A method for the cutting stock problem with different qualities

An operations research project at a Swedish company is reported. The project deals with the problem of allocating wood products with different quality requirements to be cut from wooden boards, which in turn consists of a number of quality zones. A major difficulty is the existence of distinct time limits since the cross cutting of the boards is done in a real time process. In this paper we derive a mathematical model, which includes a set packing problem, that accurately describes the real world problem. This problem is then solved using a combination of Lagrangean relaxation and subgradient optimization. Numerical results for practical problems are reported; the results indicate a valid model and satisfactory efficiency of the proposed solution procedure.