Abstract. The balance layout optimization problem for a given set of 3D-objects in a container divided by horizontal shelves into subcontainers is considered. For analytical description of non-overlapping and containment constraints, the phi-function technique is used. Combinatorial configurations describing the combinatorial structure of the problem are defined. Based on the introduced configurations, a mathematical model is constructed that takes into account not only the placement constraints and mechanical properties of the system but also the combinatorial features of the problem associated with generation of partitions of the set of objects placed inside the subcontainers. A solution strategy is proposed. The results of numerical experiments are provided.

Keywords: balance layout, combinatorial configurations, 3D-objects, phi-function method, mathematical model, optimization .