In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient...In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.展开更多
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl...A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.展开更多
In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single...In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.展开更多
The objective of the present study is to develop the irrigation planning model and to apply the same in the form of Two-Phase Multi Objective Fuzzy Linear Programming (TPMOFLP) approach for crop planning in command ar...The objective of the present study is to develop the irrigation planning model and to apply the same in the form of Two-Phase Multi Objective Fuzzy Linear Programming (TPMOFLP) approach for crop planning in command area of Jayakwadi Project Stage I, Maharashtra State, India. The development of TPMOFLP model is on the basis of various Linear Programming (LP) models and Multi Objective Fuzzy Linear Programming (MOFLP) models, these models have been applied for maximization of the Net Benefits (NB), Crop production (CP), Employment Generation (EG) and Manure Utilization (MU) respectively. The significant increase in the value of level of satisfaction (λ) has been found from 0.58 to 0.65 by using the TPMOFLP approach as compare to that of MOFLP model based on maxmin approach. The two-phase approach solution provides NB = 1503.56 Million Rupees, CP = 335729.30 Tons, EG = 29.74 Million Man days and MU = 160233.70 Tons respectively. The proposed model will be helpful for the Decision Maker (DM) to take a decision under conflicting situation while planning for different conflicting objectives simultaneously and has potential to find out an integrated irrigation planning with prime consideration for economic, social and environmental issue.展开更多
In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution o...In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.展开更多
This paper proposes an extractive generic text summarization model that generates summaries by selecting sentences according to their scores. Sentence scores are calculated using their extensive coverage of the main c...This paper proposes an extractive generic text summarization model that generates summaries by selecting sentences according to their scores. Sentence scores are calculated using their extensive coverage of the main content of the text, and summaries are created by extracting the highest scored sentences from the original document. The model formalized as a multiobjective integer programming problem. An advantage of this model is that it can cover the main content of source (s) and provide less redundancy in the generated sum- maries. To extract sentences which form a summary with an extensive coverage of the main content of the text and less redundancy, have been used the similarity of sentences to the original document and the similarity between sentences. Performance evaluation is conducted by comparing summarization outputs with manual summaries of DUC2004 dataset. Experiments showed that the proposed approach outperforms the related methods.展开更多
Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river...Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.展开更多
The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear progr...The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.展开更多
In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on ...In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on as the background of this research. They deal with the common quantities of their products, but due to their different environments, the optimal production quantity of one part can be unacceptable to another part and it may suffer a heavy loss. To avoid that kind of unacceptable situations, the common production quantities should be acceptable to all parts in one supply chain. Therefore, the motivation of this research is the necessity of the method to find the production quantities that make all decision makers acceptable is needed. However, it is difficult to find the production quantities that make all decision makers acceptable. Moreover, their acceptable ranges do not always have common ranges. In the decision making of car design, there are similar situations to this type of decision making. The performance of a car consists of purposes such as fuel efficiency, size and so on. Improving one purpose makes another worse and the relationship between these purposes is tradeoff. In these cases, Suriawase process is applied. This process consists of negotiations and reviews of the requirements of the purposes. In the step of negotiations, the requirements of the purposes are share among all decision makers and the solution that makes them as satisfied as possible. In the step of reviews of the requirements, they are reviewed based on the result of the negotiation if the result is unacceptable to some of decision makers. Therefore, through the iterations of the two steps, the solution that makes all decision makers satisfied is obtained. However, in the previous research, the effects that one decision maker reviews requirements in Suriawase process are quantified, but the mathematical model to modify the ranges of production quantities of all decision makers simultaneously is not shown. Therefore, in this research, based on Suriawase process, the mathematical model of multi-player multi-objective decision making is proposed. The mathematical model of multi-player multi-objective decision making by using linear physical programming (LPP) and robust optimization (RO) in the previous research is the basis of the methods of this research. LPP is one of the multi-objective optimization methods and RO is used to make the balance of the preference levels among decision makers. In LPP, the preference ranges of all objective functions are needed, so as the hypothesis of this research. In the research referred in this research, the method to control the effect of RO is not shown. If the effect of RO is too big, the average of the preference level becomes worse. The purpose of this research is to reproduce the mathematical model of multi-player multi-objective decision making based on Suriawase process and propose the method to control the effect of RO. In the proposed model, a set of the solutions of the negotiation problem is obtained and it is proved by the result of the numerical experiment. Therefore, the conclusion that the proposed model is available to obtain a set of the solutions of the negotiation problems in supply chain.展开更多
