Summary: Global competitive priorities are undergoing a marked shift from productivity and quality to flexibility and agility. This has resulted in a growing number of manufacturing companies realizing the importance of building customization capabilities into their production systems. Flexible assembly systems (FASs), consisting of a variety of processors such as assembly, inspection, packaging, and interactive operator consoles, provide a significant opportunity for improving product flexibility and, thereby, gaining sustainable competitive advantage. This paper formulates a decision problem for designing FASs and proves it to be NP-complete. A heuristic, called the pick and rule (PAR) heuristic, is presented to minimize the total number of processors, while determining the number of processors of each type, the sequence of the processors, and the operations to be performed at each processor. A lower bound for the minimum number of processor is derived, and used to assess the effectiveness of the PAR heuristic. An algorithm to compute this bound is also presented. An exact branch and bound algorithm is formulated to find optimal solutions and to provide guidance on the source of the gap between the PAR heuristic and the lower bound results. Computational results with the PAR heuristic, the lower bound algorithm, and the branch-and-bound algorithm are reported.