This study explores the research done into solving the job-shop scheduling problem with linear optimization and reinforcement learning methods. It looks at a timeline of the problem and how methods to solve it have changed over time. The research should give an understanding of the problem and explore possible solutions. For that, an extensive search for papers was done on Scopus, a research paper database. 27 promising papers were selected, rated, and categorized to facilitate a sound understanding of the problem and define further research fields. Two such research fields were further elaborated; Firstly, little research has been done on how reinforcement learning can be improved by implementing data or process mining strategies to further improve accuracy. Secondly, no research was found yet connecting reinforcement learning with a takt schedule. The gathered papers give an extensive overview of the problem and demonstrate a multitude of solutions to the job-shop scheduling problem, which are discussed in detail in the results of this report.