Tian Liang","doi":"10.1051/ro/2023012","DOIUrl":"https://doi.org/10.1051/ro/2023012","url":null,"abstract":"In the context of subsidy phase-out and the tightening of credit trading policy tools, enterprises producing internal combustion engine passenger cars have also started to produce new energy passenger cars, creating a competitive market with new energy passenger car enterprises. To explore the operation strategies and profit fluctuations of two enterprises in passenger car market and credit trading market, this paper develops a duopoly competition game model. Based on solving a multi-objective equilibrium problem, and performing numerical simulations with real data on Chinese passenger car market, this paper analyzes the interactive impact of policy tools on market competition. The conclusions point out that the numerical relationship between the price of positive new energy credits and credit deficit penalty is decisive to enterprises' pricing strategies. As the subsidy recedes, the competitiveness of new energy passenger car enterprise will decline. The policy tools at corporate average fuel consumption credit regulation level only have a negative interactive effect on hybrid energy passenger car enterprise's pricing and production strategy. There is a threshold for the difference between corporate average fuel consumption up-to-standard value and actual value, below which hybrid energy passenger car enterprise will produce more new energy passenger cars than internal combustion engine passenger car. The tightening of policy tools at new energy credit regulation level will drive both enterprises to raise price and reduce yield.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"54 1","pages":"649-675"},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77490194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The sustainable EPQ models that have been proposed in the inventory literature are insufficient to address the practical scenario of defects in manufacturing and subsequent rework for remedial actions. In this article, sustainable inventory model with rework for the faulty products has been studied. Promotional activities are the key factors that significantly affect the market demand for an item. The impacts of random defects and combining economic and environmental elements on the economic order quantity with price and promotional effort dependent demand have been addressed. Numerical illustrations along with sensitivity analysis are presented to reveal the relevancy as well as computational tractability of the proposed investigation. For the profit optimization, a mixed integer problem has been formulated and analyzed by using Bat metaheuristic optimization algorithm.
{"title":"Sustainable inventory prediction with random defect and rework using Bat algorithm","authors":"Madhuri Jain, Nidhi Sharma, Praveendra Singh","doi":"10.1051/ro/2023011","DOIUrl":"https://doi.org/10.1051/ro/2023011","url":null,"abstract":"The sustainable EPQ models that have been proposed in the inventory literature are insufficient to address the practical scenario of defects in manufacturing and subsequent rework for remedial actions. In this article, sustainable inventory model with rework for the faulty products has been studied. Promotional activities are the key factors that significantly affect the market demand for an item. The impacts of random defects and combining economic and environmental elements on the economic order quantity with price and promotional effort dependent demand have been addressed. Numerical illustrations along with sensitivity analysis are presented to reveal the relevancy as well as computational tractability of the proposed investigation. For the profit optimization, a mixed integer problem has been formulated and analyzed by using Bat metaheuristic optimization algorithm.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"67 1","pages":"481-501"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84056640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems as they do not require the storage of any matrices. In order to obtain a theoretically effective and numerically efficient method, two modified conjugate gradient methods ( called the MCB1 and MCB2 methods ) are proposed. In which the coefficient βk in the two proposed methods is inspired by the structure of the conjugate gradient parameters in some existing conjugate gradient methods. Under the strong Wolfe line search, the sufficient descent property and global convergence of the MCB1 method are proved. Moreover, the MCB2 method generates a descent direction independently of any line search and produces good convergence properties when the strong Wolfe line search is employed. Preliminary numerical results show that the MCB1 and MCB2 methods are effective and robust in minimizing some unconstrained optimization problems and each of these modifications outperforms the four famous conjugate gradient methods. Furthermore, the proposed algorithms were extended to solve the problem of mode function.
