LAGRANGE RELAXATION FOR FLEXIBLE FLOWSHOP SCHEDULING IN HETEROGENEOUS MULTI-FACTORY NETWORKS

This paper deals with production scheduling in a flexible flowshop with several factories trying to satisfy market demand by creating a network through a distributed network. Although these factories have their own flowshop system consisting of stages with a number of parallel machines, each job must pass through these stages to be completed; in some cases, due to the long queues in one factory, some jobs are sent to other factories to reduce the overall completion time. In other words, in this system, it is assumed that each factory, after satisfying the demand of its region, can cooperate with other factories in order to provide economic benefits and increase sales as a result of greater profitability of the production network, which means that if for any reason in the process, the production of products is disrupted or the amount of load of factories is too much, in order to improve the overall objective function, it is possible that some jobs be sent to other factories for processing. Multi-factory production takes place in several factories, which may be geographically distributed in different locations, in order to comply with and to take advantage from the trend of globalization. This allows them to be closer to their customers, to employ professionals, to comply with local laws, to focus on a few product types, to produce and market their products more effectively, and respond to market changes more quickly. Here, after introducing a flexible flowshop in the distributed network structure, a model is proposed for the problem considering the holding costs in the buffers and heterogeneity of factories in the production network. Finally, after solving the model using GAMS software, the Lagrange relaxationalgorithm has been developed for it. By comparing the GAMS and output results of the Lagrange relaxation algorithm, it is concluded that the proposed algorithm is of very high efficiency.