We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company’s primary objective is to minimise total processing time at the su...

The present work proposes new heuristics and algorithms for the 3D Cutting and Packing class of problems. Specifically the cutting stock problem and a real-world application from the retail steel distribution industry are addressed. The problem being addressed for the retail steel distribution industry is the retail steel cutting problem, which is how to cut steel in order to satisfy the custom...

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...

A linear integer minimization problem (IP) has the modiied integer roundup property (MIRUP) if the optimal value of any instance of IP is not greater than the optimal value of the corresponding LP relaxation problem rounded up plus one. The aim of this paper is to investigate numerically whether the MIRUP holds for the one-dimensional cutting stock problem. The computational experiments carried...

In this paper, we address the combined assortment and trim loss minimization problem. In real settings, when different stock lengths are available, a common problem is to select a subset of stock lengths from which to cut the ordered items. In the cutting and packing literature, this problem is known as the assortment problem. Solving the assortment and trim loss minimization problem in a singl...

A linear integer minimization problem (IP) has the modified integer round-up property (MIRUP) if the optimal value of any instance of IP is not greater than the optimal value of the corresponding LP relaxation problem rounded up plus one. The aim of this paper is to investigate numerically whether the MIRUP holds for the one-dimensional cutting stock problem. The computational experiments carri...

Many methods exist for solving the one-dimensional cutting stock optimization problem with usable leftovers (CSPUL), but none of them consider the excessive generation of usable leftovers (UL) in stock after several consecutiveorders. To highlight this problem, the COLA method for solving the CSPUL [1] was selected. We performed experiments that showed how UL in stock continuously grow when the...

In this paper, we compare the computational results of cutting pattern of Category II in One Dimensional Cutting Stock Problem in view of first order sustainable trim introduced by Powar et al, with the cutting pattern developed by Gradisar. The comparison has been carried over on the data taken by Gradisar by using the upper limit of the stock length as mentioned in the constraint and observed...

One dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which has many applications in, e.g., steel, paper and fiber industries. To define an instance of 1D-CSP, we are given sufficient number of stock rolls which have the same length L, and m types of products with given lengths (l1, l2, . . . , lm) and demands (d1, d2, . . . , dm). A cu...

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 ...