Open AccessThe paper discusses the most popular combinatorial models that are used for the synthesis of design solutions at the stage of the assembly process flow preparation. It shows that while assembling the product the relations of parts can be represented as a structure of preferences, which is formed on the basis of objective design restrictions put in at the stage of the product design. This structure is a binary preference relation pre-order. Its symmetrical part is equivalence and describes the entry of parts into the assembly unit. The asymmetric part is a partial order. It specifies part- ordering time in in the course of the assembly process. The structure of preferences is a minimal description of the restrictions and constraints in the assembly process. It can serve as a source for generating multiple assembly sequences of a product and its components, which are allowed by design. This multiplicity increases the likelihood of rational choice under uncertainty, unpredictable changes in the properties of technological or industrial systems.
Incomplete dominance relation gives grounds for further examination and better understanding of the project situation. Operation field of the study is limited to a set of disparate elements of the partial order. Different strategies for processing the disparate elements may be offered, e.g. selection of the most informative pairs, comparison of which foremost linearizes the original partial order.