{"title":"Erratum to: On interval-valued bilevel optimization problems using upper convexificators","authors":"S. Dempe, N. Gadhi","doi":"10.1051/ro/2023148","DOIUrl":"https://doi.org/10.1051/ro/2023148","url":null,"abstract":"Erratum to: RAIRO-Oper. Res. https://doi.org/10.1051/ro/2023044","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"10 1","pages":"2519"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139340477","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}
Let $G=(V,E)$ be a graph and the emph{deficiency of $G$} be $def(G)=sum_{v in V(G)} (Delta(G)-d_{G}(v))$, where $d_{G}(v)$ is the degree of a vertex $v$ in $G$. A vertex coloring $varphi :V(G)to {1,2,...,Delta(G)+1}$ is called emph{conformable} if the number of color classes (including empty color classes) of parity different from that of $|V(G)|$ is at most $def(G)$. A general characterization for conformable graphs is unknown. Conformability plays a key role in the total chromatic number theory. It is known that if $G$ is textit{Type~1}, then $G$ is conformable. In this paper, we prove that if $G$ is $k$-regular and textit{Class~1}, then $L(G)$ is conformable. As an application of this statement we establish that the line graph of complete graph $L(K_n)$ is conformable, which is a positive evidence towards the Vignesh et al.'s conjecture that $L(K_n)$ is textit{Type~1}.
设$G=(V,E)$是一个图，emph{$G$}emph{的}emph{不足}点是$def(G)=sum_{v in V(G)} (Delta(G)-d_{G}(v))$，其中$d_{G}(v)$是$G$中顶点$v$的度数。如果与$|V(G)|$的奇偶性不同的色类(包括空色类)的数量emph{不}超过$def(G)$，则称为顶点着色$varphi :V(G)to {1,2,...,Delta(G)+1}$。可合图的一般性质是未知的。顺应性在全色数理论中起着关键的作用。众所周知，如果$G$是textit{1型}，那么$G$是符合型的。本文证明了如果$G$是$k$ -正则且是第textit{1类}，则$L(G)$是相容的。作为这一表述的应用，我们建立了完全图$L(K_n)$的线形符合，这是对Vignesh et al.猜想$L(K_n)$是textit{Type 1}的积极证据。
{"title":"On the conformability of regular line graphs","authors":"Luerbio Faria, Mauro Nigro, Diana Sasaki","doi":"10.1051/ro/2023140","DOIUrl":"https://doi.org/10.1051/ro/2023140","url":null,"abstract":"Let $G=(V,E)$ be a graph and the emph{deficiency of $G$} be $def(G)=sum_{v in V(G)} (Delta(G)-d_{G}(v))$, where $d_{G}(v)$ is the degree of a vertex $v$ in $G$. A vertex coloring $varphi :V(G)to {1,2,...,Delta(G)+1}$ is called emph{conformable} if the number of color classes (including empty color classes) of parity different from that of $|V(G)|$ is at most $def(G)$. A general characterization for conformable graphs is unknown. Conformability plays a key role in the total chromatic number theory. It is known that if $G$ is textit{Type~1}, then $G$ is conformable. In this paper, we prove that if $G$ is $k$-regular and textit{Class~1}, then $L(G)$ is conformable. As an application of this statement we establish that the line graph of complete graph $L(K_n)$ is conformable, which is a positive evidence towards the Vignesh et al.'s conjecture that $L(K_n)$ is textit{Type~1}.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"24 1","pages":"2527-2536"},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82660340","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}
Bat Algorithm, is an evolutionary computation technique based on the echolocation behaviour of microbats while looking for their prey. It is used to perform global optimization. It was developed by Xin-She Yang in 2010. Since then, it has extensively been applied in various optimization problems because of its simple structure and robust performance. Continuous, discrete, or binary, many variants were proposed over the last few years, with applications to solve real-world cases in different fields. Yet, it has one major drawback: its premature convergence due to a lack in its exploration ability. In this paper, we introduce a selection-based improvement and three other modifications to the standard version of this metaheuristic in order to enhance the diversification and intensification capabilities of the algorithm. The newly proposed method has been then tested on 20 standard benchmark functions and the CEC2005 benchmark suit. Some non-parametric statistical tests were also used to compare the New Bat algorithm with other algorithms, and results indicate that the new method is very competitive and outperforms some of the state-of-the-art algorithms.
