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Under increasing globalization, enterprises view supply chains (SC) as an integration of process control and management. The bicycle industry is one of the competitive industries in Taiwan, for which there is a complete supply chain system. To internationalize and improve the competitive advantage of this industry, it is necessary for it to improve the capacity of global production and distribution. In this paper, we consider both the maximum profit of enterprises and the maximum quality of customer service, using five programming methods to construct multi-objective production and distribution models. These five methods are: compromise programming, fuzzy multi-objective programming, weighted multi-objective programming, weighted fuzzy multi-objective programming and two-phase fuzzy multi-objective programming. The results reveal that the weighted multi-objective model was better for considering the maximum profit of enterprises and the maximum quality of customer service. Finally, we use the weighted multi-objective model for sensitivity analysis. These results show that after raising the per-unit production cost in production processes, the total profit would decrease. In addition, if the unit inventory cost increases due to improving the customer service level, then the total profit might increase, but not significantly. Furthermore, the shortage cost seems have interactive behavior on the enterprises, in which an increase of inventory cost will lower shortage cost.