Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is...Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.展开更多
The continuous growth in energy demand,shortage of fossil fuels,and global climate change have raised significant attention towards renewable energy.In this paper,firstly,a three-echelon biomass-to-bioenergy supply ch...The continuous growth in energy demand,shortage of fossil fuels,and global climate change have raised significant attention towards renewable energy.In this paper,firstly,a three-echelon biomass-to-bioenergy supply chain composed of a farmer,collection station and power generation enterprise is developed.Secondly,the optimal decisions for four scenarios are investigated,namely,a decentralized decision-making model,a collaborative decision-making model between the farmer and the collection station,a collaborative decision-making model between the collection station and the power generation enterprise,and a centralized decision-making model.Thirdly,the average tree solution method of cooperative game theory is used to allocate the supply chain profits.Finally,numerical analysis is conducted by taking one biomass energy company as an example to support the results.Our research finds that:1)In a centralized decision-making scenario,the individual and overall revenues are maximized.2)For the collection station,allying with the power generation enterprise is more beneficial than allying with the farmer.3)For the power generation enterprise,forming an alliance with the collection station is greater than decision-making independently.展开更多
基金This work was partially supported by the Okawa Foundation for Information and TelecommunicationWe wish to thank the two anonymous reviewers for their constructive suggestions and comments.The comments have helped us significantly improve the paper.
文摘Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.
基金Supported by National Social Science Fund of China(22BGL111)。
文摘The continuous growth in energy demand,shortage of fossil fuels,and global climate change have raised significant attention towards renewable energy.In this paper,firstly,a three-echelon biomass-to-bioenergy supply chain composed of a farmer,collection station and power generation enterprise is developed.Secondly,the optimal decisions for four scenarios are investigated,namely,a decentralized decision-making model,a collaborative decision-making model between the farmer and the collection station,a collaborative decision-making model between the collection station and the power generation enterprise,and a centralized decision-making model.Thirdly,the average tree solution method of cooperative game theory is used to allocate the supply chain profits.Finally,numerical analysis is conducted by taking one biomass energy company as an example to support the results.Our research finds that:1)In a centralized decision-making scenario,the individual and overall revenues are maximized.2)For the collection station,allying with the power generation enterprise is more beneficial than allying with the farmer.3)For the power generation enterprise,forming an alliance with the collection station is greater than decision-making independently.
