Efficient resource allocation is a major challenge in various sectors, especially when faced with limitations in quantity, time, and cost. This study aims to examine the application of linear programming as an optimization method in solving assignment problems, where a number of resources must be optimally allocated to a number of specific tasks. Through a literature study approach, this study examines various relevant previous study results, especially in the Indonesian context. The results of the study indicate that linear programming is able to improve operational efficiency, reduce costs, and produce a more balanced task distribution. However, this model has limitations in dealing with non-linear conditions and data uncertainty, so integration with other methods such as fuzzy logic or genetic algorithms is needed. This study is expected to broaden the understanding of the benefits of linear programming and encourage its wider application in quantitative-based decision making.

This study uses a qualitative method with a literature review approach to examine the effectiveness of the two-phase method in solving linear programming problems. The two-phase method is one of the techniques in linear programming used when the objective function does not have a feasible initial solution directly. Through the exploration and analysis of various scientific literature sources from 2019 onwards, this study finds that the two-phase method can systematically provide optimal solutions, especially in complex problems with multiple constraints. Previous research has shown that this method is effective in accelerating the identification of basic feasible solutions and minimizing unnecessary iterations compared to the standard simplex method. Additionally, the two-phase method offers better numerical stability and high reliability in both industrial and educational applications. However, its effectiveness largely depends on the understanding of the algorithm and the ability to design an appropriate mathematical model. The results of this study are expected to contribute theoretically to the development of efficient solution techniques for linear optimization problems.