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
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
This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time...This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.展开更多
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.展开更多
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors estab...This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar Lagrange function for SIMFP.Further,the authors study saddle point criteria of a vector Lagrange function defined for SIMFP.展开更多
This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex func...This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.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This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.
文摘A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
文摘In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
基金supported by the Council of Scientific and Industrial Research(CSIR),New Delhi,India under Grant No.09/013(0474)/2012-EMR-1
文摘This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar Lagrange function for SIMFP.Further,the authors study saddle point criteria of a vector Lagrange function defined for SIMFP.
基金supported by Natural Science Foundation of China(Nos.11861002 and 12171601)the Key Project of North Minzu University(No.ZDZX201804)+1 种基金the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu Universit(No.YCX21157)..
文摘This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.
