Families of non-IRUP instances of the one-dimensional cutting stock problem Original Research Article

In case of the one-dimensional cutting stock problem (CSP) one can observe for any instance a very small gap between the integer optimal value and the continuous relaxation bound. These observations have initiated a series of investigations. An instance possesses the integer round-up property (IRUP) if its gap is smaller than 1. In the last 15 years, some few instances of the CSP were published possessing a gap greater than 1. In this paper, various families of non-IRUP instances are presented and methods to construct such instances are given, showing in this way, there exist much more non-equivalent non-IRUP instances as computational experiments with randomly generated instances suggest. Especially, an instance with gap equal to 109 is obtained. Furthermore, an equivalence relation for instances of the CSP is considered to become independent from the real size parameters.