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In this book, a machine scheduling problem is considered which is the problem of scheduling a number of products (n-jobs) on a single machine with multi-objectives function (with and without) set up times. Firstly, this book contained a background of the scheduling theory, the history of the scheduling problems and the scheduling problems with setup times. A brief information about the machine scheduling problems which included in chapter one as the definition, descriptions, the three-field presentation.The main problem was studied in two cases, the first case is the problem without setup times, while the second case was the problem with setup times named (problem (A)) and (problem (B)) respectively.The methodology in which it used was divided into two parts. First part was using the exact methods in which are (the complete enumeration) and (the branch & bound) to obtain the optimal solution. The second part was applying two of the local search methods in which are (genetic algorithm) and (particle swarm optimization) to get near optimal solutions.This book also contains five introduced heuristics as an initial solution for the problem involved with the setup times.