{"title":"A new modified bat algorithm for global optimization","authors":"N. Adil, H. Lakhbab","doi":"10.1051/ro/2023135","DOIUrl":"https://doi.org/10.1051/ro/2023135","url":null,"abstract":"Bat Algorithm, is an evolutionary computation technique based on the echolocation behaviour of microbats while looking for their prey. It is used to perform global optimization. It was developed by Xin-She Yang in 2010. Since then, it has extensively been applied in various optimization problems because of its simple structure and robust performance. Continuous, discrete, or binary, many variants were proposed over the last few years, with applications to solve real-world cases in different fields. Yet, it has one major drawback: its premature convergence due to a lack in its exploration ability.\u0000In this paper, we introduce a selection-based improvement and three other modifications to the standard version of this metaheuristic in order to enhance the diversification and intensification capabilities of the algorithm. The newly proposed method has been then tested on 20 standard benchmark functions and the CEC2005 benchmark suit. Some non-parametric statistical tests were also used to compare the New Bat algorithm with other algorithms, and results indicate that the new method is very competitive and outperforms some of the state-of-the-art algorithms.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"24 1","pages":"2659-2685"},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86451804","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}
Feng Lin, Weiqing Lin, Jinzhao Shi, Peng Wu, Weiyi Hong
Although upstream manufacturers with small- and mediumsized are gradually willing to invest green efforts for stimulating market demand, they have been encountering the challenge of securing sufficient working capital to develop the green supply chain. Thus, this paper systematically incorporates two types of prepayment policies including risk-free (RF) and risk-taking (RT) into a retailer’s dominated channel. Via deriving operational and financing equilibrium of the green supply chain, a series of interesting findings can be offered. Specifically, (1) this paper identifies a threshold value regarding the manufacturer’s own capital, and proposes two scenarios for assisting the retailer to decide whether offers the manufacturer prepayment policy. (2) The effectiveness of RF for the capital-constrained manufacturer depends on how well its green effort can be implemented. That is, provided that the quality effect is large enough, the manufacturer can get more upfront capital from the retailer, which may entirely cover its total production and green effort costs. (3) Under RT, if the manufacturer’s capital is relatively lower, RT enables the manufacturer to obtain sufficient capital and the retailer is willing to share partial of the manufacturer’s default risk. Otherwise, RT may not be the best prepayment policy for the retailer.
{"title":"Effects of prepayment policy on equilibrium of the retailer-dominated channel considering manufacturer effort","authors":"Feng Lin, Weiqing Lin, Jinzhao Shi, Peng Wu, Weiyi Hong","doi":"10.1051/ro/2023128","DOIUrl":"https://doi.org/10.1051/ro/2023128","url":null,"abstract":"Although upstream manufacturers with small- and mediumsized are gradually willing to invest green efforts for stimulating market demand, they have been encountering the challenge of securing sufficient working capital to develop the green supply chain. Thus, this paper systematically incorporates two types of prepayment policies including risk-free (RF) and risk-taking (RT) into a retailer’s dominated channel. Via deriving operational and financing equilibrium of the green supply chain, a series of interesting findings can be offered. Specifically, (1) this paper identifies a threshold value regarding the manufacturer’s own capital, and proposes two scenarios for assisting the retailer to decide whether offers the manufacturer prepayment policy. (2) The effectiveness of RF for the capital-constrained manufacturer depends on how well its green effort can be implemented. That is, provided that the quality effect is large enough, the manufacturer can get more upfront capital from the retailer, which may entirely cover its total production and green effort costs. (3) Under RT, if the manufacturer’s capital is relatively lower, RT enables the manufacturer to obtain sufficient capital and the retailer is willing to share partial of the manufacturer’s default risk. Otherwise, RT may not be the best prepayment policy for the retailer.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"57 1","pages":"2601-2618"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79227975","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}
Food waste and proper methods to deal with it are one of the main challenges of supply chain network management. The majority of studies on how to use mathematical models in the supply chain have focused on goods that are at their peak of freshness as soon as they are produced and deteriorate over time. While some products experience an increase in value at the start of their life cycle, this value eventually reaches its maximum level, and after this point, these products experience a decline in value before being eliminated from the consumption cycle. The objective of this study is to develop a comprehensive inventory-routing model suitable for supply chain networks where products exhibit an increase and decrease in value over time. By considering the randomness and dynamic uncertainty of market demands and the fact that each period has effects on the next period, The proposed model employs a multi-stage stochastic programming (MSSP) approach. By doing so, the model ensures a balanced flow between different components of the network while considering non-deterministic demand under various scenarios that are shown in a tree of scenarios. The utilization of MSSP leads to more reliable solutions compared to deterministic models, making it possible for chain stores to make well-informed decisions in their inventory management and distribution strategies. Ultimately, this approach results in cost savings for chain stores handling such products. This research makes a significant contribution to the existing literature by demonstrating the effectiveness of the proposed model on actual data and highlighting the benefits of using stochastic programming in supply chain optimization.
