lagrangian relaxation algorithm

In this paper, the problem of real-time scheduling of multi-factury production network in the smart manufacturing system with job shop environment is studied. In this smart manufacturing system, a number of independently owned factories are joined together to form a multi-agent production network, which is also called a virtual production network. In such a network, each factory focuses on its interests and communicates with each other by sharing information such as machine breakdowns and job transfers. Therefore, it can be stated that studying the problem of distributed scheduling in the environment of smart factories is important and will have a significant effect on obtaining desirable and ideal results. At first, a bi-objective mixed integer linear programming model is presented; then an approach to solve the dynamic real-time scheduling problem is proposed. Considering the successful applications of the Lagrangian relaxation algorithm in solving scheduling problems, in this research, the improved Lagrangian relaxation algorithm is used to solve the problem. To examine the performance of the proposed algorithm, its results were compared with solving the original model that was solved by the augmented epsilon constraint method. The obtained results showed that the proposed Lagrangian relaxation algorithm has a better performance than the augmented epsilon constraint method