The Mathematical Model of Optimal Cutting of Plastic Window Profiles

The paper presents the development of a specialized mathematical model and a onedimensional cutting program for production of doubleglazed windows. The solution is based on the branch and boundary method, which uses a matrix simplex method at each step. Simultaneous modification of the objective function and simplification of the system of constraints, i.e. elimination of inappropriate cutting options, help improve the developed solution. At the same time, the problem dimension and the time required to solve it reduce significantly. Authors have automated the stages of model engineering (based on the „cutting matrix“ generation) and searching for an initial reference plan. The existence of a valid basic solution helps save the consumed time. The practical significance of the obtained results lies in improving the efficiency of production design. This leads to lowering the costs of purchase, processing, transportation, storage, and disposal of materials. The developed methods and algorithms are easily adaptable and applicable to other production processes with one-dimensional cutting when considering additional technological limitations.