{"title":"A multi-stage stochastic programming approach for an inventory-routing problem considering life cycle","authors":"Alireza Paeizi, Ahmad Makui, M. Pishvaee","doi":"10.1051/ro/2023122","DOIUrl":"https://doi.org/10.1051/ro/2023122","url":null,"abstract":"Food waste and proper methods to deal with it are one of the main challenges of supply chain network management. The majority of studies on how to use mathematical models in the supply chain have focused on goods that are at their peak of freshness as soon as they are produced and deteriorate over time. While some products experience an increase in value at the start of their life cycle, this value eventually reaches its maximum level, and after this point, these products experience a decline in value before being eliminated from the consumption cycle. The objective of this study is to develop a comprehensive inventory-routing model suitable for supply chain networks where products exhibit an increase and decrease in value over time. By considering the randomness and dynamic uncertainty of market demands and the fact that each period has effects on the next period, The proposed model employs a multi-stage stochastic programming (MSSP) approach. By doing so, the model ensures a balanced flow between different components of the network while considering non-deterministic demand under various scenarios that are shown in a tree of scenarios. The utilization of MSSP leads to more reliable solutions compared to deterministic models, making it possible for chain stores to make well-informed decisions in their inventory management and distribution strategies. Ultimately, this approach results in cost savings for chain stores handling such products. This research makes a significant contribution to the existing literature by demonstrating the effectiveness of the proposed model on actual data and highlighting the benefits of using stochastic programming in supply chain optimization.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"68 1","pages":"2537-2559"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76030644","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}
We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t)=t 7/4 . Furthermore, we show that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.
{"title":"Interior-point algorithm for linear programming based on a new descent direction","authors":"Zaoui Billel, Benterki Djamel, Kraria Aicha, Raouache Hadjer","doi":"10.1051/ro/2023127","DOIUrl":"https://doi.org/10.1051/ro/2023127","url":null,"abstract":"We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of\u0000transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t)=t 7/4 . Furthermore, we show that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"38 1","pages":"2473-2491"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78733828","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}
Shashi Kant Mishra, Sanjeeva Kumar Singh, Mohd Hassan
In this article, we study several characterizations of solution sets of LU-quasiconvex interval-valued function. Firstly, we provide Gordan’s theorem of the alternative of interval-valued linear system. As a consequence of this theorem, we find the normalized gradient of the interval-valued function is constant over the solution set when its gradient is not zero. Further, we discuss Lagrange multiplier characterizations of solution sets of LU-quasiconvex interval-valued function and provide optimality conditions of interval-valued optimization problem under the generalized Mangasarian-Fromovitz constraint qualifications. We provide illustrative examples in the support of our theory.
{"title":"On characterizations of solution sets of interval-valued quasiconvex programming problems","authors":"Shashi Kant Mishra, Sanjeeva Kumar Singh, Mohd Hassan","doi":"10.1051/ro/2023124","DOIUrl":"https://doi.org/10.1051/ro/2023124","url":null,"abstract":"In this article, we study several characterizations of solution sets of LU-quasiconvex interval-valued function. Firstly, we provide Gordan’s theorem of the alternative of interval-valued linear system. As a consequence of this theorem, we find the normalized gradient of the interval-valued function is constant over the solution set when its gradient is not zero. Further, we discuss Lagrange multiplier characterizations of solution sets of LU-quasiconvex interval-valued function and provide optimality conditions of interval-valued optimization problem under the generalized Mangasarian-Fromovitz constraint qualifications. We provide illustrative examples in the support of our theory.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"6 1","pages":"2585-2600"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78169376","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}
M. Palma, Isabel Gonçalves, D. Sasaki, Simone Dantas
We show that all members of the SemiBlowup, Blowup and the first Loupekine snark families have equitable total chromatic number equal to 4. These results provide evidence of negative answers for the questions proposed: by Cavicchioli et al. (2003) about the smallest order of a Type 2 snark of girth at least 5; and by Dantas et al. (2016) about the existence of Type 1 cubic graph with girth at least 5 and equitable total chromatic number 5. Moreover, we show new infinite families of snarks obtained by the Kochol superpositions that are Type 1.
