Dynamic Programming algorithms and their applications in machine scheduling: A review

This paper aims at presenting a compilation of state-of art references in which dynamic programming (DP) and its variants have been applied as a solution methods for the deterministic machine scheduling problems. Overall, 183 articles have been gathered and their segmentation was carried out according to the machine environment that characterized the problems addressed by the authors and ultimately, the objective functions that were intended to be optimized. Additionally, we standardized the information provided by each article by presenting the problems discussed by the authors, comparisons between previous works on the same problem (if it was deemed necessary), the algorithms' complexities and an extension of methods to computational experiments (in case they have been stated). Finally, at the end of each section we furnish a discussion on the main contributions of DP to the each environment and also suggest some further applications of DP to machine scheduling problems, thus showing the potential resources that can be derived from the method in terms of theoretical/practical approaches.