抄録
In this article, we analyze the material cutting problem that exists in the printing industry. This problem is due to the need to use standard paper formats for positioning non-standard-sized editions. The specifics of the industry determine the need to use standard-sized sheets of material, whereas the competition for a market share determines the need to create non-standard-sized books. The authors believe that the cost of a printed edition can be reduced through rational material use, while allowing the book to remain in the non-standard-sized edition segment, which is especially important for children's books. The mathematical model proposed in this paper makes it possible to determine an optimal format for the printed edition in terms of selecting a sheet format for printing editions of an irregular size, the use of which will maximize the efficiency of the material use. The multicriteria statement of the problem, in which the criteria of solution efficiency are, among others, a minimum of material waste, maximum efficiency of the printing plates, and minimum cost of the plates, is considered in the article. An analysis of the feasible solutions for the problem is presented. The adequacy of the proposed mathematical model is tested through a series of computational experiments using a series of well-known methods, including cost-efficiency analysis and the additive multicriteria estimation method.
