We introduce a zero-one integer programming model for the simultaneous solution of the cell formation and operation allocation problem in cellular manufacturing. We assume that there is a set of existing machines in a manufacturing shop and that there is a set of part types to be processed on these machines. Each part type is assumed to have more than one process plan, and each operation of a part type may be performed on more than one machine. The objective of the model is to simultaneously form machine groups (cells) and allocate operations of the part types to the regrouped machines in such a way as to minimize the sum of operation costs, refixturing costs and transportation costs. Computational results are provided to demonstrate the viability of the model.