Efficient solution generation for multiple objective linear programming based on extreme ray generation method

Ida, Masaaki

doi:10.1016/j.ejor.2003.08.039

Cited by 19 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Discrete representation of the efficient solutions set were given in these papers. Also, there are many approaches that just obtaining efficient extreme points and efficient extreme rays, see, for instance [4,8,11] and references therein [20]. As approach developed by Yan et al in [20], the approach proposed in this paper avoids the degeneration problem.…”

Section: Introductionmentioning

confidence: 83%

Determining maximal efficient faces in multiobjective linear programming problem

Pourkarimi

Yaghoobi

Mashinchi

2009

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Keywords:Multiobjective linear programming Maximal efficient face Minimal index set Efficiency Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly.

show abstract

Section: Introductionmentioning

confidence: 83%

Determining maximal efficient faces in multiobjective linear programming problem

Pourkarimi

Yaghoobi

Mashinchi

2009

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Although the structure of this algorithm is similar to the previous one because it uses a branch and bound method, the efficiency tests do not require solving linear programming problems. Ida (2000aIda ( ,b, 2005 also suggested a solution generation procedure based on the extreme ray generation method that sequentially generates efficient points and rays by adding inequality constraints to the polyhedral feasible region.…”

Section: Necessarily Efficiency Solutions: Methods and Extensionsmentioning

confidence: 98%

“…Bitran, 1980;Ida, 1999Ida, , 2000aIda, ,b, 2005Inuiguchi and Sakawa, 1996;Steuer, 1981;Wang and Wang, 2001a,b). Bitran (1980) suggested, in this context, two kinds of efficient solutions to the interval MOLP: a solution is called ''necessarily efficient'' if it is efficient for any given objective function coefficient vectors within their admissible range of variation (Fig.…”

Section: Introductionmentioning

confidence: 95%

Multiple objective linear programming models with interval coefficients – an illustrated overview

Oliveira

Antunes

2007

European Journal of Operational Research

154

View full text Add to dashboard Cite

“…In the literature, a variety of algorithms [ 6,2,15,14,7,11,13,4,9,8,3,12] for finding efficient solutions to multi-objective optimization problems have been proposed. For getting good solution from a set of efficient solutions, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution.…”

Section: Introductionmentioning

confidence: 99%

Determining efficient solutions to multiple objective linear programming problems

Pandian¹,

Jayalakshmi²

2013

ams

View full text Add to dashboard Cite

A new posteriori method namely, moving optimal method is proposed for solving multiple objective linear programming problems. It provides efficient solution line segments to the problem with the percentage level of satisfaction of each of the objective at each point on it which is very much useful to decision makers for choosing an efficient solution according to their level of satisfaction on the objective functions. Illustrative example is presented to clarify the idea of the proposed approach.Mathematics Subject Classification : 90B06, 9050, 90C05, 90C29

show abstract

Efficient solution generation for multiple objective linear programming based on extreme ray generation method

Cited by 19 publications

References 11 publications

Determining maximal efficient faces in multiobjective linear programming problem

Determining maximal efficient faces in multiobjective linear programming problem

Multiple objective linear programming models with interval coefficients – an illustrated overview

Determining efficient solutions to multiple objective linear programming problems

Contact Info

Product

Resources

About