In the problem under study, a paced unidirectional machining line, consisting of a number of stations, has to be configured to produce parts of several types. A given set of operations is required for each part type and the same operation can be required for different part types. Re-assignment of operations, when switching from one part type to another, is not allowed. All operations assigned to the same station are performed simultaneously. The objective is to assign operations to stations in order to minimize the number of stations and the station activation costs, with respect to precedence and zoning constraints. The two objectives are considered in a lexicographic order, the former being the primary objective. Activation costs refer to the costs induced by the energy consumption, equipment maintenance, setup activities or labor requirement which occur whenever a station is used. Computational complexity for various special cases is established. Heuristic algorithms, integer linear programming formulations, and computer experiments are presented. Instances of practical dimension, with 40–80 operations, are solved in an hour on a conventional computer.