This paper describes a method for solving one-dimensional cutting stock problem with usable leftover (CSPUL) in cases where the ratio between the average stock and average order length is less than 3. The proposed method can solve general CSPUL where standard stock lengths, non-standard stock lengths, or a combination of both are cut in the exact required number of pieces. The solutions of samp...

In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are a...

We consider the well-known one-dimensional cutting stock problem (1CSP). It is shown that all possible instances of the 1CSP can be divided into a finite number of equivalence classes when the number of items m is fixed. A method for enumerating all these classes is investigated. This method is improved for searching proper non-IRUP instances with minimal number of items. We found the minimal n...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

Over a decade ago, the European Journal of Operational Research published its first special issue on Cutting and Packing [1] in conjunction with the founding of SICUP, the Special Interest Group on Cutting and Packing. The majority of the papers in the first special issue were focused on cutting problems in the aluminium, paper, and canvas industry, as well as container loading problems. In 199...