An industrial engineering problem is under study. It consists in optimal configuration of a multi-part production line. A line is a sequence of workstations, at which the manufacturing operations at each workstation are executed in parallel. Parallel execution of operations is inherent for multi-spindle heads in mechanical industry, for example. Each machine part of a specific type f requires a specific set of operations. Different sets can contain common operations. The total number of operations per workstation cannot exceed a given upper bound. Parts move along the stations in the same direction. If there is at least one operation attributed to the part type arriving at a station, this station is set up. Setup costs are part type dependent and they appear due to additional resources required for processing of a part at stations. There are two criteria: minimization of the number of stations, and minimization of the total setup cost. A solution of the problem implies the number of stations and the assignment of operations to these stations. Properties of an optimal solution were established. Basing on these properties, optimal algorithms were developed for the cases f = 2, f = 3, and an arbitrary f. The algorithms employ combinatorial optimization and linear algebra techniques. They run in a constant time if f is a constant.