{"title":"Two modified conjugate gradient methods for solving unconstrained optimization and application","authors":"Abd Elhamid Mehamdia, Y. Chaib, T. Bechouat","doi":"10.1051/ro/2023010","DOIUrl":"https://doi.org/10.1051/ro/2023010","url":null,"abstract":"Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems as they do not require the storage of any matrices. In order to obtain a theoretically effective and numerically efficient method, two modified conjugate gradient methods ( called the MCB1 and MCB2 methods ) are proposed. In which the coefficient βk in the two proposed methods is inspired by the structure of the conjugate gradient parameters in some existing conjugate gradient methods. Under the strong Wolfe line search, the sufficient descent property and global convergence of the MCB1 method are proved. Moreover, the MCB2 method generates a descent direction independently of any line search and produces good convergence properties when the strong Wolfe line search is employed. Preliminary numerical results show that the MCB1 and MCB2 methods are effective and robust in minimizing some unconstrained optimization problems and each of these modifications outperforms the four famous conjugate gradient methods. Furthermore, the proposed algorithms were extended to solve the problem of mode function.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"146 6 1","pages":"333-350"},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83117111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sanchari Ganguly, Mithu Rani Kuiti, Pritha Das, M. Maiti
Cognitive biases - fairness and overconfidence, affect the decision-making process. The manufacturer/retailer prefers to sell the products as bundles in a duopoly market because it fetches more benefits to supply chain (SC) partners. Till now, none considered the pricing of substitute bundles, produced and sold at the manufacturer’s level. Considering these, the effects of the above cognitive behaviours on the bundlingpricing strategy are investigated. We develop several SC models, depending on the partner’s cognitive biases, with two manufacturers, producing substitute bundles of two uncorrelated items and selling through a retailer. Using the Stackelberg game, prices and profits are evaluated. It is observed that overconfidence does not increase retailer’s and overconfident - manufacturer’s profits but is beneficial for another rational manufacturer. Against the retailer’s fairness concern, her profit is augmented, but both manufacturers’ profits are adversely affected. The combined effect of both cognitive biases is adjuvant for the retailer but maleficent for manufacturers. Managerial insights are presented.
{"title":"Effect of fairness and overconfidence on pricing strategy of substitute bundles in a two-echelon supply chain","authors":"Sanchari Ganguly, Mithu Rani Kuiti, Pritha Das, M. Maiti","doi":"10.1051/ro/2023009","DOIUrl":"https://doi.org/10.1051/ro/2023009","url":null,"abstract":"Cognitive biases - fairness and overconfidence, affect the decision-making process. The manufacturer/retailer prefers to sell the products as bundles in a duopoly market because it fetches more benefits to supply chain (SC) partners. Till now, none considered the pricing of substitute bundles, produced and sold at the manufacturer’s level. Considering these, the effects of the above cognitive behaviours on the bundlingpricing strategy are investigated. We develop several SC models, depending on the partner’s cognitive biases, with two manufacturers, producing substitute bundles of two uncorrelated items and selling through a retailer. Using the Stackelberg game, prices and profits are evaluated. It is observed that overconfidence does not increase retailer’s and overconfident - manufacturer’s profits but is beneficial for another rational manufacturer. Against the retailer’s fairness concern, her profit is augmented, but both manufacturers’ profits are adversely affected. The combined effect of both cognitive biases is adjuvant for the retailer but maleficent for manufacturers. Managerial insights are presented.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"388 1","pages":"401-425"},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79440828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammad Hossein Dehghani Sadrabadi, Fatemeh Sabouhi, A. Bozorgi-Amiri, M. Sheikhalishahi
The primary activities of any organization rely on the procurement of the required goods and services at the shortest time and highest quality possible. On this basis, the problem of supplier evaluation, ranking, and selection is considered critically important. Data envelopment analysis is a well-known and successful approach in this field. In this study, we propose a robust-stochastic data envelopment analysis model to measure the efficiency of decision-making units under uncertainty. We measure efficiency through a standard and an inverted model in terms of resilience and agility. In order to demonstrate the practical potential of the proposed model, we apply the model to a case study of the Iranian telecom industry with 90 decision-making units. Numerical results reveal that human resources and cash assets are the most important input criteria. Also, the output indicators, including adaptability, reliability, visibility, and coordination, have high importance in measuring the efficiency of decision-making units. It should be noted that employing the robust-stochastic optimization approach leads to controlling the fluctuations of uncertain parameters and maintaining a desirable optimal level of efficiency for decision-making units under different scenarios. The results suggest that the model is sufficiently valid and reliable for evaluating the performance of suppliers in the telecom industry, may be employed under uncertain conditions, and can incorporate decision-makers' varying preferences. The managerial insights derived from this research indicate that, in the short term, uncertainty throughout the evaluation process of suppliers often leads to reduced efficiency among the decision-making units. However, operating under uncertainty is associated with several advantages in the long term, such as increased decision-making consistency and improved vital ability to cope with uncertainty.
