Pipelines are widely used in transport systems and public utilities and infrastructures. To produce their components, specially designed multi-positional machines are employed. Since the cost of the equipment used affects the cost of final pipelines, the design of such machines is an important financial issue. This paper presents such a design problem formulated as a combinatorial optimization problem. Two mathematical models and an efficient solution approach are suggested. Industrial examples are also considered in order to demonstrate the use of the method developed.