Scheduling problem is a widespread problem in industrial production fields. It aims to efficient utilization of resources, to respond demands quickly and strict conformity of jobs delivery times with predefined due dates. In general scheduling problems, one or more criteria can be considered simultaneously that using information of all jobs. Scheduling problem with a number of agents is another type of scheduling problem which was studied increasingly in recent years. In such problems, the criterion of each agent is independent of the other agents and limited resources are used in share. In addition, scheduling problems are considered in different production environments. Flowshop is one of these environments which operations of all jobs have to be done in the same order and same route. The study of two machine flowshop has been considered by many researchers because of its application as well as the fact that it’s an introduction to study of flowshop problem with more than two machines. In this study two scheduling problems are investigated. At first, minimizing total tardiness in two machine flowshop is considered, then two agent flowshop scheduling problem in a two machines environment is discussed. According to studies accomplished for the first problem, in this study the efficient methods for solving this problem including development of branch and bound algorithm and relative mathematical model are discussed. To solve the second problem, two exact methods including branch and bound algorithm and mathematical model are developed to achieve optimal solutions. For large size problems, exact methods can’t reach optimal solutions, and then two meta-heuristic methods based on Tabu search are developed to achieve near-optimal solutions. Computational results showed that the optimum properties and theorems which were developed in this study, improved the exact methods of minimizing total tardiness in a two-machine flowshop problem. Also Results showed the mathematical models had the best performance through exact methods that provided for two agent scheduling problem. For the instances with 20 to 40 jobs in size, the most effective mathematical model is able to solve all instance problems in 96.60% of groups. These results for the problem with 20 jobs up to 60 and 80 jobs is 84.56% and 81.94%, respectively. The results of the meta-heuristic algorithms, which proposed to solve instance problems up to 150 jobs in size, showed that these algorithms have a good performance in achieving near-optimal solutions in the large problem instances; such that their average absolute errors are lower than 0.2% for instances with 20 to 60 jobs in size and their average relative errors are less than 0.3% for instances with 40 to 150 jobs in size.
