In this study, a dynamic programming approach to deal with the unconstrained twodimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer’s pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. Since a counterexamp...

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

We investigate two cutting problems and their variants in which orthogonal rotations are allowed. We present a dynamic programming based algorithm for the Two-dimensional Guillotine Cutting Problem with Value (GCV) that uses the recurrence formula proposed by Beasley and the discretization points defined by Herz. We show that if the items are not so small compared to the dimension of the bin, t...

Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the ...

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 paper we study the two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and ins...

The two-dimensional orthogonal non-guillotine cutting problem (NGCP) appears in many industries (like wood and steel industries) and consists in cutting a rectangular master surface into a number of rectangular pieces, each with a given size and value. The pieces must be cut with their edges always parallel or orthogonal to the edges of the master surface (orthogonal cuts). The objective is to ...

We investigate a new application of DC (Difference of Convex functions) programming and DCA (DC Algorithm) in solving the constrained two-dimensional non-guillotine cutting problem. This problem consists of cutting a number of rectangular pieces from a large rectangular object. The cuts are done under some constraints and the objective is to maximize the total value of the pieces cut. We reform...