A Solution Approach for a Class of Parametric Linear Programming Problems

Objective & Hypothesis:Depending on the nature, objectives, and constraints of the decision variables; linear programming, nonlinear programming, integer programming, mixed integer programming etc. can be classified.

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Key Findings & Data:Extensive research has been conducted to solve all types of these problems in a parametric context.

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Conclusion & Impact:A numerical experiment is illustrated to present the effectiveness of the proposed approach.

🔬Design:Modeling & Simulation

📍Scope:Comprehensive Sample

⚙️Variables:Parametric linear programming · linearization technique · Taylor series expansion

Abstract

Depending on the nature, objectives, and constraints of the decision variables; linear programming, nonlinear programming, integer programming, mixed integer programming etc. can be classified. Extensive research has been conducted to solve all types of these problems in a parametric context. In this paper, to solve optimization problems having uncertainties represented by a single parameter on the objective function, a systematic linearization approach is developed considering the parametric expression as nonlinear. In the proposed approach, the objective function is considered as nonlinear which is converted into linear by using first order Taylor series expansion at the points making the parametric costs zero. Thus, the optimal solution is obtained from the constructed linear programming problem. In this way, by determining the intervals in which the optimal solution changes, the solution of the parametric linear programming problem is obtained. A numerical experiment is illustrated to present the effectiveness of the proposed approach.

Özet

Depending on the nature, objectives, and constraints of the decision variables; linear programming, nonlinear programming, integer programming, mixed integer programming etc. can be classified. Extensive research has been conducted to solve all types of these problems in a parametric context. In this paper, to solve optimization problems having uncertainties represented by a single parameter on the objective function, a systematic linearization approach is developed considering the parametric expression as nonlinear. In the proposed approach, the objective function is considered as nonlinear which is converted into linear by using first order Taylor series expansion at the points making the parametric costs zero. Thus, the optimal solution is obtained from the constructed linear programming problem. In this way, by determining the intervals in which the optimal solution changes, the solution of the parametric linear programming problem is obtained. A numerical experiment is illustrated to present the effectiveness of the proposed approach.

Keywords

Parametric linear programming linearization technique Taylor series expansion

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Cite This Article

SİVRİ, M., ALBAYRAK, İ., ALAN, K. Ş., TEMELCAN, G. (2020). A Solution Approach for a Class of Parametric Linear Programming Problems. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 10 - Sayı: 4, 2901–2906. https://ajindex.com/articles/256443

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