In the emerging modern technology of additive manufacturing, the need for optimization can be found in literature in many places. Additive manufacturing (AM) is making an object layer by layer directly from digital data. Previous works of literature have classified additive manufacturing processes into seven types. However, there is a lack of comprehensive review describing the optimization challenges and opportunities in the material extrusion process (polymer technology) and also the need for FDM polymer materials application in impeller making. In this review paper, a specific optimization method called multicriteria decision-making (MCDM) from the mathematical programming technique used in additive manufacturing polymer technology (AMPT) is discussed. The other topics such as different types of optimization techniques, applications of different MCDM tools and their applications in different fields including AM, and the optimization challenges and opportunities in AMPT particularly impeller application are discussed.