DOI: https://doi.org/10.14710/medstat.17.1.57-68

ANALYSIS OF MULTI-OBJECTIVE LINEAR ROBUST OPTIMIZATION MODEL WITH LEXICOGRAPHICAL METHOD

Chusnul Chatimah Azis  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
*Diah Chaerani  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
Endang Rusyaman  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
Open Access Copyright (c) 2024 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
Problems in robust multi-objective linear optimization are a class of optimization problems with uncertain data parameters which aim in the decision-making process to obtain the best results in certain circumstances by choosing various solution methods for the multi-objective. This research aims to formulate a multi-objective Robust Optimization (RO) model using the Lexicographic Method, then analyzing the existence and uniqueness of the solution. Furthermore, gap analysis on the topic was carried out using a Systematic Literature Review (SLR) approach with the Preferred Reporting Items for Systematic Review and Meta Analysis (PRISMA) method. Results in SLR, the analysis results also shows that the Lexicographic Method is effective in handling data uncertainty with the objective functions sorted by priority. The robust formulation with polyhedral uncertainty sets ensures the flexibility and adaptability of the model. Convexity analysis and application of the Karush-Kuhn-Tucker (KKT) method prove that the resulting solution is exist and unique.
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Keywords: Analysis Convex; Lexicographic Method; Multi-objective Optimization; Polyhedral Uncertainty Set; Robust Optimization.
Funding: Kemendikbudristek under contract 3018/UN6.3.1/PT.00/2023

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