Vector Minimum Problem Research Articles

A Fuzzy Goal Programming Approach to Multiobjective Transportation Problems

The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal programming is suggested. Different solutions are obtained according to the priorities of the decision maker in the proposed model. With respect to its properties, at least a weakly efficient solution is yielded by solving the new model. To demonstrate the validity and strengths of the suggested model, some numerical examples are given. Further, a comparison is made with different existing methods.

FUZZY GOAL PROGRAMMING TECHNIQUE TO SOLVE MULTIOBJECTIVE TRANSPORTATION PROBLEMS WITH SOME NON-LINEAR MEMBERSHIP FUNCTIONS

The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to solve multiobjective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.

English

In a transportation problem generally a single criterion of minimizing the total transportation cost is considered but in certain practical situations two or more objectives are relevant. For example, the objectives may be minimization of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques, but the computational efforts needed would be prohibitive in many cases. In this paper, The Bi-objective transportation problem, where only objectives are considered as fuzzy. We apply the fuzzy programming technique with hyperbolic membership function to solve a biobjective transportation problem as vector minimum problem.

Regularity Conditions in Vector Optimization

By exploiting very recent results concerning linear separation between a set and a convex cone, the image space approach allows us to achieve new regularity conditions for vector minimum problems. In particular, we obtain very general Mangasarian–Fromovitz type conditions.

Fuzzy programming approach to multiobjective solid transportation problem

The linear multiobjective solid transportation problem is a special type of vector minimum problem in which constraints are all equally type and the objectives are conflicting in nature. A generalization of the linear multiobjective solid transportation problem, in which the supply, demand, and capacity constraints are not only of equality type but also of inequality type, is considered. This paper presents an application of fuzzy linear programming to the linear multiobjective solid transportation problem. It gives efficient solutions as well as an optimal compromise. For this method, a Fortran program has been developed based on the fuzzy linear programming algorithm. This method is compared with some existing algorithms using numerical example.

Fuzzy programming technique to solve multi-objective geometric programming problems

Abstract In this paper fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programming problem. Two numerical examples are presented to illustrate the method.

Proper Efficiency in Convex Vector Minimum Problems

Abstract A nonlinear vector minimum problem (NVMP) is considered, Kuhn-Tucker type conditions are derived which are necessary for an efficient solution and sufficient for a properly efficient solution. These results imply that under a constraint qualification every efficient solution of a convex vector minimum problem is properly efficient. Moreover, Fritz John type necessary and sufficient conditions for an efficient solution of (NVMP) are also obtained and an example is discussed to illustrate the results.

Fuzzy programming approach to multicriteria decision making transportation problem

Abstract The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conflicting in nature. All existing methods generate a set of nondominated solutions or construct a single compromise solution. This paper presents an application of fuzzy linear programming to the linear multiobjective transportation problem. It gives efficient solutions as well as an optimal compromise solution. For this method, an efficient Fortran program has been developed based on the fuzzy linear programming algorithm, which is an extended version of the simplex algorithm. This method is compared with two existing interactive algorithms using two numerical examples.

Duality in nonconvex vector minimum problems

A nonlinear vector minimum problem is considered. Duality theorems are proved for Mond-Weir type dual and their application to a certain nonlinear fractional vector minimum problem is discussed.

Effiziente, optimale effiziente wege in graphen and diskret-differentielle prozesse mit vektorwertigem funktional

At first discrete-differential processes are reduced to “shortest-path-problems” in graphs without approximation. For vector minimum problems, especially shortest-path-problems with vector-valued lengths of arcs, the notion of an optimal-efficient solution,. of an optimal-efficient path resp. with regard to a real-valued valuation is introduced. To compute an optimal-efficient path, analog of the algorithms of Bellman, Ford, Floyd and Dantzing for vector-valued lengths of arcs and generalized measures of paths are given.

The optimal flow-pattern of multiple effect evaporator systems

The optimization of the flow-pattern for a multiple effect evaporator system is discussed as a vector minimum problem. First a new program to solve the design problem for various flow-patterns with no stream mixing or splitting and an arbitrary number of effects is described. Second the set of noninferior flow-patterns is generated by enumerating one-by-one for all flow-patterns. This method works well in synthesizing multiple effect evaporator configuration.