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Researchers and scientists have developed various approaches and methodologies over time to model and analyze different types of linear programming problems, such as assignment problems and parametric programming problems. This paper provides a critical review and classification of existing modelling approaches and solution methods related to linear programming problems. Moreover, the simplex method is discussed in detail through a comprehensive literature review. The paper concludes by presenting an integrated research framework that is directly applicable to the present context, along with suggestions for future research directions.