This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for...This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.展开更多
该文提出一种考虑故障后多阶段恢复的智能软开关(soft open point,SOP)柔性互联配电网(flexible interconnected distribution network,FIDN)可靠性评估方法,其特征在于将基于SOP的FIDN网络拓扑状态通过优化过程的决策变量显式表达,建...该文提出一种考虑故障后多阶段恢复的智能软开关(soft open point,SOP)柔性互联配电网(flexible interconnected distribution network,FIDN)可靠性评估方法,其特征在于将基于SOP的FIDN网络拓扑状态通过优化过程的决策变量显式表达,建立面向FIDN可靠性评估的混合整数线性规划模型,从而实现FIDN可靠性评估。首先,分析FIDN多阶段恢复过程,提出一种多阶段恢复过程解耦建模的FIDN可靠性评估框架;然后,基于SOP正常运行和不同故障下的外特性,建立面向可靠性评估的SOP等效模型,构建FIDN节点-支路状态关联模型以实现网络拓扑状态显式化;之后,考虑SOP转供功率约束及短时过载能力,建立不同策略下的SOP快速转供模型;在此基础上,考虑SOP快速转供、故障点上游恢复、联络开关切换转供、孤岛运行等多阶段恢复过程,建立面向FIDN可靠性评估的混合整数线性规划模型;最后,在改进的37节点系统上验证所提方法的有效性。展开更多
It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria...It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria is incomplete certain. A new multiple criteria decision- making method with incomplete certain information based on ternary AHP is proposed. This improves on Takeda＇s method. In this method, the ternary comparison matrix of the alternatives under each pseudo-criteria is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained as to normalize priority vector of the alternatives, then the order of alternatives is obtained by solving two kinds of linear programming problems. Finally, an example is given to show the feasibility and effectiveness of the method.展开更多
In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and M...In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and Manure Utilization (MU) under conflicting situation and also, for maximization of Releases for Irrigation (RI) and Releases for Power (RP) simultaneously under uncertainty by considering the fuzziness in the objective functions. The developed models have been applied using the LINGO 13 (Language for Interactive General Optimization) optimization software to the case study of the Jayakwadi Project Stage-II across Sindhphana River, in the State of Maharashtra India. The various constraints have been taken into consideration like sowing area, affinity to crop, labour availability, manure availability, water availability for optimal cropping pattern planning. Similarly constraints to find the optimal reservoir operating policy are releases for power and turbine capacity, irrigation demand, reservoir storage capacity, reservoir storage continuity. The level of satisfaction for a compromised solution of optimal cropping pattern planning for four conflicting objectives under fuzzy environment is worked out to be λ = 0.68. The MOFLP compromised solution provides NB = 1088.46 (Million Rupees), CP = 241003 (Tons), EG = 23.13 (Million Man days) and MU = 111454.70 (Tons) respectively. The compromised solution for optimal operation of multi objective reservoir yields the level of satisfaction (λ) = 0.533 for maximizing the releases for irrigation and power simultaneously by satisfying the constraint of the system under consideration. The compromised solution provides the optimal releases, i.e. RI = 348.670 Mm3 and RP = 234.285 Mm3 respectively.展开更多
文摘In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.
文摘A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
文摘In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.
文摘The objective of the present study is to develop the irrigation planning model and to apply the same in the form of Two-Phase Multi Objective Fuzzy Linear Programming (TPMOFLP) approach for crop planning in command area of Jayakwadi Project Stage I, Maharashtra State, India. The development of TPMOFLP model is on the basis of various Linear Programming (LP) models and Multi Objective Fuzzy Linear Programming (MOFLP) models, these models have been applied for maximization of the Net Benefits (NB), Crop production (CP), Employment Generation (EG) and Manure Utilization (MU) respectively. The significant increase in the value of level of satisfaction (λ) has been found from 0.58 to 0.65 by using the TPMOFLP approach as compare to that of MOFLP model based on maxmin approach. The two-phase approach solution provides NB = 1503.56 Million Rupees, CP = 335729.30 Tons, EG = 29.74 Million Man days and MU = 160233.70 Tons respectively. The proposed model will be helpful for the Decision Maker (DM) to take a decision under conflicting situation while planning for different conflicting objectives simultaneously and has potential to find out an integrated irrigation planning with prime consideration for economic, social and environmental issue.
文摘In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.
文摘This paper proposes an extractive generic text summarization model that generates summaries by selecting sentences according to their scores. Sentence scores are calculated using their extensive coverage of the main content of the text, and summaries are created by extracting the highest scored sentences from the original document. The model formalized as a multiobjective integer programming problem. An advantage of this model is that it can cover the main content of source (s) and provide less redundancy in the generated sum- maries. To extract sentences which form a summary with an extensive coverage of the main content of the text and less redundancy, have been used the similarity of sentences to the original document and the similarity between sentences. Performance evaluation is conducted by comparing summarization outputs with manual summaries of DUC2004 dataset. Experiments showed that the proposed approach outperforms the related methods.
文摘Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.
文摘The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.
