The paper is devoted to a preliminary design problem of paced automatic transfer lines. At this design stage, the following decisions are to be made: the partitioning of the given set of operations into subsets performed by one spindle head; the grouping of the spindle heads into workstations, the choice of operating modes for each spindle head. The aim is to minimise the line life cycle cost per part under the given productivity and technological constraints. The paper focuses on a mathematical model of the problem and methods to solve it. The model is formulated in terms of mixed (discrete and non-linear) programming. For solving the optimisation problem, a special decomposition scheme is proposed, which is based on parametric decomposition technique as well as on Branch-and-Bound and multi-criteria shortest path algorithms.