Numerical investigations on the MIRUP of the 2-stage guillotine cutting stock problem

The MIRUP (Modified Integer Round-Up Property) leads to an upper bound for the gap between the optimal value of the integer problem and that of the corresponding continuous relaxation rounded up. This property is known to hold for many instances of the one-dimensional cutting stock problem but there are not known so far any results with respect to the two-dimensional case. In this paper we investigate numerically three variants of the so-called 2-stage guillotine cutting stock problem with respect to the MIRUP. The variants differ by allowing either only horizontal or only vertical or horizontal and vertical guillotine cuts in the first stage. Within a sample of 900 randomly generated instances there did not arise any instance with gap larger than 1. Moreover, for more than 60% of the instances an optimal solution was found.