"Concepts in manufacturing such as CIMS (Computer Integrated Manufacturing Systems), JIT (Just In Time), Lean Production, Virtual Manufacturing, and Flexible Fixturing have been proposed to meet the fundamental requirements of manufacturing - decrease the cost and satisfy the needs of customers. Fast fixture generation and fixture reusability are essential in the current manufacturing environment. The dissertation focuses on the models, methods, and algorithms for fixture synthesis and variation that satisfy the functional requirements specified by on-site industrial engineers. With the reusability of a fixture base combined with variation of other fixture components, fixture configuration can be rapidly adapted and accommodated to the new workpiece. The dissertation presents methods and algorithms for fixture base synthesis, which directly result in fixture reusability. Optimization functions are derived based on engineering requirements due to the mass production nature of automotive parts. Specific optimization algorithms are developed and their complexities, compared to other alternatives, are comprehensively evaluated according to different optimization functions. The fixture variation and reusability provide an engineering tool to rapidly generate and validate fixtures in production planning stage. It applies scientific reasoning methodology in combination with best knowledge of fixture designs, which heavily relies on designers' manufacturing knowledge and experience. It also provides means to bridge the gap between CAD and CAM integration and therefore reduces the new product and production development cycle time and cost while maintaining the quality of fixtures."