Interactive procedures in large-scale two-dimensional cutting stock problems

This paper discusses basic problem formulation, and solution procedures for solving a particular large-scale two-dimensional cutting stock problem at a furniture factory. In recent years there has been an explosion of interests in this application area. The cutting stock problems are met in many branches of industry. There is a large economical incentive to find more effective solution procedures, and it is easy to compare alternative solution procedures and to identify potential benefits of using a proposed procedure. The paper concentrates on the case in which both stock and ordered sizes are rectangular. We present a mathematical model of the problem, propose an optimization algorithm and describe its basic properties. The mathematical model of the optimization problem relies on the Gilmore and Gomory approach. To decrease the total computing time we propose an interactive procedure based on the forecasting of the criterion functions values.