{"title":"A robust-stochastic data envelopment analysis model for supplier performance evaluation of the telecommunication industry under uncertainty","authors":"Mohammad Hossein Dehghani Sadrabadi, Fatemeh Sabouhi, A. Bozorgi-Amiri, M. Sheikhalishahi","doi":"10.1051/ro/2023008","DOIUrl":"https://doi.org/10.1051/ro/2023008","url":null,"abstract":"The primary activities of any organization rely on the procurement of the required goods and services at the shortest time and highest quality possible. On this basis, the problem of supplier evaluation, ranking, and selection is considered critically important. Data envelopment analysis is a well-known and successful approach in this field. In this study, we propose a robust-stochastic data envelopment analysis model to measure the efficiency of decision-making units under uncertainty. We measure efficiency through a standard and an inverted model in terms of resilience and agility. In order to demonstrate the practical potential of the proposed model, we apply the model to a case study of the Iranian telecom industry with 90 decision-making units. Numerical results reveal that human resources and cash assets are the most important input criteria. Also, the output indicators, including adaptability, reliability, visibility, and coordination, have high importance in measuring the efficiency of decision-making units. It should be noted that employing the robust-stochastic optimization approach leads to controlling the fluctuations of uncertain parameters and maintaining a desirable optimal level of efficiency for decision-making units under different scenarios. The results suggest that the model is sufficiently valid and reliable for evaluating the performance of suppliers in the telecom industry, may be employed under uncertain conditions, and can incorporate decision-makers' varying preferences. The managerial insights derived from this research indicate that, in the short term, uncertainty throughout the evaluation process of suppliers often leads to reduced efficiency among the decision-making units. However, operating under uncertainty is associated with several advantages in the long term, such as increased decision-making consistency and improved vital ability to cope with uncertainty.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"67 1","pages":"263-290"},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81615364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Seyed Parsa Parvasi, A. Taleizadeh, L. Cárdenas-Barrón
Drawing on the Stackelberg game approach to solving the pricing problem in a supply chain, this paper develops a bi-level model whereby a domestic company and a foreign manufacturer compete to gain more profit from the market of a retailer. The domestic company acts as the leader and the retailer as the follower. The domestic company has two manufacturers each of whom produces and sells a different quality of the product. The retailer decides to purchase products based on the prices offered by the low-quality manufacturer, the high-quality manufacturer, and the foreign manufacturer, known as an exogenous factor. In fact, the first level seeks to maximize its profits and the second level seeks to reduce the cost of purchasing. In this paper, the price of the products of each manufacturer is considered a contributing factor to the retailer’s tendency to buy from each manufacturer. This assumption is designed by the multinomial logit model. As the proposed model has binary variables in its follower segment, a novel hybrid exact method based on explicit enumeration method and Lambert-W function is applied to solve it. In other words, to calculate the optimal selling price of domestic products and their profit first by using the explicit enumeration method, the bi-level model is transformed into a single-level problem. The problem is, then, solved precisely by applying the Lambert-W function. The efficiency of the proposed model is proven by the results obtained from solving the model and the sensitivity analysis of the main parameters of the model. Moreover, to have a detailed managerial analysis of each manufacturer’s profit on the competitive market environment, the market is studied in view of three different scenarios: 1) when there is a sense of patriotism regarding domestic manufacturers; 2) when customers have low incomes; and 3) when customers have high incomes. Finally, the study results conclude that if the domestic company has two manufacturers that produce a different type of quality can lead to an increase in the profit of the domestic company. Indeed, the proposed model can increase the competitive power of the domestic company against imported products by providing appropriate pricing on its products.
{"title":"Retail price competition of domestic and international companies: A bi-level game theoretical optimization approach","authors":"Seyed Parsa Parvasi, A. Taleizadeh, L. Cárdenas-Barrón","doi":"10.1051/ro/2023007","DOIUrl":"https://doi.org/10.1051/ro/2023007","url":null,"abstract":"Drawing on the Stackelberg game approach to solving the pricing problem in a supply chain, this paper develops a bi-level model whereby a domestic company and a foreign manufacturer compete to gain more profit from the market of a retailer. The domestic company acts as the leader and the retailer as the follower. The domestic company has two manufacturers each of whom produces and sells a different quality of the product. The retailer decides to purchase products based on the prices offered by the low-quality manufacturer, the high-quality manufacturer, and the foreign manufacturer, known as an exogenous factor. In fact, the first level seeks to maximize its profits and the second level seeks to reduce the cost of purchasing. In this paper, the price of the products of each manufacturer is considered a contributing factor to the retailer’s tendency to buy from each manufacturer. This assumption is designed by the multinomial logit model. As the proposed model has binary variables in its follower segment, a novel hybrid exact method based on explicit enumeration method and Lambert-W function is applied to solve it. In other words, to calculate the optimal selling price of domestic products and their profit first by using the explicit enumeration method, the bi-level model is transformed into a single-level problem. The problem is, then, solved precisely by applying the Lambert-W function. The efficiency of the proposed model is proven by the results obtained from solving the model and the sensitivity analysis of the main parameters of the model. Moreover, to have a detailed managerial analysis of each manufacturer’s profit on the competitive market environment, the market is studied in view of three different scenarios: 1) when there is a sense of patriotism regarding domestic manufacturers; 2) when customers have low incomes; and 3) when customers have high incomes. Finally, the study results conclude that if the domestic company has two manufacturers that produce a different type of quality can lead to an increase in the profit of the domestic company. Indeed, the proposed model can increase the competitive power of the domestic company against imported products by providing appropriate pricing on its products.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"20 1","pages":"291-323"},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86987942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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