Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Abstract

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

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Abbreviations

LPP:

Linear programming problem

LPLFPP:

Linear plus linear fractional programming problem

MOLPLFPP:

Multi-objective linear plus linear fractional programming problem

FMONLFPP:

Fuzzy multi-objective nonlinear fractional programming problem

FMOLPP:

Fuzzy multi-objective linear programming problem

FMOLFPP:

Fuzzy multi-objective linear fractional programming problem

MOLPP:

Multi-objective linear programming problem

FFLFPP:

Fully fuzzy linear fractional programming problem

MOFPP:

Multi-objective fractional programming problem

MOMIFCSTP:

Multi-objective multi-item fixed-charge solid transportation problem

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Correspondence to S. Sharanya.

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Veeramani, C., Sharanya, S. & Ebrahimnejad, A. Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach. Math Sci (2020). https://doi.org/10.1007/s40096-020-00333-w

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Keywords

  • Goal programming
  • Linear programming problem
  • Multi-objective nonlinear programming problem
  • Multi-objective linear plus linear fractional programming problem