文摘In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on as the background of this research. They deal with the common quantities of their products, but due to their different environments, the optimal production quantity of one part can be unacceptable to another part and it may suffer a heavy loss. To avoid that kind of unacceptable situations, the common production quantities should be acceptable to all parts in one supply chain. Therefore, the motivation of this research is the necessity of the method to find the production quantities that make all decision makers acceptable is needed. However, it is difficult to find the production quantities that make all decision makers acceptable. Moreover, their acceptable ranges do not always have common ranges. In the decision making of car design, there are similar situations to this type of decision making. The performance of a car consists of purposes such as fuel efficiency, size and so on. Improving one purpose makes another worse and the relationship between these purposes is tradeoff. In these cases, Suriawase process is applied. This process consists of negotiations and reviews of the requirements of the purposes. In the step of negotiations, the requirements of the purposes are share among all decision makers and the solution that makes them as satisfied as possible. In the step of reviews of the requirements, they are reviewed based on the result of the negotiation if the result is unacceptable to some of decision makers. Therefore, through the iterations of the two steps, the solution that makes all decision makers satisfied is obtained. However, in the previous research, the effects that one decision maker reviews requirements in Suriawase process are quantified, but the mathematical model to modify the ranges of production quantities of all decision makers simultaneously is not shown. Therefore, in this research, based on Suriawase process, the mathematical model of multi-player multi-objective decision making is proposed. The mathematical model of multi-player multi-objective decision making by using linear physical programming (LPP) and robust optimization (RO) in the previous research is the basis of the methods of this research. LPP is one of the multi-objective optimization methods and RO is used to make the balance of the preference levels among decision makers. In LPP, the preference ranges of all objective functions are needed, so as the hypothesis of this research. In the research referred in this research, the method to control the effect of RO is not shown. If the effect of RO is too big, the average of the preference level becomes worse. The purpose of this research is to reproduce the mathematical model of multi-player multi-objective decision making based on Suriawase process and propose the method to control the effect of RO. In the proposed model, a set of the solutions of the negotiation problem is obtained and it is proved by the result of the numerical experiment. Therefore, the conclusion that the proposed model is available to obtain a set of the solutions of the negotiation problems in supply chain.
文摘This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.
文摘该文提出一种考虑故障后多阶段恢复的智能软开关(soft open point,SOP)柔性互联配电网(flexible interconnected distribution network,FIDN)可靠性评估方法,其特征在于将基于SOP的FIDN网络拓扑状态通过优化过程的决策变量显式表达,建立面向FIDN可靠性评估的混合整数线性规划模型,从而实现FIDN可靠性评估。首先,分析FIDN多阶段恢复过程,提出一种多阶段恢复过程解耦建模的FIDN可靠性评估框架;然后,基于SOP正常运行和不同故障下的外特性,建立面向可靠性评估的SOP等效模型,构建FIDN节点-支路状态关联模型以实现网络拓扑状态显式化;之后,考虑SOP转供功率约束及短时过载能力,建立不同策略下的SOP快速转供模型;在此基础上,考虑SOP快速转供、故障点上游恢复、联络开关切换转供、孤岛运行等多阶段恢复过程,建立面向FIDN可靠性评估的混合整数线性规划模型;最后,在改进的37节点系统上验证所提方法的有效性。
文摘It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria is incomplete certain. A new multiple criteria decision- making method with incomplete certain information based on ternary AHP is proposed. This improves on Takeda＇s method. In this method, the ternary comparison matrix of the alternatives under each pseudo-criteria is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained as to normalize priority vector of the alternatives, then the order of alternatives is obtained by solving two kinds of linear programming problems. Finally, an example is given to show the feasibility and effectiveness of the method.
文摘In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and Manure Utilization (MU) under conflicting situation and also, for maximization of Releases for Irrigation (RI) and Releases for Power (RP) simultaneously under uncertainty by considering the fuzziness in the objective functions. The developed models have been applied using the LINGO 13 (Language for Interactive General Optimization) optimization software to the case study of the Jayakwadi Project Stage-II across Sindhphana River, in the State of Maharashtra India. The various constraints have been taken into consideration like sowing area, affinity to crop, labour availability, manure availability, water availability for optimal cropping pattern planning. Similarly constraints to find the optimal reservoir operating policy are releases for power and turbine capacity, irrigation demand, reservoir storage capacity, reservoir storage continuity. The level of satisfaction for a compromised solution of optimal cropping pattern planning for four conflicting objectives under fuzzy environment is worked out to be λ = 0.68. The MOFLP compromised solution provides NB = 1088.46 (Million Rupees), CP = 241003 (Tons), EG = 23.13 (Million Man days) and MU = 111454.70 (Tons) respectively. The compromised solution for optimal operation of multi objective reservoir yields the level of satisfaction (λ) = 0.533 for maximizing the releases for irrigation and power simultaneously by satisfying the constraint of the system under consideration. The compromised solution provides the optimal releases, i.e. RI = 348.670 Mm3 and RP = 234.285 Mm3 respectively.
