Multi-objective interval fractional programming problems : An approach for obtaining efficient solutions

Bhurjee, Ajay Kumar; Panda, Geetanjali

doi:10.1007/s12597-014-0175-4

Cited by 25 publications

(11 citation statements)

References 12 publications

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“…We also note that x = 1 is a feasible solution to (IVP3) and corresponding objective value is [5,27].…”

Section: Wolfe-type Dualitymentioning

confidence: 99%

“…Zhou and Wang [29] discussed mixed type duality for a class of nonlinear interval-valued optimization problem. Recently, by using the parametric form of interval-valued functions, Bhurjee and Panda [4] derived the relations between the primal and dual problems and in [5], a methodology had developed to influence its efficient solutions for multi-objective fractional programming problem whose parameters are considered as intervals.…”

Section: Introductionmentioning

confidence: 99%

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Optimality conditions and duality for interval-valued optimization problems using convexifactors

Jayswal

Stancu-Minasian

Banerjee

2015

Rend. Circ. Mat. Palermo

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This paper is devoted to the applications of convexifactors on interval-valued programming problem. Based on the concept of LU optimal solution, sufficient optimality conditions are established under generalized ∂ * -convexity assumptions. Furthermore, appropriate duality theorems are derived for two types of dual problem, namely Mond-Weir and Wolfe type duals. We also construct examples to manifest the established relations.

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“…We also note that x = 1 is a feasible solution to (IVP3) and corresponding objective value is [5,27].…”

Section: Wolfe-type Dualitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimality conditions and duality for interval-valued optimization problems using convexifactors

Jayswal

Stancu-Minasian

Banerjee

2015

Rend. Circ. Mat. Palermo

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“…Example Consider a nonlinear multiobjective fractional programming problem with interval parameters (Bhurjee and Panda , )

\begin{matrix} true \\ right MFP : trueprefixmin & left \{{\hat{p}}_{1} (x) ⊘ {\hat{q}}_{1} (x), {\hat{p}}_{2} (x) ⊘ {\hat{q}}_{2} (x)\} \\ right subject to & left [1, 2] x_{1} \oplus [3, 3] x_{2} ⪯ [1, 10], \\ left x_{1}, x_{2} \geq 0, \end{matrix}

where

\begin{matrix} true \\ right {\hat{p}}_{1} (x) & ≜ & left [4, 10] x_{1}^{2} \oplus [- 1, 1] x_{1} x_{2} \oplus [10, 20] x_{2}^{2} \\ right {\hat{q}}_{1} (x) & ≜ & left [- 5, - 3] x_{1} \oplus [1, 2] x_{2} \\ right {\hat{p}}_{2} (x) & ≜ & left [- 1, 2] x_{1} \oplus [1, 1] x_{2}^{2} \\ right {\hat{q}}_{2} (x) & ≜ \end{matrix}

…”

Section: Numerical Examplementioning

confidence: 99%

“…Hladík () considered a linear fractional programming problem with interval parameters and computed the bounds for optimal values. The multiobjective fractional programming problem with interval parameters has been studied by Bhurjee and Panda (). In this paper, a methodology is developed to find an efficient solution of a nonlinear multiobjective fractional programming that depends on the choice of weight function.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the presence of uncertainty in the original model, and choice of weight function, solution of this model may be more or less acceptable for the decision maker. The satisfactory level of the solution by the decision makers is not discussed in Bhurjee and Panda (). In this work, we consider an interval multiobjective fractional programming problem that addresses both linear and nonlinear interval valued functions in the objective function as well as in the constraints.…”

Section: Introductionmentioning

confidence: 99%

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Existence of χ‐efficient solution of multiobjective fractional programming problem with bounded parameters

Jana

Panda

2016

Int Trans Operational Res

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In this paper, a methodology is developed to solve a multiobjective fractional programming problem in which the coefficients of the objective functions and constraints are intervals. This model is transformed into an interval-free equivalent optimization problem. A new partial ordering is introduced and the relation between the original problem and the transformed problem is established using this partial ordering. The proposed methodology is illustrated through a numerical example.

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Optimality and duality in constrained interval-valued optimization

Luu

Thi

2018

4OR-Q J Oper Res

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Multi-objective interval fractional programming problems : An approach for obtaining efficient solutions

Cited by 25 publications

References 12 publications

Optimality conditions and duality for interval-valued optimization problems using convexifactors

Optimality conditions and duality for interval-valued optimization problems using convexifactors

Existence of χ‐efficient solution of multiobjective fractional programming problem with bounded parameters

Optimality and duality in constrained interval-valued optimization

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