{"title":"On total coloring and equitable total coloring of infinite snark families","authors":"M. Palma, Isabel Gonçalves, D. Sasaki, Simone Dantas","doi":"10.1051/ro/2023129","DOIUrl":"https://doi.org/10.1051/ro/2023129","url":null,"abstract":"We show that all members of the SemiBlowup, Blowup and the first Loupekine snark families have equitable total chromatic number equal to 4. These results provide evidence of negative answers for the questions proposed: by Cavicchioli et al. (2003) about the smallest order of a Type 2 snark of girth at least 5; and by Dantas et al. (2016) about the existence of Type 1 cubic graph with girth at least 5 and equitable total chromatic number 5. Moreover, we show new infinite families of snarks obtained by the Kochol superpositions that are Type 1.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"227 1","pages":"2619-2637"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79476071","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}
K. Haghparast, J. Amjadi, M. Chellali, S. M. Sheikholeslami
A restrained ${2}$-dominating function (R${2}$-DF) on a graph $G=(V,E)$ is a function $f:Vrightarrow{0,1,2}$ such that : textrm{(i)} $f(N[v])geq2$ for all $vin V,$ where $N[v]$ is the set containing $v$ and all vertices adjacent to $v;$ textrm{(ii)} the subgraph induced by the vertices assigned 0 under $f$ has no isolated vertices. The weight of an R${2}$-DF is the sum of its function values over all vertices, and the restrained ${2}$-domination number $gamma_{r{2}}(G)$ is the minimum weight of an R${2}$-DF on $G.$ In this paper, we initiate the study of the restrained ${2}$-domination number. We first prove that the problem of computing this parameter is NP-complete, even when restricted to bipartite graphs. Then we give various bounds on this parameter. In particular, we establish upper and lower bound on the restrained ${2}$-domination number of a tree $T$ in terms of the order, the numbers of leaves and support vertices.
{"title":"Restrained {2}-domination in graphs","authors":"K. Haghparast, J. Amjadi, M. Chellali, S. M. Sheikholeslami","doi":"10.1051/ro/2023120","DOIUrl":"https://doi.org/10.1051/ro/2023120","url":null,"abstract":"A restrained ${2}$-dominating function (R${2}$-DF) on a graph $G=(V,E)$ is\u0000a function $f:Vrightarrow{0,1,2}$ such that : textrm{(i)} $f(N[v])geq2$\u0000for all $vin V,$ where $N[v]$ is the set containing $v$ and all vertices\u0000adjacent to $v;$ textrm{(ii)} the subgraph induced by the vertices assigned 0\u0000under $f$ has no isolated vertices. The weight of an R${2}$-DF is the sum of\u0000its function values over all vertices, and the restrained ${2}$-domination\u0000number $gamma_{r{2}}(G)$ is the minimum weight of an R${2}$-DF on $G.$ In\u0000this paper, we initiate the study of the restrained ${2}$-domination number.\u0000We first prove that the problem of computing this parameter is NP-complete,\u0000even when restricted to bipartite graphs. Then we give various\u0000bounds on this parameter. In particular, we establish upper and\u0000lower bound on the restrained ${2}$-domination number of a tree $T$ in terms\u0000of the order, the numbers of leaves and support vertices.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"66 1","pages":"2393-2410"},"PeriodicalIF":0.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89282600","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}
Currently, sustainability is of widespread concern among consumers and branders, compelling an increasing number of suppliers to invest in sustainable practices. This paper establishes a supply chain model comprising a supplier with private investment efficiency and a brander. By employing signaling and reverse selection theories, the equilibrium strategies of the supplier and the brander are explored. Additionally, the impact of investment efficiency and the probability of H-type on the brander’s information strategy and optimal cooperation mode are analyzed. Our analyses reveal that concealing private information may not be beneficial to the supplier under the quotation mode. Moreover, when the probability of H-type is low, the supplier prefers to signal its exact type to the brander. Under the bidding mode, the brander may benefit more from not obtaining the exact supplier type. When the efficiency difference is higher and the probability of H-type is smaller, the brander indicates a preference for the quotation mode and is more willing to await a signal from the supplier. Furthermore, different information structures yield different optimal cooperation modes for the brander.
{"title":"Optimal cooperation modes and information strategies under asymmetric sustainable investment efficiency","authors":"Jianheng Zhou, Yiting Shen, Hong Li, Xingli Chen","doi":"10.1051/ro/2023119","DOIUrl":"https://doi.org/10.1051/ro/2023119","url":null,"abstract":"Currently, sustainability is of widespread concern among consumers and branders, compelling an increasing number of suppliers to invest in sustainable practices. This paper establishes a supply chain model comprising a supplier with private investment efficiency and a brander. By employing signaling and reverse selection theories, the equilibrium strategies of the supplier and the brander are explored. Additionally, the impact of investment efficiency and the probability of H-type on the brander’s information strategy and optimal cooperation mode are analyzed. Our analyses reveal that concealing private information may not be beneficial to the supplier under the quotation mode. Moreover, when the probability of H-type is low, the supplier prefers to signal its exact type to the brander. Under the bidding mode, the brander may benefit more from not obtaining the exact supplier type. When the efficiency difference is higher and the probability of H-type is smaller, the brander indicates a preference for the quotation mode and is more willing to await a signal from the supplier. Furthermore, different information structures yield different optimal cooperation modes for the brander.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":"39 1","pages":"2411-2434"},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76720154","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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