MATHEMATICAL MODEL AND SYSTEM COMPUTATIONAL FOR THE SOLUTION EFFICIENT FROM 2D CUTTING PROBLEMS THROUGH LINEAR PROGRAMMING IN INTEGER

Abstract

This article summarizes the most important results out of an investigation whose general objective was defined as “using Integer Linear Programming (ILP) to resolve two-dimensional (2D) material cutting of rectangular pieces”. It presents an alternative approach of material cutting different than the classic methods, addressing the problem by using “cutting of substitution variants” (e.g. larger pieces are considered as though they were raw material too). These substitution-variants are later defined as new unknowns in the mathematical modeling of the situation being studied, to generally reduce the number of variables in the model. A Software was designed and implemented with an algorithm for the generation of 2D cutting variants, which executes the mathematical processing from the model and interprets the results obtained in a practical way. Also as an example, this article shows the results on comparing the use of the proposed solution versus the heuristic route when solving 2D cutting problems. The Software was deployed in a polygraphic company whose production process involves the cutting of rectangular pieces of cardboard, with satisfactory results in the control of the production and a significant reduction in raw material waste.