Most of the past cloud manufacturing (CMfg) studies investigated the short-term production planning or job scheduling of a CMfg system, while the mid-term or long-term capacity and production planning of a CMfg system has rarely been addressed. In addition, most existing methods are suitable for CMfg systems comprising three-dimensional (3D) printers, computer numerical control (CNC) machines or robots, but ignore the coordination and transportation required for moving jobs across factories. To fill these gaps, a fuzzy mid-term capacity and production planning model for a manufacturer with cloud-based capacity is proposed in this study. The proposed methodology guides a manufacturer in choosing between noncloud-based capacity and cloud-based capacity. It can be applied to factories utilizing machines with different degrees of automation including highly automatic equipment (such as 3D printers, CNC machines, and robots) and lowly automatic (legacy) machines, while existing methods assume that orders can be easily transferred between machines that are often highly automatic. In the proposed methodology, first, various types of capacity are unequally prioritized. Then, a fuzzy mixed-integer nonlinear programming model is formulated and optimized to make the mid-term or long-term capacity and production plan of a factory. The fuzzy capacity and production planning model is designed for factories with parallel machines. The proposed methodology has been applied to a case to illustrate its applicability. According to the experimental results, the proposed methodology successfully reduced total costs by up to 8%. The advantage of the proposed methodology over existing practices in fulfilling customers' demand was also obvious.