A comparison of two optimization procedures for 1- and 1 1/2-dimensional cutting stock problems

Abstract

There are two different LP-model formulations to obtain the optimal solution of 1- and 1 1/2-dimensional cutting stock problems. On the one hand there is the complete-cut LP-model which may be solved by the well-known column generation approach of Gilmore and Gomory [9, 10], while on the other hand Rao [17] and Dyckhoff [2, 4] propose an LP-model based on one-cuts to describe the cutting process, to be solved by standard LP software. For both models and solution approaches their commonalities and differences are elaborated, providing insights into possible application areas and the advantages of each approach. We will consider the standard cutting stock problem as well as real world extensions — like the limited availability of standard lengths and the evaluation of residual lengths. Furthermore, three reduction-rules are indicated which can reduce the solution effort. Test runs based on three cutting stock problems mentioned in the literature demonstrate the pros and cons of the two approaches.